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<h3>
Clint Adams pushed to branch master
at <a href="https://salsa.debian.org/haskell-team/DHG_packages">Debian Haskell Group / DHG_packages</a>
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<h4>
Commits:
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<strong><a href="https://salsa.debian.org/haskell-team/DHG_packages/commit/db12a9461ed86772e71ef282a5d7ad694c973320">db12a946</a></strong>
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<span>by Clint Adams</span>
<i>at 2018-04-16T14:25:40-04:00</i>
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<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">polynomial: add in missing tests
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<h4>3 changed files:</h4>
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<a href="#a97b2937e18ecbd7552179b5c3e3d041e54a52c7">
p/haskell-polynomial/debian/changelog
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+
p/haskell-polynomial/debian/patches/missing-tests
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<a href="#a633f3baf8b065f9e5fe520968bdb989558bd840">
p/haskell-polynomial/debian/patches/series
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<h4>Changes:</h4>
<li id="a97b2937e18ecbd7552179b5c3e3d041e54a52c7">
<a href="https://salsa.debian.org/haskell-team/DHG_packages/commit/db12a9461ed86772e71ef282a5d7ad694c973320#a97b2937e18ecbd7552179b5c3e3d041e54a52c7"><strong>p/haskell-polynomial/debian/changelog</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="plaintext">haskell-polynomial (0.7.3-3) unstable; urgency=medium</span>
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="plaintext"> * Add in missing tests.</span>
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<pre style="margin: 0;">+<span id="LC4" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC5" class="line" lang="plaintext"> -- Clint Adams <clint@debian.org> Mon, 16 Apr 2018 14:25:28 -0400</span>
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<pre style="margin: 0;">+<span id="LC6" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC7" class="line" lang="plaintext">haskell-polynomial (0.7.3-2) unstable; urgency=medium</span>
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<pre style="margin: 0;"> <span id="LC8" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC9" class="line" lang="plaintext"> * Enable testsuite.</span>
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<li id="1a19db0e5690b5c51b6b052887129db8b0707156">
<a href="https://salsa.debian.org/haskell-team/DHG_packages/commit/db12a9461ed86772e71ef282a5d7ad694c973320#1a19db0e5690b5c51b6b052887129db8b0707156"><strong>p/haskell-polynomial/debian/patches/missing-tests</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="diff"><span class="gd" style="color: #000; background-color: #fdd;">--- /dev/null</span></span>
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+++ b/test/TestUtils.hs</span></span>
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<pre style="margin: 0;">+<span id="LC3" class="line" lang="diff"><span class="gu" style="color: #800080; font-weight: 600;">@@ -0,0 +1,67 @@</span></span>
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<pre style="margin: 0;">+<span id="LC4" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+{-# LANGUAGE FlexibleInstances, TypeSynonymInstances, TypeFamilies #-}</span></span>
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<pre style="margin: 0;">+<span id="LC5" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+module TestUtils where</span></span>
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<pre style="margin: 0;">+<span id="LC6" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC7" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Control.Applicative</span></span>
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<pre style="margin: 0;">+<span id="LC8" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Control.Monad</span></span>
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<pre style="margin: 0;">+<span id="LC9" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Data.List</span></span>
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<pre style="margin: 0;">+<span id="LC10" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Data.VectorSpace</span></span>
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<pre style="margin: 0;">+<span id="LC11" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial</span></span>
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<pre style="margin: 0;">+<span id="LC12" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial.Type</span></span>
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<pre style="margin: 0;">+<span id="LC13" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.QuickCheck</span></span>
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<pre style="margin: 0;">+<span id="LC14" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import qualified Data.Vector as V</span></span>
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<pre style="margin: 0;">+<span id="LC15" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC16" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+instance Arbitrary Endianness where</span></span>
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17
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<pre style="margin: 0;">+<span id="LC17" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ arbitrary = elements [BE, LE]</span></span>
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18
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<pre style="margin: 0;">+<span id="LC18" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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19
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<pre style="margin: 0;">+<span id="LC19" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+instance (Num a, Eq a, Arbitrary a) => Arbitrary (Poly a) where</span></span>
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20
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<pre style="margin: 0;">+<span id="LC20" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ arbitrary = polyCon <*> arbitrary <*> arbitrary</span></span>
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<pre style="margin: 0;">+<span id="LC21" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where</span></span>
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22
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<pre style="margin: 0;">+<span id="LC22" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyCon = elements</span></span>
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23
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<pre style="margin: 0;">+<span id="LC23" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ poly</span></span>
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24
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<pre style="margin: 0;">+<span id="LC24" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , rawListPoly</span></span>
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<pre style="margin: 0;">+<span id="LC25" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , \e -> rawVectorPoly e . V.fromList</span></span>
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<pre style="margin: 0;">+<span id="LC26" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC27" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC28" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+newtype SmallPoly a = SmallPoly (Poly a)</span></span>
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<pre style="margin: 0;">+<span id="LC29" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ deriving (Eq, Show)</span></span>
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<pre style="margin: 0;">+<span id="LC30" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+instance (Num a, Eq a, Arbitrary a) => Arbitrary (SmallPoly a) where</span></span>
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<pre style="margin: 0;">+<span id="LC31" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ arbitrary = SmallPoly <$> (polyCon <*> arbitrary <*> smallList)</span></span>
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<pre style="margin: 0;">+<span id="LC32" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where</span></span>
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<pre style="margin: 0;">+<span id="LC33" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyCon = elements</span></span>
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34
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<pre style="margin: 0;">+<span id="LC34" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ poly</span></span>
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<pre style="margin: 0;">+<span id="LC35" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , rawListPoly</span></span>
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<pre style="margin: 0;">+<span id="LC36" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , \e -> rawVectorPoly e . V.fromList</span></span>
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<pre style="margin: 0;">+<span id="LC37" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC38" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ </span></span>
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<pre style="margin: 0;">+<span id="LC39" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ smallList = do</span></span>
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<pre style="margin: 0;">+<span id="LC40" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let binom n k = product [k+1 .. n] `div` product [1 .. n-k]</span></span>
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<pre style="margin: 0;">+<span id="LC41" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n <- frequency [ (fromInteger (binom 10 k), return k) | k <- [0..10]]</span></span>
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<pre style="margin: 0;">+<span id="LC42" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ replicateM (fromInteger n) arbitrary</span></span>
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<pre style="margin: 0;">+<span id="LC43" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC44" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- instance AdditiveGroup Rational where</span></span>
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<pre style="margin: 0;">+<span id="LC45" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- zeroV = 0</span></span>
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<pre style="margin: 0;">+<span id="LC46" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- (^+^) = (+)</span></span>
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<pre style="margin: 0;">+<span id="LC47" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- negateV = negate</span></span>
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<pre style="margin: 0;">+<span id="LC48" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- instance VectorSpace Rational where</span></span>
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<pre style="margin: 0;">+<span id="LC49" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- type Scalar Rational = Rational</span></span>
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<pre style="margin: 0;">+<span id="LC50" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- (*^) = (*)</span></span>
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<pre style="margin: 0;">+<span id="LC51" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC52" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+rev BE = LE</span></span>
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<pre style="margin: 0;">+<span id="LC53" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+rev LE = BE</span></span>
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<pre style="margin: 0;">+<span id="LC54" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC55" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+sep [] = []</span></span>
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<pre style="margin: 0;">+<span id="LC56" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+sep rts = uniq : sep (rts \\ uniq)</span></span>
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<pre style="margin: 0;">+<span id="LC57" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where uniq = nub rts</span></span>
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<pre style="margin: 0;">+<span id="LC58" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC59" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- arbitrary function mapping the real line to the unit interval</span></span>
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<pre style="margin: 0;">+<span id="LC60" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+onUnitInterval x = x - fromIntegral (floor x)</span></span>
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<pre style="margin: 0;">+<span id="LC61" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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62
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<pre style="margin: 0;">+<span id="LC62" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+onInterval a b x = a + w * onUnitInterval x</span></span>
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63
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<pre style="margin: 0;">+<span id="LC63" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where</span></span>
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64
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<pre style="margin: 0;">+<span id="LC64" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ w = b - a</span></span>
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<pre style="margin: 0;">+<span id="LC65" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC66" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+distinct [] = True</span></span>
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<pre style="margin: 0;">+<span id="LC67" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+distinct (x:xs) = all (/= x) xs && distinct xs</span></span>
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68
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<pre style="margin: 0;">+<span id="LC68" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC69" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+relErr 0 0 = 0</span></span>
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<pre style="margin: 0;">+<span id="LC70" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+relErr x y = abs (x - y) / max (abs x) (abs y)</span></span>
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<pre style="margin: 0;">+<span id="LC71" class="line" lang="diff"><span class="gd" style="color: #000; background-color: #fdd;">--- /dev/null</span></span>
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<pre style="margin: 0;">+<span id="LC72" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+++ b/test/Tests/Bernstein.hs</span></span>
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<pre style="margin: 0;">+<span id="LC73" class="line" lang="diff"><span class="gu" style="color: #800080; font-weight: 600;">@@ -0,0 +1,94 @@</span></span>
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<pre style="margin: 0;">+<span id="LC74" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+{-# LANGUAGE ExtendedDefaultRules #-}</span></span>
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<pre style="margin: 0;">+<span id="LC75" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+module Tests.Bernstein (bernsteinTests) where</span></span>
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<pre style="margin: 0;">+<span id="LC76" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC77" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial</span></span>
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<pre style="margin: 0;">+<span id="LC78" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial.Bernstein</span></span>
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<pre style="margin: 0;">+<span id="LC79" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework (testGroup)</span></span>
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<pre style="margin: 0;">+<span id="LC80" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.QuickCheck2 (testProperty)</span></span>
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81
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<pre style="margin: 0;">+<span id="LC81" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.QuickCheck</span></span>
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<pre style="margin: 0;">+<span id="LC82" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import TestUtils</span></span>
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<pre style="margin: 0;">+<span id="LC83" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC84" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+default (Integer, Rational)</span></span>
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<pre style="margin: 0;">+<span id="LC85" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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86
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<pre style="margin: 0;">+<span id="LC86" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+bernsteinTests =</span></span>
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87
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<pre style="margin: 0;">+<span id="LC87" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "bernstein" bernstein_tests</span></span>
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88
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<pre style="margin: 0;">+<span id="LC88" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalBernstein" evalBernstein_tests</span></span>
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89
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<pre style="margin: 0;">+<span id="LC89" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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90
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<pre style="margin: 0;">+<span id="LC90" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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91
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<pre style="margin: 0;">+<span id="LC91" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+bernstein_tests =</span></span>
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92
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<pre style="margin: 0;">+<span id="LC92" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sum" prop_bernstein_sum</span></span>
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93
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<pre style="margin: 0;">+<span id="LC93" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "recurrence" prop_bernstein_recurrence</span></span>
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94
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<pre style="margin: 0;">+<span id="LC94" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "symmetry" prop_bernstein_symmetry</span></span>
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95
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<pre style="margin: 0;">+<span id="LC95" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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96
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<pre style="margin: 0;">+<span id="LC96" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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97
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<pre style="margin: 0;">+<span id="LC97" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- prop_bernstein_sum can be very time and space intensive if we let it</span></span>
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98
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<pre style="margin: 0;">+<span id="LC98" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- look too far into the table. We also don't really gain much if any </span></span>
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99
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<pre style="margin: 0;">+<span id="LC99" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- additional confidence in the correctness of the implementation by doing</span></span>
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100
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<pre style="margin: 0;">+<span id="LC100" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- so, so here's a limit for 'n' in the "bernstein :: [[Poly Integer]]" tests.</span></span>
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101
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<pre style="margin: 0;">+<span id="LC101" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+bernsteinLimit = 500</span></span>
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102
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<pre style="margin: 0;">+<span id="LC102" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC103" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_bernstein_sum (NonNegative n) =</span></span>
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104
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<pre style="margin: 0;">+<span id="LC104" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyIsOne (sumPolys (bernstein !! (n `mod` bernsteinLimit)))</span></span>
