o *ήc—wã @s‚dZddlZddlmZedƒZesdZejdd…dkrdZddlmZdd l m Z m Z m Z m Z mZmZmZmZmZdd lmZdd lmZdd lmZdd lmZddlmZddlmZ ddl!m"Z"m#Z#m$Z$m%Z%ddl&m'Z'm(Z)ddl*m+Z+ddl,m-Z-ddl.m/Z/ddl0m1Z1ddl2m3Z3e-dƒ\ Z4Z5Z6Z7Z8Z9Z:Z;Zdd„Z?dd„Z@dd„ZAd d!„ZBd"d#„ZCd$d%„ZDd&d'„ZEdS)(zõ Tests for Rubi Algebraic 1.2 rules. Parsed from Maple syntax All tests: http://www.apmaths.uwo.ca/~arich/IntegrationProblems/MapleSyntaxFiles/MapleSyntaxFiles.html Note: Some tests are commented since they depend rules other than Algebraic1.2. éN)Ú import_moduleÚmatchpyTé)éé)Úrubi_integrate) ÚlogÚsqrtÚexpÚcosÚsinÚtanÚsecÚcscÚcot)Úatanh)Úasinh)Úacosh)Úatan)Úasin)Úacos)Ú EllipticEÚ EllipticFÚ hypergeomÚ rubi_test)ÚIÚpi)ÚS)Úsymbols)Ú exp_polar)Úhyper)Úsimplifyza b c d e f m n x ucCs¾tdƒ tdƒttdƒtdƒ tdƒtgtttdƒttgtttdƒttgttttdƒttdƒttdƒtgttdƒttdƒtdƒtdƒttdƒgttdƒtdƒttdƒtdƒtdƒttdƒtdƒgttdƒtdƒttdƒtdƒtdƒttdƒtdƒgtdƒttdƒtdƒttdƒtdƒtdƒttdƒtdƒgttdƒtttttdƒtdƒtd ƒtttd ƒtdƒtdƒtttdƒgttttdƒttdƒttdƒttdƒ tttdƒttdƒttttƒgg }|D]C}t|d |dƒ}t|ƒdkrKt ||d|dd d d sIt ||d|d d d d sIJ‚qt ||d|dd d d s[J‚qdS) NrréédéeéééérT©ÚexpandÚ_diff) rÚxÚPiÚaÚmÚbrrÚlenr©ÚtestÚiÚr©r6úU/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rubi_tests/tests/test_1_2.pyÚtest_1%s$.*.>>F^`ö <€$ûr8cCs  ttttttdƒtttttƒgttdƒtttttdƒttdƒtttdƒtdƒtdƒttdƒttdƒttdƒtdƒtdƒttdƒttdƒttdƒtdƒtdƒtttdƒttdƒtdƒtdƒttdƒtttdƒttttƒttdƒgtdƒttttdƒttdƒtdƒ ttttgtdƒtttttdƒttdƒtdƒtdƒtttttdƒtdƒttdƒtttttƒttdƒttttƒttdƒgtdƒtdƒtdƒtttdƒtdƒtdƒttdƒtƒgtdƒttdƒttttdƒttƒttdƒttƒgttdƒttttƒttdƒtdƒ tdƒttdƒttttdƒtdƒttdƒtdƒtdƒttdƒttttdƒtdƒttdƒtdƒtdƒtttttdƒtdƒttdƒtdƒtdƒttttdƒtdƒttdƒgttttdƒtdƒttdƒtdƒtdƒttttdƒtdƒtgttdƒttttƒttdƒtd ƒ tdƒttdƒttttdƒtdƒttdƒtd ƒtdƒttdƒttttdƒtdƒttdƒtd ƒtdƒtttttdƒtdƒttdƒtdƒtdƒttttdƒtdƒttdƒtdƒttdƒttttƒttdƒgtdƒttttƒttdƒtdƒttttƒtgtdƒtttttdƒtdƒttdƒtdƒ tttttƒttƒƒttdƒtdƒtdƒtttttƒgtdƒttdƒt tttdƒtdƒttdƒtdƒ tttt ttƒttƒƒttdƒtdƒtdƒ tttt ttƒtdƒtt ttƒttdƒtgttdƒttttdƒtdƒttdƒtdƒ tdƒttdƒttttdƒtdƒttdƒtdƒtdƒttdƒttttdƒtdƒttdƒtdƒtd ƒtttttd ƒtdƒttdƒtdƒtd ƒttttd ƒtdƒttdƒgttdƒttttdƒtdƒttdƒtdƒtdƒttdƒttttdƒtdƒttdƒtdƒtdƒtttttd ƒtdƒttdƒtdƒtd ƒttttd ƒtdƒttdƒgttdƒttttdƒtdƒttdƒtdƒtdƒttdƒttttdƒtdƒttdƒtdƒtdƒtttttdƒtdƒttdƒtdƒtd ƒttttd ƒtdƒttdƒgttdƒt tttdƒtdƒttdƒtdƒtdƒttdƒt tttdƒtdƒttdƒtdƒtdƒttdƒt tttdƒtdƒttdƒtdƒtd ƒtt tttd ƒtdƒttdƒtdƒtd ƒt tttd ƒtdƒttdƒgg}|D]C}t|d|dƒ}t |ƒdkr¼t ||d|ddddsºt ||d|ddddsºJ‚qŠt ||d|ddddsÌJ‚qŠdS)Nrr%r(r"rrr&é r'é é é é rTr)) r.r0r,rrr ÚarctanhÚarctanrr1rr2r6r6r7Útest_2:s:*þ<žB>þ"RþR:„Æþ.