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105
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<pre style="margin: 0;">+<span id="LC105" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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106
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<pre style="margin: 0;">+<span id="LC106" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_bernstein_recurrence (Positive a) (Positive b) =</span></span>
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107
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<pre style="margin: 0;">+<span id="LC107" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let a' = a `mod` bernsteinLimit</span></span>
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108
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<pre style="margin: 0;">+<span id="LC108" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ b' = b `mod` bernsteinLimit</span></span>
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109
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<pre style="margin: 0;">+<span id="LC109" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n = 1 + max a' b'; n' = fromIntegral n</span></span>
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110
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<pre style="margin: 0;">+<span id="LC110" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a' b'; v' = fromIntegral v</span></span>
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111
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<pre style="margin: 0;">+<span id="LC111" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in addPoly (scalePoly ((n'-v')/n') (fmap toRational (bernstein !! n !! v )))</span></span>
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112
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<pre style="margin: 0;">+<span id="LC112" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (scalePoly ((v'+ 1)/n') (fmap toRational (bernstein !! n !! (v+1))))</span></span>
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113
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<pre style="margin: 0;">+<span id="LC113" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == fmap toRational (bernstein !! (n-1) !! v)</span></span>
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114
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<pre style="margin: 0;">+<span id="LC114" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ </span></span>
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115
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<pre style="margin: 0;">+<span id="LC115" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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116
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<pre style="margin: 0;">+<span id="LC116" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_bernstein_symmetry (Positive a) (Positive b) =</span></span>
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117
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<pre style="margin: 0;">+<span id="LC117" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let a' = a `mod` bernsteinLimit</span></span>
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118
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<pre style="margin: 0;">+<span id="LC118" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ b' = b `mod` bernsteinLimit</span></span>
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119
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<pre style="margin: 0;">+<span id="LC119" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n = max a' b'</span></span>
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120
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<pre style="margin: 0;">+<span id="LC120" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a' b'</span></span>
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121
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<pre style="margin: 0;">+<span id="LC121" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in bernstein !! n !! (n-v)</span></span>
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122
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<pre style="margin: 0;">+<span id="LC122" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == composePoly (bernstein !! n !! v) (poly LE [1, -1])</span></span>
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123
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<pre style="margin: 0;">+<span id="LC123" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ </span></span>
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124
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<pre style="margin: 0;">+<span id="LC124" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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125
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<pre style="margin: 0;">+<span id="LC125" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalBernstein_tests = </span></span>
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126
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<pre style="margin: 0;">+<span id="LC126" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalBernstein_sane</span></span>
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127
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<pre style="margin: 0;">+<span id="LC127" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sign" prop_evalBernstein_sign</span></span>
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128
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<pre style="margin: 0;">+<span id="LC128" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "local max" prop_evalBernstein_local_max</span></span>
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129
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<pre style="margin: 0;">+<span id="LC129" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "symmetry" prop_evalBernstein_symmetry</span></span>
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130
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<pre style="margin: 0;">+<span id="LC130" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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131
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<pre style="margin: 0;">+<span id="LC131" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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132
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<pre style="margin: 0;">+<span id="LC132" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalBernstein_sane (NonNegative a) (NonNegative b) x =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="133" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
133
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<pre style="margin: 0;">+<span id="LC133" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = max a b</span></span>
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134
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<pre style="margin: 0;">+<span id="LC134" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="135" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
135
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<pre style="margin: 0;">+<span id="LC135" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in n <= bernsteinLimit ==></span></span>
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<td class="diff-line-num new new_line" data-linenumber="136" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
136
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<pre style="margin: 0;">+<span id="LC136" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (fmap toRational (bernstein !! n !! v)) x</span></span>
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<td class="diff-line-num new new_line" data-linenumber="137" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
137
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<pre style="margin: 0;">+<span id="LC137" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalBernstein n v x</span></span>
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138
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<pre style="margin: 0;">+<span id="LC138" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<td class="diff-line-num new new_line" data-linenumber="139" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
139
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<pre style="margin: 0;">+<span id="LC139" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalBernstein_sign (NonNegative a) (NonNegative b) x =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="140" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
140
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<pre style="margin: 0;">+<span id="LC140" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = max a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="141" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
141
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<pre style="margin: 0;">+<span id="LC141" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="142" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
142
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<pre style="margin: 0;">+<span id="LC142" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in signum (evalBernstein n v x) == evalBernstein_sign n v x</span></span>
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143
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<pre style="margin: 0;">+<span id="LC143" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<td class="diff-line-num new new_line" data-linenumber="144" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
144
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<pre style="margin: 0;">+<span id="LC144" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalBernstein_local_max (NonNegative a) (NonNegative b) x =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="145" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
145
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<pre style="margin: 0;">+<span id="LC145" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = max a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="146" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
146
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<pre style="margin: 0;">+<span id="LC146" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="147" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
147
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<pre style="margin: 0;">+<span id="LC147" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ xMax = fromIntegral v / fromIntegral n</span></span>
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<td class="diff-line-num new new_line" data-linenumber="148" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
148
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<pre style="margin: 0;">+<span id="LC148" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in n >= 0 ==></span></span>
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<td class="diff-line-num new new_line" data-linenumber="149" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
149
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<pre style="margin: 0;">+<span id="LC149" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalBernstein n v (onUnitInterval x) <= evalBernstein n v xMax</span></span>
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150
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<pre style="margin: 0;">+<span id="LC150" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<td class="diff-line-num new new_line" data-linenumber="151" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
151
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<pre style="margin: 0;">+<span id="LC151" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalBernstein_symmetry (NonNegative a) (NonNegative b) x =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="152" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
152
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<pre style="margin: 0;">+<span id="LC152" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = max a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="153" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
153
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<pre style="margin: 0;">+<span id="LC153" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ v = min a b</span></span>
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<td class="diff-line-num new new_line" data-linenumber="154" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
154
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<pre style="margin: 0;">+<span id="LC154" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in evalBernstein n (n-v) x</span></span>
</pre>
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<td class="diff-line-num new new_line" data-linenumber="155" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
155
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<pre style="margin: 0;">+<span id="LC155" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalBernstein n v (1-x)</span></span>
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156
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<pre style="margin: 0;">+<span id="LC156" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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157
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<pre style="margin: 0;">+<span id="LC157" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalBernstein_sign 0 0 _ = 1</span></span>
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158
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<pre style="margin: 0;">+<span id="LC158" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalBernstein_sign n v 0 = delta v 0</span></span>
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159
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<pre style="margin: 0;">+<span id="LC159" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalBernstein_sign n v 1 = delta v n</span></span>
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160
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<pre style="margin: 0;">+<span id="LC160" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalBernstein_sign n v x</span></span>
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161
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<pre style="margin: 0;">+<span id="LC161" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | x > 0 && x < 1 = 1</span></span>
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162
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<pre style="margin: 0;">+<span id="LC162" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | even n || x < 0 = if even v then 1 else -1</span></span>
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163
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<pre style="margin: 0;">+<span id="LC163" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | otherwise = if odd v then 1 else -1 </span></span>
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164
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<pre style="margin: 0;">+<span id="LC164" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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165
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<pre style="margin: 0;">+<span id="LC165" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+delta x y</span></span>
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166
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<pre style="margin: 0;">+<span id="LC166" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | x == y = 1</span></span>
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167
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<pre style="margin: 0;">+<span id="LC167" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | otherwise = 0</span></span>
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168
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<pre style="margin: 0;">+<span id="LC168" class="line" lang="diff"><span class="gd" style="color: #000; background-color: #fdd;">--- /dev/null</span></span>
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169
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<pre style="margin: 0;">+<span id="LC169" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+++ b/test/Tests/Chebyshev.hs</span></span>
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170
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<pre style="margin: 0;">+<span id="LC170" class="line" lang="diff"><span class="gu" style="color: #800080; font-weight: 600;">@@ -0,0 +1,142 @@</span></span>
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171
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<pre style="margin: 0;">+<span id="LC171" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+{-# LANGUAGE ExtendedDefaultRules #-}</span></span>
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172
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<pre style="margin: 0;">+<span id="LC172" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+module Tests.Chebyshev (chebyshevTests) where</span></span>
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173
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<pre style="margin: 0;">+<span id="LC173" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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174
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<pre style="margin: 0;">+<span id="LC174" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial</span></span>
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175
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<pre style="margin: 0;">+<span id="LC175" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial.Chebyshev</span></span>
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176
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<pre style="margin: 0;">+<span id="LC176" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework (testGroup)</span></span>
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177
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<pre style="margin: 0;">+<span id="LC177" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.QuickCheck2 (testProperty)</span></span>
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178
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<pre style="margin: 0;">+<span id="LC178" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.QuickCheck</span></span>
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179
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<pre style="margin: 0;">+<span id="LC179" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import TestUtils</span></span>
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180
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<pre style="margin: 0;">+<span id="LC180" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Text.Show.Functions ()</span></span>
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181
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<pre style="margin: 0;">+<span id="LC181" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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182
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<pre style="margin: 0;">+<span id="LC182" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+default (Integer, Rational)</span></span>
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183
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<pre style="margin: 0;">+<span id="LC183" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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184
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<pre style="margin: 0;">+<span id="LC184" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+chebyshevTests =</span></span>
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185
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<pre style="margin: 0;">+<span id="LC185" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "ts" ts_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="186" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
186
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<pre style="margin: 0;">+<span id="LC186" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "us" us_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="187" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
187
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<pre style="margin: 0;">+<span id="LC187" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "Pell's equation" prop_pell's_eqn</span></span>
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<td class="diff-line-num new new_line" data-linenumber="188" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
188
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<pre style="margin: 0;">+<span id="LC188" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "t n == ts !! n" $ \(NonNegative a) -> let n = a `mod` 1000 in t n == ts !! n</span></span>
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<td class="diff-line-num new new_line" data-linenumber="189" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
189
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<pre style="margin: 0;">+<span id="LC189" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "u n == us !! n" $ \(NonNegative a) -> let n = a `mod` 1000 in u n == us !! n</span></span>
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<td class="diff-line-num new new_line" data-linenumber="190" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
190
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<pre style="margin: 0;">+<span id="LC190" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalT" evalT_tests</span></span>
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191
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<pre style="margin: 0;">+<span id="LC191" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalU" evalU_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="192" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
192
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<pre style="margin: 0;">+<span id="LC192" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "tRoots" tRoots_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="193" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
193
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<pre style="margin: 0;">+<span id="LC193" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "tExtrema" tExtrema_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="194" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
194
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<pre style="margin: 0;">+<span id="LC194" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "chebyshevFit" chebyshevFit_tests</span></span>
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<td class="diff-line-num new new_line" data-linenumber="195" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
195
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<pre style="margin: 0;">+<span id="LC195" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalChebyshevSeries" evalChebyshevSeries_tests</span></span>
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196
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<pre style="margin: 0;">+<span id="LC196" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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197
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<pre style="margin: 0;">+<span id="LC197" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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198
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<pre style="margin: 0;">+<span id="LC198" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ts_tests =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="199" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
199
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<pre style="margin: 0;">+<span id="LC199" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "recurrence" prop_ts_recurrence</span></span>
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<td class="diff-line-num new new_line" data-linenumber="200" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
200
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<pre style="margin: 0;">+<span id="LC200" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "parity" prop_ts_parity</span></span>
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201
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<pre style="margin: 0;">+<span id="LC201" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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202
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<pre style="margin: 0;">+<span id="LC202" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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203
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<pre style="margin: 0;">+<span id="LC203" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_ts_recurrence (NonNegative 0) = ts !! 0 == one</span></span>
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204
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<pre style="margin: 0;">+<span id="LC204" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_ts_recurrence (NonNegative 1) = ts !! 1 == x</span></span>
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205
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<pre style="margin: 0;">+<span id="LC205" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_ts_recurrence (NonNegative a) =</span></span>
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206
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<pre style="margin: 0;">+<span id="LC206" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = 1 + a `mod` 1200</span></span>
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207
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<pre style="margin: 0;">+<span id="LC207" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in (multPoly (scalePoly 2 x) (ts !! n))</span></span>
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208
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<pre style="margin: 0;">+<span id="LC208" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == addPoly (ts !! (n-1)) (ts !! (n+1))</span></span>
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209
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<pre style="margin: 0;">+<span id="LC209" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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210
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<pre style="margin: 0;">+<span id="LC210" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_ts_parity (NonNegative n)</span></span>
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211
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<pre style="margin: 0;">+<span id="LC211" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | even n = composePoly t (negatePoly x) == t</span></span>
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212
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<pre style="margin: 0;">+<span id="LC212" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | otherwise = composePoly t (negatePoly x) == negatePoly t</span></span>
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213
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<pre style="margin: 0;">+<span id="LC213" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where t = ts !! (n `mod` 1200)</span></span>
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214
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<pre style="margin: 0;">+<span id="LC214" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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215
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<pre style="margin: 0;">+<span id="LC215" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+us_tests =</span></span>
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216
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<pre style="margin: 0;">+<span id="LC216" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "recurrence" prop_us_recurrence</span></span>
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217
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<pre style="margin: 0;">+<span id="LC217" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "parity" prop_us_parity</span></span>
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218
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<pre style="margin: 0;">+<span id="LC218" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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219
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<pre style="margin: 0;">+<span id="LC219" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC220" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_us_recurrence (NonNegative 0) = us !! 0 == one</span></span>
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<pre style="margin: 0;">+<span id="LC221" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_us_recurrence (NonNegative 1) = us !! 1 == scalePoly 2 x</span></span>
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<pre style="margin: 0;">+<span id="LC222" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_us_recurrence (NonNegative a) =</span></span>
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223
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<pre style="margin: 0;">+<span id="LC223" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = 1 + a `mod` 1200</span></span>
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224
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<pre style="margin: 0;">+<span id="LC224" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in (multPoly (scalePoly 2 x) (us !! n))</span></span>
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225
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<pre style="margin: 0;">+<span id="LC225" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == addPoly (us !! (n-1)) (us !! (n+1))</span></span>
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226
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<pre style="margin: 0;">+<span id="LC226" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC227" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_us_parity (NonNegative n)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="228" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
228
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<pre style="margin: 0;">+<span id="LC228" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | even n = composePoly u (negatePoly x) == u</span></span>
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229
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<pre style="margin: 0;">+<span id="LC229" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | otherwise = composePoly u (negatePoly x) == negatePoly u</span></span>
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230
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<pre style="margin: 0;">+<span id="LC230" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where u = us !! (n `mod` 1200)</span></span>
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231
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<pre style="margin: 0;">+<span id="LC231" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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232
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<pre style="margin: 0;">+<span id="LC232" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_pell's_eqn (Positive a) =</span></span>
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233
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<pre style="margin: 0;">+<span id="LC233" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = 1 + a `mod` 400</span></span>
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234
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<pre style="margin: 0;">+<span id="LC234" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in powPoly (ts !! n) 2</span></span>
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235
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<pre style="margin: 0;">+<span id="LC235" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == addPoly one (multPoly (poly BE [1,0,-1]) (powPoly (us !! (n-1)) 2))</span></span>
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236
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<pre style="margin: 0;">+<span id="LC236" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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237
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<pre style="margin: 0;">+<span id="LC237" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalT_tests =</span></span>
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238
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<pre style="margin: 0;">+<span id="LC238" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalT_sane</span></span>
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<td class="diff-line-num new new_line" data-linenumber="239" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
239
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<pre style="margin: 0;">+<span id="LC239" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "limits (Float)" (prop_evalT_limits (1e-7 :: Float))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="240" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
240
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<pre style="margin: 0;">+<span id="LC240" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "limits (Double)" (prop_evalT_limits (1e-15 :: Double))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="241" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
241
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<pre style="margin: 0;">+<span id="LC241" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "endpoints" prop_evalT_endpoints</span></span>
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242
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<pre style="margin: 0;">+<span id="LC242" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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243
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<pre style="margin: 0;">+<span id="LC243" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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244
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<pre style="margin: 0;">+<span id="LC244" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalT_sane (NonNegative a) x =</span></span>
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245
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<pre style="margin: 0;">+<span id="LC245" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = a `mod` 1000</span></span>
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246
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<pre style="margin: 0;">+<span id="LC246" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in evalT n x == evalPoly (t n) x</span></span>
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247
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<pre style="margin: 0;">+<span id="LC247" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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248
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<pre style="margin: 0;">+<span id="LC248" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalT_limits eps (NonNegative n) x = abs (evalT (n `mod` 1000) (onInterval (-1) 1 x)) <= 1 + eps</span></span>
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249
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<pre style="margin: 0;">+<span id="LC249" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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250
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<pre style="margin: 0;">+<span id="LC250" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalT_endpoints (NonNegative a) True =</span></span>
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251
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<pre style="margin: 0;">+<span id="LC251" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = a `mod` 5000</span></span>
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252
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<pre style="margin: 0;">+<span id="LC252" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in evalT n 1 == 1</span></span>
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253
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<pre style="margin: 0;">+<span id="LC253" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalT_endpoints (NonNegative a) False =</span></span>
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254
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<pre style="margin: 0;">+<span id="LC254" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = a `mod` 5000</span></span>
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255
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<pre style="margin: 0;">+<span id="LC255" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in evalT n (-1) == if even n then 1 else -1</span></span>
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256
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<pre style="margin: 0;">+<span id="LC256" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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257
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<pre style="margin: 0;">+<span id="LC257" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalU_tests =</span></span>
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258
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<pre style="margin: 0;">+<span id="LC258" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalU_sane</span></span>
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259
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<pre style="margin: 0;">+<span id="LC259" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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260
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<pre style="margin: 0;">+<span id="LC260" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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261
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<pre style="margin: 0;">+<span id="LC261" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalU_sane (NonNegative a) x =</span></span>
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262
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<pre style="margin: 0;">+<span id="LC262" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = a `mod` 1000</span></span>
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263
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<pre style="margin: 0;">+<span id="LC263" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in evalT n x == evalPoly (t n) x</span></span>
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264
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<pre style="margin: 0;">+<span id="LC264" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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265
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<pre style="margin: 0;">+<span id="LC265" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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266
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<pre style="margin: 0;">+<span id="LC266" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+tRoots_tests =</span></span>
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267
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<pre style="margin: 0;">+<span id="LC267" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "distinct (Float)" (prop_tRoots_distinct (undefined :: Float))</span></span>
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268
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<pre style="margin: 0;">+<span id="LC268" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "distinct (Double)" (prop_tRoots_distinct (undefined :: Double))</span></span>
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269
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<pre style="margin: 0;">+<span id="LC269" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ -- I could test that the roots are roots, but numerically they aren't,</span></span>
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270
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<pre style="margin: 0;">+<span id="LC270" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ -- and with the insanely large derivatives at some of the roots, I don't</span></span>
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271
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<pre style="margin: 0;">+<span id="LC271" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ -- expect 'evalT n' to even be particularly close to zero at many of the</span></span>
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272
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<pre style="margin: 0;">+<span id="LC272" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ -- "roots".</span></span>
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273
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<pre style="margin: 0;">+<span id="LC273" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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274
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<pre style="margin: 0;">+<span id="LC274" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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275
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<pre style="margin: 0;">+<span id="LC275" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_tRoots_distinct w (NonNegative n') = distinct (tRoots n `asTypeOf` [w])</span></span>
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276
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<pre style="margin: 0;">+<span id="LC276" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n = n' `mod` 1200</span></span>
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277
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<pre style="margin: 0;">+<span id="LC277" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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278
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<pre style="margin: 0;">+<span id="LC278" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+tExtrema_tests =</span></span>
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<td class="diff-line-num new new_line" data-linenumber="279" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
279
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<pre style="margin: 0;">+<span id="LC279" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "distinct (Float)" (prop_tExtrema_distinct (undefined :: Float))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="280" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
280
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<pre style="margin: 0;">+<span id="LC280" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "distinct (Double)" (prop_tExtrema_distinct (undefined :: Double))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="281" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
281
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<pre style="margin: 0;">+<span id="LC281" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "near 1 (Float)" (prop_tExtrema_near_1 (\n -> n * 1e-7 :: Float))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="282" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
282
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<pre style="margin: 0;">+<span id="LC282" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "near 1 (Double)" (prop_tExtrema_near_1 (\n -> n * 1e-16 :: Double))</span></span>
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283
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<pre style="margin: 0;">+<span id="LC283" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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284
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<pre style="margin: 0;">+<span id="LC284" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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285
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<pre style="margin: 0;">+<span id="LC285" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_tExtrema_distinct w (NonNegative n') = distinct (tExtrema n `asTypeOf` [w])</span></span>
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286
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<pre style="margin: 0;">+<span id="LC286" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n = n' `mod` 1200</span></span>
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287
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<pre style="margin: 0;">+<span id="LC287" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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288
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<pre style="margin: 0;">+<span id="LC288" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_tExtrema_near_1 eps (NonNegative n') = all (near1.abs.evalT n) (tExtrema n)</span></span>
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289
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<pre style="margin: 0;">+<span id="LC289" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where </span></span>
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290
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<pre style="margin: 0;">+<span id="LC290" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n = n' `mod` 1200</span></span>
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291
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<pre style="margin: 0;">+<span id="LC291" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ near1 y = abs (y-1) <= eps (fromIntegral n)</span></span>
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292
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<pre style="margin: 0;">+<span id="LC292" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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293
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<pre style="margin: 0;">+<span id="LC293" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+chebyshevFit_tests =</span></span>
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294
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<pre style="margin: 0;">+<span id="LC294" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane (Double)" (prop_chebyshevFit_sane (\n -> 1e-11 * n^2 :: Double))</span></span>
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295
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<pre style="margin: 0;">+<span id="LC295" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane (Float)" (prop_chebyshevFit_sane (\n -> 1e-4 * n^2 :: Float))</span></span>
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296
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<pre style="margin: 0;">+<span id="LC296" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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297
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<pre style="margin: 0;">+<span id="LC297" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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298
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<pre style="margin: 0;">+<span id="LC298" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_chebyshevFit_sane epsF (NonNegative n') f =</span></span>
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299
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<pre style="margin: 0;">+<span id="LC299" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n' < 100 ==> all (<= eps) [relErr (f x) (f' x) | x <- tRoots n]</span></span>
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300
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<pre style="margin: 0;">+<span id="LC300" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where </span></span>
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301
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<pre style="margin: 0;">+<span id="LC301" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ eps = epsF (fromIntegral n)</span></span>
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302
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<pre style="margin: 0;">+<span id="LC302" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ n = n' `mod` 500</span></span>
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303
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<pre style="margin: 0;">+<span id="LC303" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ cs = chebyshevFit n f</span></span>
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304
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<pre style="margin: 0;">+<span id="LC304" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ f' = evalChebyshevSeries cs</span></span>
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305
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<pre style="margin: 0;">+<span id="LC305" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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306
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<pre style="margin: 0;">+<span id="LC306" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalChebyshevSeries_tests =</span></span>
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307
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<pre style="margin: 0;">+<span id="LC307" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalChebyshevSeries_sane</span></span>
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308
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<pre style="margin: 0;">+<span id="LC308" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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309
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<pre style="margin: 0;">+<span id="LC309" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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310
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<pre style="margin: 0;">+<span id="LC310" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalChebyshevSeries_sane cs x </span></span>
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311
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<pre style="margin: 0;">+<span id="LC311" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = evalChebyshevSeries cs x </span></span>
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312
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<pre style="margin: 0;">+<span id="LC312" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == sum (zipWith (*) cs (evalTs x))</span></span>
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313
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<pre style="margin: 0;">+<span id="LC313" class="line" lang="diff"><span class="gd" style="color: #000; background-color: #fdd;">--- /dev/null</span></span>
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314
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<pre style="margin: 0;">+<span id="LC314" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+++ b/test/Tests/Core.hs</span></span>
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315
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<pre style="margin: 0;">+<span id="LC315" class="line" lang="diff"><span class="gu" style="color: #800080; font-weight: 600;">@@ -0,0 +1,290 @@</span></span>
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316
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<pre style="margin: 0;">+<span id="LC316" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+{-# LANGUAGE ExtendedDefaultRules #-}</span></span>
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317
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<pre style="margin: 0;">+<span id="LC317" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+module Tests.Core (coreTests) where</span></span>
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318
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<pre style="margin: 0;">+<span id="LC318" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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319
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<pre style="margin: 0;">+<span id="LC319" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Data.List</span></span>
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320
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<pre style="margin: 0;">+<span id="LC320" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Data.VectorSpace</span></span>
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321
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<pre style="margin: 0;">+<span id="LC321" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial</span></span>
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322
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<pre style="margin: 0;">+<span id="LC322" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial.Lagrange</span></span>
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<pre style="margin: 0;">+<span id="LC323" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework (testGroup)</span></span>
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<pre style="margin: 0;">+<span id="LC324" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.HUnit (testCase)</span></span>
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325
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<pre style="margin: 0;">+<span id="LC325" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.QuickCheck2 (testProperty)</span></span>
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326
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<pre style="margin: 0;">+<span id="LC326" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.HUnit</span></span>
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327
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<pre style="margin: 0;">+<span id="LC327" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.QuickCheck</span></span>
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328
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<pre style="margin: 0;">+<span id="LC328" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import TestUtils</span></span>
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329
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<pre style="margin: 0;">+<span id="LC329" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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330
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<pre style="margin: 0;">+<span id="LC330" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- Use exact math everywhere; we're not testing stability or speed,</span></span>
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331
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<pre style="margin: 0;">+<span id="LC331" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+-- just mathematical soundness.</span></span>
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332
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<pre style="margin: 0;">+<span id="LC332" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+default (Integer, Rational)</span></span>
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<pre style="margin: 0;">+<span id="LC333" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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334
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<pre style="margin: 0;">+<span id="LC334" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+coreTests = </span></span>
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335
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<pre style="margin: 0;">+<span id="LC335" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "constants"</span></span>
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336
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<pre style="margin: 0;">+<span id="LC336" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "zero"</span></span>
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337
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<pre style="margin: 0;">+<span id="LC337" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "polyIsZero zero" (assert (polyIsZero zero))</span></span>
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338
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<pre style="margin: 0;">+<span id="LC338" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testCase "polyDegree zero == (-1)" (assert (polyDegree zero == (-1)))</span></span>
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339
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<pre style="margin: 0;">+<span id="LC339" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "(p == zero) == polyIsZero p" $ \p -></span></span>
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340
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<pre style="margin: 0;">+<span id="LC340" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (p == zero) == polyIsZero p</span></span>
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341
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<pre style="margin: 0;">+<span id="LC341" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "evalPoly zero x == 0" $ \x -></span></span>
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342
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<pre style="margin: 0;">+<span id="LC342" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly zero x == 0</span></span>
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343
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<pre style="margin: 0;">+<span id="LC343" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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344
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<pre style="margin: 0;">+<span id="LC344" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "one"</span></span>
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345
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<pre style="margin: 0;">+<span id="LC345" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "polyIsOne one" (assert (polyIsOne one))</span></span>
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346
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<pre style="margin: 0;">+<span id="LC346" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testCase "polyDegree one == 0" (assert (polyDegree one == 0))</span></span>
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347
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<pre style="margin: 0;">+<span id="LC347" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "(p == one) == polyIsOne p" $ \p -></span></span>
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348
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<pre style="margin: 0;">+<span id="LC348" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (p == one) == polyIsOne p</span></span>
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349
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<pre style="margin: 0;">+<span id="LC349" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "evalPoly one x == 1" $ \x -></span></span>
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350
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<pre style="margin: 0;">+<span id="LC350" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly one x == 1</span></span>
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351
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<pre style="margin: 0;">+<span id="LC351" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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352
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<pre style="margin: 0;">+<span id="LC352" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "x"</span></span>
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353
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<pre style="margin: 0;">+<span id="LC353" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "evalPoly x t == t" $ \t -></span></span>
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354
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<pre style="margin: 0;">+<span id="LC354" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly x t == t</span></span>
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355
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<pre style="margin: 0;">+<span id="LC355" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testCase "polyDegree x == 1" (assert (polyDegree x == 1))</span></span>
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356
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<pre style="margin: 0;">+<span id="LC356" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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357
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<pre style="margin: 0;">+<span id="LC357" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "constPoly"</span></span>
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358
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<pre style="margin: 0;">+<span id="LC358" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "evalPoly (constPoly x) == const x" $ \a b -> </span></span>
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359
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<pre style="margin: 0;">+<span id="LC359" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (constPoly a) b == const a b</span></span>
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360
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<pre style="margin: 0;">+<span id="LC360" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "polyDegree (constPoly x) == if x == 0 then -1 else 0" $ \x -> </span></span>
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361
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<pre style="margin: 0;">+<span id="LC361" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDegree (constPoly x) == if x == 0 then -1 else 0</span></span>
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362
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<pre style="margin: 0;">+<span id="LC362" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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363
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<pre style="margin: 0;">+<span id="LC363" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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364
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<pre style="margin: 0;">+<span id="LC364" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "constructors"</span></span>
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365
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<pre style="margin: 0;">+<span id="LC365" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "polyCoeffs LE . poly LE" $ \cs -></span></span>
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366
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<pre style="margin: 0;">+<span id="LC366" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case stripPrefix (polyCoeffs LE (poly LE cs)) cs of</span></span>
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367
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<pre style="margin: 0;">+<span id="LC367" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Just zs -> all (== 0) zs</span></span>
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368
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<pre style="margin: 0;">+<span id="LC368" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Nothing -> False</span></span>
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369
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<pre style="margin: 0;">+<span id="LC369" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "polyCoeffs LE . poly BE" $ \cs -></span></span>
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370
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<pre style="margin: 0;">+<span id="LC370" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case stripPrefix (polyCoeffs LE (poly BE cs)) (reverse cs) of</span></span>
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<td class="diff-line-num new new_line" data-linenumber="371" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
371
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<pre style="margin: 0;">+<span id="LC371" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Just zs -> all (== 0) zs</span></span>
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372
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<pre style="margin: 0;">+<span id="LC372" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Nothing -> False</span></span>
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<td class="diff-line-num new new_line" data-linenumber="373" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
373
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<pre style="margin: 0;">+<span id="LC373" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "polyCoeffs BE . poly LE" $ \cs -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="374" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
374
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<pre style="margin: 0;">+<span id="LC374" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case stripPrefix (reverse (polyCoeffs BE (poly LE cs))) cs of</span></span>
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<td class="diff-line-num new new_line" data-linenumber="375" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
375
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<pre style="margin: 0;">+<span id="LC375" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Just zs -> all (== 0) zs</span></span>
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<td class="diff-line-num new new_line" data-linenumber="376" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
376
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<pre style="margin: 0;">+<span id="LC376" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Nothing -> False</span></span>
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<td class="diff-line-num new new_line" data-linenumber="377" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
377
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<pre style="margin: 0;">+<span id="LC377" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "polyCoeffs BE . poly BE" $ \cs -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="378" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
378
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<pre style="margin: 0;">+<span id="LC378" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case stripPrefix (reverse (polyCoeffs BE (poly BE cs))) (reverse cs) of</span></span>
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379
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<pre style="margin: 0;">+<span id="LC379" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Just zs -> all (== 0) zs</span></span>
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380
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<pre style="margin: 0;">+<span id="LC380" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ Nothing -> False</span></span>
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381
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<pre style="margin: 0;">+<span id="LC381" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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382
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<pre style="margin: 0;">+<span id="LC382" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "instances"</span></span>
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383
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<pre style="margin: 0;">+<span id="LC383" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "Eq"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="384" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
384
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<pre style="margin: 0;">+<span id="LC384" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "reflexive" $ \p -> p == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="385" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
385
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<pre style="margin: 0;">+<span id="LC385" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "symmetric" $ \p q -> (p==q) == (q==p)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="386" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
386
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<pre style="margin: 0;">+<span id="LC386" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "transitive" $ \p q r -> (p == q && q == r) ==> p == r</span></span>
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<td class="diff-line-num new new_line" data-linenumber="387" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
387
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<pre style="margin: 0;">+<span id="LC387" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \cs ds end1 end2 -> </span></span>
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<td class="diff-line-num new new_line" data-linenumber="388" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
388
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<pre style="margin: 0;">+<span id="LC388" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let p = poly end1 cs; q = poly end1 ds</span></span>
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<td class="diff-line-num new new_line" data-linenumber="389" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
389
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<pre style="margin: 0;">+<span id="LC389" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in (p==q) == (polyCoeffs end2 p == polyCoeffs end2 q)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="390" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
390
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<pre style="margin: 0;">+<span id="LC390" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "endianness-independent" $ \cs end -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="391" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
391
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<pre style="margin: 0;">+<span id="LC391" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ poly end cs == poly (rev end) (reverse cs)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="392" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
392
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<pre style="margin: 0;">+<span id="LC392" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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393
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<pre style="margin: 0;">+<span id="LC393" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "AdditiveGroup"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="394" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
394
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<pre style="margin: 0;">+<span id="LC394" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "zeroV"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="395" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
395
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<pre style="margin: 0;">+<span id="LC395" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "polyIsZero zeroV" (assert (polyIsZero zeroV))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="396" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
396
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<pre style="margin: 0;">+<span id="LC396" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "(p == zeroV) == polyIsZero p" $ \p -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="397" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
397
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<pre style="margin: 0;">+<span id="LC397" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (p == zeroV) == polyIsZero p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="398" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
398
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<pre style="margin: 0;">+<span id="LC398" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "evalPoly zeroV x == zeroV" $ \x -></span></span>
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399
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<pre style="margin: 0;">+<span id="LC399" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly zeroV x == zeroV</span></span>
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400
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<pre style="margin: 0;">+<span id="LC400" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="401" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
401
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<pre style="margin: 0;">+<span id="LC401" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "^+^"</span></span>
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402
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<pre style="margin: 0;">+<span id="LC402" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "left unit" $ \p -> zeroV ^+^ p == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="403" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
403
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<td class="line_content new noteable_line" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC403" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right unit" $ \p -> p ^+^ zeroV == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="404" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
404
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<pre style="margin: 0;">+<span id="LC404" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "commutative" $ \p q -> p ^+^ q == q ^+^ p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="405" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
405
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<pre style="margin: 0;">+<span id="LC405" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "associative" $ \p q r -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="406" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
406
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<pre style="margin: 0;">+<span id="LC406" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ p ^+^ (q ^+^ r) == (p ^+^ q) ^+^ r</span></span>
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<td class="diff-line-num new new_line" data-linenumber="407" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
407
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<pre style="margin: 0;">+<span id="LC407" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \p q x -></span></span>
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408
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<pre style="margin: 0;">+<span id="LC408" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (p ^+^ q) x ==</span></span>
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409
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<pre style="margin: 0;">+<span id="LC409" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly p x ^+^ evalPoly q x</span></span>
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410
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<pre style="margin: 0;">+<span id="LC410" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="411" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
411
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<pre style="margin: 0;">+<span id="LC411" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "negateV"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="412" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
412
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<pre style="margin: 0;">+<span id="LC412" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p -> p ^+^ negateV p == zeroV</span></span>
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<td class="diff-line-num new new_line" data-linenumber="413" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
413
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<pre style="margin: 0;">+<span id="LC413" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="414" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
414
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<pre style="margin: 0;">+<span id="LC414" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
</pre>
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<td class="diff-line-num new new_line" data-linenumber="415" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
415
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<pre style="margin: 0;">+<span id="LC415" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "VectorSpace"</span></span>
</pre>
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<td class="diff-line-num new new_line" data-linenumber="416" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
416
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<pre style="margin: 0;">+<span id="LC416" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \s p x -></span></span>
</pre>
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<td class="diff-line-num new new_line" data-linenumber="417" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
417
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<pre style="margin: 0;">+<span id="LC417" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (s *^ (p :: Poly Rational)) x == s *^ evalPoly p x</span></span>
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418
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<pre style="margin: 0;">+<span id="LC418" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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419
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<pre style="margin: 0;">+<span id="LC419" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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420
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<pre style="margin: 0;">+<span id="LC420" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "addPoly"</span></span>
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421
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<pre style="margin: 0;">+<span id="LC421" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "left unit" $ \p -> addPoly zero p == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="422" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
422
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<pre style="margin: 0;">+<span id="LC422" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right unit" $ \p -> addPoly p zero == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="423" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
423
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<pre style="margin: 0;">+<span id="LC423" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "commutative" $ \p q -> addPoly p q == addPoly q p</span></span>
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424
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<pre style="margin: 0;">+<span id="LC424" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "associative" $ \p q r -></span></span>
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425
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<pre style="margin: 0;">+<span id="LC425" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ addPoly p (addPoly q r) == addPoly (addPoly p q) r</span></span>
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426
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<pre style="margin: 0;">+<span id="LC426" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \p q x -></span></span>
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427
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<pre style="margin: 0;">+<span id="LC427" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (addPoly p q) x ==</span></span>
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428
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<pre style="margin: 0;">+<span id="LC428" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly p x + evalPoly q x</span></span>
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429
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<pre style="margin: 0;">+<span id="LC429" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \p q -> </span></span>
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430
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<pre style="margin: 0;">+<span id="LC430" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n = polyDegree p</span></span>
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431
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<pre style="margin: 0;">+<span id="LC431" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ m = polyDegree q</span></span>
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432
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<pre style="margin: 0;">+<span id="LC432" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ r = addPoly p q</span></span>
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433
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<pre style="margin: 0;">+<span id="LC433" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in if n /= m</span></span>
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434
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<pre style="margin: 0;">+<span id="LC434" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ || polyIsZero p || polyIsZero q</span></span>
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435
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<pre style="margin: 0;">+<span id="LC435" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ || head (polyCoeffs BE p) + head (polyCoeffs BE q) /= 0</span></span>
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436
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<pre style="margin: 0;">+<span id="LC436" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ then polyDegree r == max m n</span></span>
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437
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<pre style="margin: 0;">+<span id="LC437" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ else polyDegree r < max m n</span></span>
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438
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<pre style="margin: 0;">+<span id="LC438" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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439
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<pre style="margin: 0;">+<span id="LC439" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "sumPoly"</span></span>
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440
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<pre style="margin: 0;">+<span id="LC440" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \ps -> sumPolys ps == foldl' addPoly zero ps</span></span>
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441
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<pre style="margin: 0;">+<span id="LC441" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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442
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<pre style="margin: 0;">+<span id="LC442" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "negatePoly"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="443" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
443
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<pre style="margin: 0;">+<span id="LC443" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p -> polyIsZero (addPoly p (negatePoly p))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="444" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
444
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<pre style="margin: 0;">+<span id="LC444" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \p -> polyDegree p == polyDegree (negatePoly p)</span></span>
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445
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<pre style="margin: 0;">+<span id="LC445" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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446
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<pre style="margin: 0;">+<span id="LC446" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "composePoly"</span></span>
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447
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<pre style="margin: 0;">+<span id="LC447" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \f g x -> </span></span>
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448
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<pre style="margin: 0;">+<span id="LC448" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDegree f * polyDegree g <= 250 ==></span></span>
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449
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<pre style="margin: 0;">+<span id="LC449" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (composePoly f g) x </span></span>
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450
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<pre style="margin: 0;">+<span id="LC450" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalPoly f (evalPoly g x)</span></span>
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451
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<pre style="margin: 0;">+<span id="LC451" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "associative" $ \(SmallPoly f) (SmallPoly g) (SmallPoly h) -> </span></span>
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452
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<pre style="margin: 0;">+<span id="LC452" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDegree f * polyDegree g * polyDegree h <= 500 ==></span></span>
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453
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<pre style="margin: 0;">+<span id="LC453" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ composePoly f (composePoly g h)</span></span>
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454
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<pre style="margin: 0;">+<span id="LC454" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == composePoly (composePoly f g) h</span></span>
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<td class="diff-line-num new new_line" data-linenumber="455" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
455
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<pre style="margin: 0;">+<span id="LC455" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "left cancel" $ \p k -></span></span>
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456
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<pre style="margin: 0;">+<span id="LC456" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ composePoly p (constPoly k) == constPoly (evalPoly p k)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="457" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
457
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<pre style="margin: 0;">+<span id="LC457" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right cancel" $ \k p -></span></span>
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458
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<pre style="margin: 0;">+<span id="LC458" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ composePoly (constPoly k) p == constPoly k</span></span>
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<td class="diff-line-num new new_line" data-linenumber="459" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
459
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<pre style="margin: 0;">+<span id="LC459" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "left identity" $ \p -></span></span>
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460
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<pre style="margin: 0;">+<span id="LC460" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ composePoly p x == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="461" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
461
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<pre style="margin: 0;">+<span id="LC461" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right identity" $ \p -></span></span>
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462
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<pre style="margin: 0;">+<span id="LC462" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ composePoly x p == p</span></span>
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463
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<pre style="margin: 0;">+<span id="LC463" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \(SmallPoly p) (SmallPoly q) -> </span></span>
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464
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<pre style="margin: 0;">+<span id="LC464" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDegree (composePoly p q)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="465" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
465
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<pre style="margin: 0;">+<span id="LC465" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ <= (1 + polyDegree p) * (1 + polyDegree q)</span></span>
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466
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<pre style="margin: 0;">+<span id="LC466" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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467
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<pre style="margin: 0;">+<span id="LC467" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "scalePoly"</span></span>
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468
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<pre style="margin: 0;">+<span id="LC468" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \s p x -></span></span>
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469
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<pre style="margin: 0;">+<span id="LC469" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (scalePoly s p) x == s * evalPoly p x</span></span>
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470
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<pre style="margin: 0;">+<span id="LC470" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \s p -> </span></span>
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471
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<pre style="margin: 0;">+<span id="LC471" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDegree (scalePoly s p) == if s == 0 then -1 else polyDegree p</span></span>
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472
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<pre style="margin: 0;">+<span id="LC472" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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473
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<pre style="margin: 0;">+<span id="LC473" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "multPoly"</span></span>
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474
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<pre style="margin: 0;">+<span id="LC474" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "left cancel" $ \p -> polyIsZero (multPoly zero p)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="475" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
475
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<pre style="margin: 0;">+<span id="LC475" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right cancel" $ \p -> polyIsZero (multPoly p zero)</span></span>
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476
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<pre style="margin: 0;">+<span id="LC476" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "left unit" $ \p -> multPoly one p == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="477" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
477
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<pre style="margin: 0;">+<span id="LC477" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right unit" $ \p -> multPoly p one == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="478" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
478
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<pre style="margin: 0;">+<span id="LC478" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "commutative" $ \p q -> multPoly p q == multPoly q p</span></span>
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479
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<pre style="margin: 0;">+<span id="LC479" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "associative" $ \p q r -></span></span>
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480
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<pre style="margin: 0;">+<span id="LC480" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ multPoly p (multPoly q r) == multPoly (multPoly p q) r</span></span>
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481
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<pre style="margin: 0;">+<span id="LC481" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "distributive" $ \p q r -></span></span>
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482
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<pre style="margin: 0;">+<span id="LC482" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ multPoly p (addPoly q r) == addPoly (multPoly p q) (multPoly p r)</span></span>
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483
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<pre style="margin: 0;">+<span id="LC483" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \p q x -></span></span>
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484
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<pre style="margin: 0;">+<span id="LC484" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly (multPoly p q) x ==</span></span>
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485
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<pre style="margin: 0;">+<span id="LC485" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPoly p x * evalPoly q x</span></span>
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486
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<pre style="margin: 0;">+<span id="LC486" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \p q -> </span></span>
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487
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<pre style="margin: 0;">+<span id="LC487" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ if polyIsZero p || polyIsZero q</span></span>
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488
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<pre style="margin: 0;">+<span id="LC488" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ then polyDegree (multPoly p q) == (-1)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="489" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
489
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<pre style="margin: 0;">+<span id="LC489" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ else polyDegree (multPoly p q) == polyDegree p + polyDegree q</span></span>
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490
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<pre style="margin: 0;">+<span id="LC490" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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491
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<pre style="margin: 0;">+<span id="LC491" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "powPoly"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="492" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
492
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<pre style="margin: 0;">+<span id="LC492" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "cancel" $ \p -> polyIsOne (powPoly p 0)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="493" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
493
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<pre style="margin: 0;">+<span id="LC493" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "unit" $ \p -> powPoly p 1 == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="494" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
494
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<pre style="margin: 0;">+<span id="LC494" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "multiply" $ \(SmallPoly p) (NonNegative a) (NonNegative b) -></span></span>
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495
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<pre style="margin: 0;">+<span id="LC495" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let a' = a `mod` 8; b' = b `mod` 8</span></span>
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496
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<pre style="margin: 0;">+<span id="LC496" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in multPoly (powPoly p a') (powPoly p b') == powPoly p (a' + b')</span></span>
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497
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<pre style="margin: 0;">+<span id="LC497" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "compose" $ \(SmallPoly p) (NonNegative a) (NonNegative b) -></span></span>
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498
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<pre style="margin: 0;">+<span id="LC498" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let a' = a `mod` 6; b' = b `mod` 6</span></span>
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499
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<pre style="margin: 0;">+<span id="LC499" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in powPoly (powPoly p b') a' == powPoly p (a' * b')</span></span>
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500
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<pre style="margin: 0;">+<span id="LC500" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \(SmallPoly p) (NonNegative n) -></span></span>
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501
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<pre style="margin: 0;">+<span id="LC501" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n' = n `mod` 16</span></span>
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502
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<pre style="margin: 0;">+<span id="LC502" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in powPoly p n' == foldl' multPoly one (replicate n' p)</span></span>
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503
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<pre style="margin: 0;">+<span id="LC503" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "degree" $ \p (NonNegative n) -></span></span>
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504
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<pre style="margin: 0;">+<span id="LC504" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let n' = n `mod` 16</span></span>
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505
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<pre style="margin: 0;">+<span id="LC505" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in polyDegree (powPoly p n') == max (-1) (n' * polyDegree p)</span></span>
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506
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<pre style="margin: 0;">+<span id="LC506" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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507
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<pre style="margin: 0;">+<span id="LC507" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "quotRemPoly"</span></span>
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508
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<pre style="margin: 0;">+<span id="LC508" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \a (SmallPoly b) -> </span></span>
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509
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<pre style="margin: 0;">+<span id="LC509" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (polyIsZero b) ==> case quotRemPoly a b of</span></span>
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510
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<pre style="margin: 0;">+<span id="LC510" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (q, r) -> polyDegree r < polyDegree b </span></span>
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511
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<pre style="margin: 0;">+<span id="LC511" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ && addPoly (multPoly q b) r == a</span></span>
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512
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<pre style="margin: 0;">+<span id="LC512" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="513" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
513
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<pre style="margin: 0;">+<span id="LC513" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "quotPoly"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="514" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
514
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<pre style="margin: 0;">+<span id="LC514" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \a b -> </span></span>
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<td class="diff-line-num new new_line" data-linenumber="515" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
515
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<pre style="margin: 0;">+<span id="LC515" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (polyIsZero b) ==> </span></span>
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<td class="diff-line-num new new_line" data-linenumber="516" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
516
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<pre style="margin: 0;">+<span id="LC516" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ quotPoly a b == fst (quotRemPoly a b)</span></span>
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517
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<pre style="margin: 0;">+<span id="LC517" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="518" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
518
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<pre style="margin: 0;">+<span id="LC518" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "remPoly"</span></span>
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519
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<pre style="margin: 0;">+<span id="LC519" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \a b -> </span></span>
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520
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<pre style="margin: 0;">+<span id="LC520" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (polyIsZero b) ==> </span></span>
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521
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<pre style="margin: 0;">+<span id="LC521" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ remPoly a b == snd (quotRemPoly a b)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="522" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
522
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<pre style="margin: 0;">+<span id="LC522" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="523" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
523
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<pre style="margin: 0;">+<span id="LC523" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalPolyDeriv"</span></span>
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<td class="diff-line-num new new_line" data-linenumber="524" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
524
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<pre style="margin: 0;">+<span id="LC524" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "zero" $ \t -> evalPolyDeriv zero t == (0,0)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="525" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
525
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<pre style="margin: 0;">+<span id="LC525" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "one" $ \t -> evalPolyDeriv one t == (1,0)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="526" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
526
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<pre style="margin: 0;">+<span id="LC526" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "constPoly" $ \t k -> evalPolyDeriv (constPoly k) t == (k,0)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="527" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
527
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<pre style="margin: 0;">+<span id="LC527" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "x" $ \t -> evalPolyDeriv x t == (t,1)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="528" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
528
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<pre style="margin: 0;">+<span id="LC528" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "chain rule" $ \p q x -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="529" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
529
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<pre style="margin: 0;">+<span id="LC529" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ snd (evalPolyDeriv (multPoly p q) x)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="530" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
530
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<pre style="margin: 0;">+<span id="LC530" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == snd (evalPolyDeriv p x) * evalPoly q x + snd (evalPolyDeriv q x) * evalPoly p x</span></span>
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<td class="diff-line-num new new_line" data-linenumber="531" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
531
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<pre style="margin: 0;">+<span id="LC531" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "sane" $ \p x -></span></span>
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<td class="diff-line-num new new_line" data-linenumber="532" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
532
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<pre style="margin: 0;">+<span id="LC532" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ evalPolyDeriv p x == (evalPoly p x, evalPoly (polyDeriv p) x)</span></span>
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533
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<pre style="margin: 0;">+<span id="LC533" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<td class="diff-line-num new new_line" data-linenumber="534" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
534
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<pre style="margin: 0;">+<span id="LC534" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalPolyDerivs"</span></span>
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535
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<pre style="margin: 0;">+<span id="LC535" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p x -></span></span>
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536
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<pre style="margin: 0;">+<span id="LC536" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ and $ zipWith (==) </span></span>
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537
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<pre style="margin: 0;">+<span id="LC537" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (evalPolyDerivs p x) </span></span>
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538
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<pre style="margin: 0;">+<span id="LC538" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [evalPoly p x | p <- iterate polyDeriv p]</span></span>
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539
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<pre style="margin: 0;">+<span id="LC539" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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540
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<pre style="margin: 0;">+<span id="LC540" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "contractPoly"</span></span>
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541
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<pre style="margin: 0;">+<span id="LC541" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p a -> </span></span>
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542
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<pre style="margin: 0;">+<span id="LC542" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case contractPoly p a of</span></span>
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543
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<pre style="margin: 0;">+<span id="LC543" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (q, r) -> addPoly (multPoly q (poly BE [1,-a])) (constPoly r) == p</span></span>
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544
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<pre style="margin: 0;">+<span id="LC544" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "root" $ \p a -></span></span>
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545
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<pre style="margin: 0;">+<span id="LC545" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ case contractPoly p a of</span></span>
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546
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<pre style="margin: 0;">+<span id="LC546" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (q, r) -> evalPoly (addPoly p (poly BE [-r])) a == 0</span></span>
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547
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<pre style="margin: 0;">+<span id="LC547" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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548
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<pre style="margin: 0;">+<span id="LC548" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "monicPoly"</span></span>
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549
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<pre style="margin: 0;">+<span id="LC549" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p -></span></span>
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550
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<pre style="margin: 0;">+<span id="LC550" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ if polyIsZero p </span></span>
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551
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<pre style="margin: 0;">+<span id="LC551" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ then polyIsZero (monicPoly p)</span></span>
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552
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<pre style="margin: 0;">+<span id="LC552" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ else head (polyCoeffs BE (monicPoly p)) == 1</span></span>
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553
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<pre style="margin: 0;">+<span id="LC553" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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554
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<pre style="margin: 0;">+<span id="LC554" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "gcdPoly"</span></span>
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555
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<pre style="margin: 0;">+<span id="LC555" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p q -></span></span>
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556
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<pre style="margin: 0;">+<span id="LC556" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (polyDegree p + polyDegree q <= 20) &&</span></span>
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557
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<pre style="margin: 0;">+<span id="LC557" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (all polyIsZero [p,q]) ==></span></span>
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558
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<pre style="margin: 0;">+<span id="LC558" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let g = gcdPoly p q</span></span>
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559
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<pre style="margin: 0;">+<span id="LC559" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in all polyIsZero [p `remPoly` g, q `remPoly` g]</span></span>
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560
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<pre style="margin: 0;">+<span id="LC560" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "monic" $ \p q -></span></span>
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561
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<pre style="margin: 0;">+<span id="LC561" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (polyDegree p + polyDegree q <= 20) &&</span></span>
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562
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<pre style="margin: 0;">+<span id="LC562" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (all polyIsZero [p,q]) ==></span></span>
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563
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<pre style="margin: 0;">+<span id="LC563" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ head (polyCoeffs BE (gcdPoly p q)) == 1</span></span>
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<td class="diff-line-num new new_line" data-linenumber="564" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
564
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<pre style="margin: 0;">+<span id="LC564" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "right cancel" $ \p -> gcdPoly p one == one</span></span>
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<td class="diff-line-num new new_line" data-linenumber="565" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
565
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<pre style="margin: 0;">+<span id="LC565" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "left cancel" $ \p -> gcdPoly one p == one</span></span>
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566
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<pre style="margin: 0;">+<span id="LC566" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "commutative" $ \p q -> </span></span>
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567
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<pre style="margin: 0;">+<span id="LC567" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (polyDegree p + polyDegree q <= 20) &&</span></span>
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568
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<pre style="margin: 0;">+<span id="LC568" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (all polyIsZero [p,q]) ==></span></span>
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569
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<pre style="margin: 0;">+<span id="LC569" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ gcdPoly p q == gcdPoly q p</span></span>
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570
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<pre style="margin: 0;">+<span id="LC570" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "associative" $ \p q r -> </span></span>
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571
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<pre style="margin: 0;">+<span id="LC571" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (polyDegree p + polyDegree q + polyDegree r <= 20) &&</span></span>
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572
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<pre style="margin: 0;">+<span id="LC572" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ not (any (all polyIsZero) [[p,q], [p,r], [q,r]]) ==></span></span>
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573
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<pre style="margin: 0;">+<span id="LC573" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ gcdPoly (gcdPoly p q) r == gcdPoly p (gcdPoly q r)</span></span>
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574
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<pre style="margin: 0;">+<span id="LC574" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "roots" $ \pScale (Ordered pRoots) qScale (Ordered qRoots) -></span></span>
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575
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<pre style="margin: 0;">+<span id="LC575" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (length pRoots + length qRoots <= 20) ==></span></span>
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576
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<pre style="margin: 0;">+<span id="LC576" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ let p = scalePoly pScale (lagrange pRoots)</span></span>
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577
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<pre style="margin: 0;">+<span id="LC577" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ q = scalePoly qScale (lagrange qRoots)</span></span>
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578
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<pre style="margin: 0;">+<span id="LC578" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ r = lagrange (intersect pRoots qRoots)</span></span>
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579
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<pre style="margin: 0;">+<span id="LC579" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ in not (null pRoots && null qRoots)</span></span>
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580
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<pre style="margin: 0;">+<span id="LC580" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ==> r == gcdPoly p q</span></span>
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581
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<pre style="margin: 0;">+<span id="LC581" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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582
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<pre style="margin: 0;">+<span id="LC582" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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583
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<pre style="margin: 0;">+<span id="LC583" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "polyDeriv"</span></span>
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584
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<pre style="margin: 0;">+<span id="LC584" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "zero" $ do</span></span>
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585
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<pre style="margin: 0;">+<span id="LC585" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ assert (polyDeriv zero == zero)</span></span>
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586
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<pre style="margin: 0;">+<span id="LC586" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testCase "one" $ do</span></span>
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587
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<pre style="margin: 0;">+<span id="LC587" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ assert (polyDeriv one == zero)</span></span>
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588
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<pre style="margin: 0;">+<span id="LC588" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "constPoly" $ \k -> </span></span>
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589
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<pre style="margin: 0;">+<span id="LC589" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDeriv (constPoly k) == zero</span></span>
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590
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<pre style="margin: 0;">+<span id="LC590" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testCase "x" $ do</span></span>
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591
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<pre style="margin: 0;">+<span id="LC591" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ assert (polyDeriv x == one)</span></span>
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592
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<pre style="margin: 0;">+<span id="LC592" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "chain rule" $ \p q -></span></span>
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593
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<pre style="margin: 0;">+<span id="LC593" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ (polyDegree p + polyDegree q <= 20) ==></span></span>
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594
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<pre style="margin: 0;">+<span id="LC594" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ polyDeriv (multPoly p q) == addPoly (multPoly p (polyDeriv q)) (multPoly q (polyDeriv p))</span></span>
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595
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<pre style="margin: 0;">+<span id="LC595" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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596
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<pre style="margin: 0;">+<span id="LC596" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "polyIntegral"</span></span>
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597
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<pre style="margin: 0;">+<span id="LC597" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \p -> polyDeriv (polyIntegral p) == p</span></span>
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<td class="diff-line-num new new_line" data-linenumber="598" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
598
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<pre style="margin: 0;">+<span id="LC598" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "constant factor" $ \p -> evalPoly (polyIntegral p) 0 == 0</span></span>
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599
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<pre style="margin: 0;">+<span id="LC599" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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600
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<pre style="margin: 0;">+<span id="LC600" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "separateRoots"</span></span>
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601
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<pre style="margin: 0;">+<span id="LC601" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" $ \(NonEmpty rts) -></span></span>
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602
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<pre style="margin: 0;">+<span id="LC602" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ length rts < 10 ==></span></span>
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603
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<pre style="margin: 0;">+<span id="LC603" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ separateRoots (lagrange rts) == map lagrange (sep rts)</span></span>
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604
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<pre style="margin: 0;">+<span id="LC604" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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605
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<pre style="margin: 0;">+<span id="LC605" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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606
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<pre style="margin: 0;">+<span id="LC606" class="line" lang="diff"><span class="gd" style="color: #000; background-color: #fdd;">--- /dev/null</span></span>
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<pre style="margin: 0;">+<span id="LC607" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+++ b/test/Tests/Hermite.hs</span></span>
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<pre style="margin: 0;">+<span id="LC608" class="line" lang="diff"><span class="gu" style="color: #800080; font-weight: 600;">@@ -0,0 +1,119 @@</span></span>
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609
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<pre style="margin: 0;">+<span id="LC609" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+{-# LANGUAGE ExtendedDefaultRules #-}</span></span>
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610
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<pre style="margin: 0;">+<span id="LC610" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+module Tests.Hermite (hermiteTests) where</span></span>
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611
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<pre style="margin: 0;">+<span id="LC611" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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612
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<pre style="margin: 0;">+<span id="LC612" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Data.VectorSpace</span></span>
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613
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<pre style="margin: 0;">+<span id="LC613" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial</span></span>
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<pre style="margin: 0;">+<span id="LC614" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Math.Polynomial.Hermite</span></span>
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<pre style="margin: 0;">+<span id="LC615" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework (testGroup)</span></span>
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<pre style="margin: 0;">+<span id="LC616" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.HUnit (testCase)</span></span>
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<pre style="margin: 0;">+<span id="LC617" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.Framework.Providers.QuickCheck2 (testProperty)</span></span>
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<pre style="margin: 0;">+<span id="LC618" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.HUnit</span></span>
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<pre style="margin: 0;">+<span id="LC619" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import Test.QuickCheck</span></span>
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<pre style="margin: 0;">+<span id="LC620" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+import TestUtils</span></span>
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<pre style="margin: 0;">+<span id="LC621" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC622" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+default (Integer, Rational)</span></span>
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<pre style="margin: 0;">+<span id="LC623" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC624" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+hermiteLimit = 500</span></span>
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<pre style="margin: 0;">+<span id="LC625" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC626" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+hermiteTests =</span></span>
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<pre style="margin: 0;">+<span id="LC627" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testGroup "probHermite" probHermite_tests</span></span>
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628
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<pre style="margin: 0;">+<span id="LC628" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "physHermite" physHermite_tests</span></span>
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629
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<pre style="margin: 0;">+<span id="LC629" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalProbHermite" evalProbHermite_tests</span></span>
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630
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<pre style="margin: 0;">+<span id="LC630" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalPhysHermite" evalPhysHermite_tests</span></span>
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<pre style="margin: 0;">+<span id="LC631" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalProbHermiteDeriv" evalProbHermiteDeriv_tests</span></span>
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<pre style="margin: 0;">+<span id="LC632" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testGroup "evalPhysHermiteDeriv" evalPhysHermiteDeriv_tests</span></span>
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<pre style="margin: 0;">+<span id="LC633" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC634" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC635" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+probHermite_tests =</span></span>
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<pre style="margin: 0;">+<span id="LC636" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "known values" case_probHermite_knownValues</span></span>
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<pre style="margin: 0;">+<span id="LC637" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "recurrence" prop_probHermite_recurrence </span></span>
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<pre style="margin: 0;">+<span id="LC638" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC639" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC640" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+probHermite_knownValues :: [(Int, Poly Integer)]</span></span>
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<pre style="margin: 0;">+<span id="LC641" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+probHermite_knownValues =</span></span>
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<pre style="margin: 0;">+<span id="LC642" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ ( 0, one)</span></span>
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<pre style="margin: 0;">+<span id="LC643" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 1, x)</span></span>
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<pre style="margin: 0;">+<span id="LC644" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 2, poly BE [1, 0, -1])</span></span>
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<pre style="margin: 0;">+<span id="LC645" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 3, poly BE [1, 0, -3, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC646" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 4, poly BE [1, 0, -6, 0, 3])</span></span>
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<pre style="margin: 0;">+<span id="LC647" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 5, poly BE [1, 0, -10, 0, 15, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC648" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 6, poly BE [1, 0, -15, 0, 45, 0, -15])</span></span>
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<pre style="margin: 0;">+<span id="LC649" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 7, poly BE [1, 0, -21, 0, 105, 0, -105, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC650" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 8, poly BE [1, 0, -28, 0, 210, 0, -420, 0, 105])</span></span>
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<pre style="margin: 0;">+<span id="LC651" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 9, poly BE [1, 0, -36, 0, 378, 0, -1260, 0, 945, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC652" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , (10, poly BE [1, 0, -45, 0, 630, 0, -3150, 0, 4725, 0, -945])</span></span>
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<pre style="margin: 0;">+<span id="LC653" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC654" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+case_probHermite_knownValues = sequence_</span></span>
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<pre style="margin: 0;">+<span id="LC655" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ assertEqual ("probHermite !! " ++ show n) (probHermite !! n) value</span></span>
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<pre style="margin: 0;">+<span id="LC656" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | (n, value) <- probHermite_knownValues</span></span>
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<pre style="margin: 0;">+<span id="LC657" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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658
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<pre style="margin: 0;">+<span id="LC658" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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659
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<pre style="margin: 0;">+<span id="LC659" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_probHermite_recurrence (Positive n)</span></span>
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<pre style="margin: 0;">+<span id="LC660" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = probHermite !! (n'+1)</span></span>
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661
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<pre style="margin: 0;">+<span id="LC661" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == multPoly x (probHermite !! n') ^-^ polyDeriv (probHermite !! n')</span></span>
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662
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<pre style="margin: 0;">+<span id="LC662" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span>
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<pre style="margin: 0;">+<span id="LC663" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC664" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+physHermite_tests =</span></span>
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<pre style="margin: 0;">+<span id="LC665" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testCase "known values" case_physHermite_knownValues</span></span>
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<pre style="margin: 0;">+<span id="LC666" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , testProperty "recurrence" prop_physHermite_recurrence </span></span>
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<pre style="margin: 0;">+<span id="LC667" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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<pre style="margin: 0;">+<span id="LC668" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC669" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+physHermite_knownValues :: [(Int, Poly Integer)]</span></span>
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<pre style="margin: 0;">+<span id="LC670" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+physHermite_knownValues =</span></span>
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<pre style="margin: 0;">+<span id="LC671" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ ( 0, one)</span></span>
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<pre style="margin: 0;">+<span id="LC672" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 1, poly BE [ 2, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC673" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 2, poly BE [ 4, 0, -2])</span></span>
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<pre style="margin: 0;">+<span id="LC674" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 3, poly BE [ 8, 0, -12, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC675" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 4, poly BE [ 16, 0, -48, 0, 12])</span></span>
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<pre style="margin: 0;">+<span id="LC676" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 5, poly BE [ 32, 0, -160, 0, 120, 0])</span></span>
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<pre style="margin: 0;">+<span id="LC677" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 6, poly BE [ 64, 0, -480, 0, 720, 0, -120])</span></span>
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678
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<pre style="margin: 0;">+<span id="LC678" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 7, poly BE [ 128, 0, -1344, 0, 3360, 0, -1680, 0])</span></span>
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679
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<pre style="margin: 0;">+<span id="LC679" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 8, poly BE [ 256, 0, -3584, 0, 13440, 0, -13440, 0, 1680])</span></span>
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680
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<pre style="margin: 0;">+<span id="LC680" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , ( 9, poly BE [ 512, 0, -9216, 0, 48384, 0, -80640, 0, 30240, 0])</span></span>
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681
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<pre style="margin: 0;">+<span id="LC681" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ , (10, poly BE [1024, 0, -23040, 0, 161280, 0, -403200, 0, 302400, 0, -30240])</span></span>
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682
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<pre style="margin: 0;">+<span id="LC682" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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683
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<pre style="margin: 0;">+<span id="LC683" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+case_physHermite_knownValues = sequence_</span></span>
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684
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<pre style="margin: 0;">+<span id="LC684" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ assertEqual ("physHermite !! " ++ show n) (physHermite !! n) value</span></span>
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685
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<pre style="margin: 0;">+<span id="LC685" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ | (n, value) <- physHermite_knownValues</span></span>
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686
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<pre style="margin: 0;">+<span id="LC686" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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687
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<pre style="margin: 0;">+<span id="LC687" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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688
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<pre style="margin: 0;">+<span id="LC688" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_physHermite_recurrence (Positive n)</span></span>
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689
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<pre style="margin: 0;">+<span id="LC689" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = physHermite !! (n'+1)</span></span>
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690
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<pre style="margin: 0;">+<span id="LC690" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == scalePoly 2 (multPoly x (physHermite !! n')) ^-^ polyDeriv (physHermite !! n')</span></span>
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691
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<pre style="margin: 0;">+<span id="LC691" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span>
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692
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<pre style="margin: 0;">+<span id="LC692" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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693
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<pre style="margin: 0;">+<span id="LC693" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalProbHermite_tests =</span></span>
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694
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<pre style="margin: 0;">+<span id="LC694" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalProbHermite_sane</span></span>
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695
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<pre style="margin: 0;">+<span id="LC695" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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696
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<pre style="margin: 0;">+<span id="LC696" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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697
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<pre style="margin: 0;">+<span id="LC697" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalProbHermite_sane n x</span></span>
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698
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<pre style="margin: 0;">+<span id="LC698" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = evalProbHermite n' x</span></span>
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699
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<pre style="margin: 0;">+<span id="LC699" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalPoly (fmap fromIntegral (probHermite !! n')) x</span></span>
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700
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<pre style="margin: 0;">+<span id="LC700" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span>
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701
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<pre style="margin: 0;">+<span id="LC701" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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702
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<pre style="margin: 0;">+<span id="LC702" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalPhysHermite_tests =</span></span>
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703
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<pre style="margin: 0;">+<span id="LC703" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalPhysHermite_sane</span></span>
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704
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<pre style="margin: 0;">+<span id="LC704" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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705
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<pre style="margin: 0;">+<span id="LC705" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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706
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<pre style="margin: 0;">+<span id="LC706" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalPhysHermite_sane n x</span></span>
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707
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<pre style="margin: 0;">+<span id="LC707" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = evalPhysHermite n' x</span></span>
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708
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<pre style="margin: 0;">+<span id="LC708" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalPoly (fmap fromIntegral (physHermite !! n')) x</span></span>
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709
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<pre style="margin: 0;">+<span id="LC709" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span>
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710
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<pre style="margin: 0;">+<span id="LC710" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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711
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<pre style="margin: 0;">+<span id="LC711" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalProbHermiteDeriv_tests =</span></span>
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712
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<pre style="margin: 0;">+<span id="LC712" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalProbHermiteDeriv_sane</span></span>
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713
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<pre style="margin: 0;">+<span id="LC713" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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714
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<pre style="margin: 0;">+<span id="LC714" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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715
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<pre style="margin: 0;">+<span id="LC715" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalProbHermiteDeriv_sane n x</span></span>
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716
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<pre style="margin: 0;">+<span id="LC716" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = evalProbHermiteDeriv n' x</span></span>
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717
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<pre style="margin: 0;">+<span id="LC717" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalPolyDeriv (fmap fromIntegral (probHermite !! n')) x</span></span>
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718
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<pre style="margin: 0;">+<span id="LC718" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span>
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719
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<pre style="margin: 0;">+<span id="LC719" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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720
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<pre style="margin: 0;">+<span id="LC720" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+evalPhysHermiteDeriv_tests =</span></span>
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721
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<pre style="margin: 0;">+<span id="LC721" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ [ testProperty "sane" prop_evalPhysHermiteDeriv_sane</span></span>
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722
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<pre style="margin: 0;">+<span id="LC722" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ ]</span></span>
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723
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<pre style="margin: 0;">+<span id="LC723" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+</span></span>
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<pre style="margin: 0;">+<span id="LC724" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+prop_evalPhysHermiteDeriv_sane n x</span></span>
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725
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<pre style="margin: 0;">+<span id="LC725" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ = evalPhysHermiteDeriv n' x</span></span>
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726
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<pre style="margin: 0;">+<span id="LC726" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ == evalPolyDeriv (fmap fromIntegral (physHermite !! n')) x</span></span>
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727
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<pre style="margin: 0;">+<span id="LC727" class="line" lang="diff"><span class="gi" style="color: #000; background-color: #dfd;">+ where n' = n `mod` hermiteLimit</span></span></pre>
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<a href="https://salsa.debian.org/haskell-team/DHG_packages/commit/db12a9461ed86772e71ef282a5d7ad694c973320#a633f3baf8b065f9e5fe520968bdb989558bd840"><strong>p/haskell-polynomial/debian/patches/series</strong></a>
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1
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<pre style="margin: 0;"> <span id="LC1" class="line" lang="plaintext">newer-hunit</span>
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2
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="plaintext">missing-tests</span></pre>
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