ææþ6ð<€$ûr@cCs°tttttttdƒtttdƒttdƒttttdƒttdƒtgttdƒtdƒtttttdƒtdƒtdƒtttdƒtdƒtdƒtdƒtttdƒtdƒgttdƒtdƒtttttdƒtdƒ tdƒtttdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒttdƒtdƒtttƒttƒttƒƒttdƒtdƒtdƒttdƒttƒttdƒgttdƒtdƒtttttdƒtdƒtdƒttdƒtdƒttdƒttdƒtdƒtttƒttƒttƒƒttdƒtdƒtdƒtttƒttdƒgttdƒtdƒt ttttdƒtdƒtdƒtttdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒttdƒtdƒtttƒttƒttƒƒttdƒtdƒtdƒttdƒttƒttdƒgttdƒtdƒttttƒttdƒtdƒ td ƒttdƒtttƒttƒttttƒƒttdƒtdƒtdƒtd ƒttdƒttdƒtdƒttttƒttdƒtdƒtd ƒtttdƒtdƒttttƒttdƒtdƒttdƒtdƒttttƒtdƒtd ƒttdƒttƒttttƒttdƒgttdƒtdƒttttƒttdƒtdƒtd ƒttdƒtttƒttƒttttƒƒttdƒtdƒtdƒtd ƒtttdƒtdƒttttƒttdƒtdƒttdƒtdƒttttƒtdƒtd ƒttdƒttƒttttƒttdƒgttdƒtdƒttttƒttdƒtdƒ td ƒttdƒtttƒttƒttttƒƒttdƒtdƒtdƒtd ƒtttdƒtdƒttttƒttdƒtdƒtdƒttdƒtdƒttttƒttdƒtd ƒttdƒttƒttttƒttdƒgttƒttttƒttdƒt tttƒttƒttttƒƒttdƒtdƒttƒttttƒtgttdƒtdƒtttttdƒtdƒtdƒtttdƒtdƒtdƒtd ƒtttd ƒtdƒgttdƒtdƒtttttdƒtdƒtdƒtttdƒtdƒtdƒtdƒtttdƒtdƒgttdƒtdƒtttttdƒtdƒ tdƒtttdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒtdƒttdƒtdƒtttdƒtdƒttdƒtdƒttdƒtdƒƒttd ƒtdƒtdƒtdƒttdƒtdƒttttƒttd ƒtdƒttdƒtdƒtttdƒtdƒtdƒttdƒtdƒttdƒtdƒttdƒtdƒttdƒƒƒttdƒƒttd ƒtdƒgttdƒtdƒtttttdƒtdƒ tttdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒtdƒttdƒtdƒtttdƒtdƒttdƒtdƒttdƒtdƒƒttdƒtdƒtdƒtdƒttdƒtdƒttttƒttdƒtdƒttdƒtdƒtttdƒtdƒtdƒttdƒtdƒttdƒtdƒttdƒtdƒttdƒƒƒttdƒƒttdƒtdƒgtdƒttdƒtdƒtdƒtttdƒtdƒtdƒttdƒtdƒtdƒtdƒtdƒtdƒttdƒttdƒtdƒtdƒtdƒtdƒƒtdƒtdƒtdƒtdƒttdƒttdƒtdƒtdƒtdƒtdƒƒgttttttdƒttdƒttdƒttdƒttdƒttdƒttttdƒttdƒtttdƒttdƒttdƒtgg}|D]C}t |d|dƒ}t |ƒdkrDt ||d|ddddsBt ||d|ddddsBJ‚qt ||d|ddddsTJ‚qdS)Nrr"r%r&r9rr(ré@é`ér'r:rTr)) r,r/r.r0rr?r r>rrr1rr2r6r6r7Útest_3Vs:Zvøºøþ~þ0þ>xvvþâþÚþžñ<€$ûrDcCsòttttttdƒttdƒttdƒtttdƒtdƒtgtdƒtgt ttƒttdƒtdƒtgttttdƒtdƒtƒttdƒttdƒtttdƒtdƒtdƒtgtdƒtgtdƒ tdƒtƒtdƒtttdƒƒgttttttttdƒttdƒtttttttdƒtt gtdƒtgt ttƒtdƒttdƒttttgttdƒ tttttttdƒtttdƒtttttttgtdƒtgt ttƒtttttgtt ttttdƒtdƒttdƒtdƒtdƒtt ttttdƒtdƒtt gtt ttttdƒtdƒttdƒtdƒtdƒtt ttttdƒtdƒtt gttttdƒtt tt ttdƒttdƒttdƒtt tdƒgtttttttttdƒttdƒtdƒ tdƒtttdƒttttdƒttdƒtdƒttdƒttttdƒtgttttttdƒtttttdƒtdƒ ttdƒttdƒttttdƒttttdƒttdƒtdƒttdƒttttdƒttdƒttdƒttdƒt tttƒtgtdƒttttdƒtttttttdƒtdƒ tdƒtttttttdƒtdƒt tttƒttdƒttgtdƒttdƒtdƒtdƒttdƒtdƒttdƒtdƒtdƒtdƒttdƒtdƒtdƒttdƒtdƒtdƒtd ƒtdƒttdƒtdƒtdƒttdƒtdƒtdƒtd ƒtdƒttdƒtdƒtdƒttdƒtdƒgtdƒttdƒtdƒtdƒttdƒtdƒttdƒtdƒtdƒt tƒtdƒtd ƒtdƒttdƒtdƒttdƒtƒtdƒtdƒtdƒttdƒtdƒttdƒtƒtdƒtdƒttdƒtƒttdƒtƒgg }|D]C}t |d |dƒ}t|ƒdkråt||d|dd d dsãt||d|dd d dsãJ‚q³t||d|dd d dsõJ‚q³dS)Nrr"rr%r&r(r'r9é#éirrTr))r,r/r.r0rrr ÚnÚcÚdrr>Úarcsinrr1rr2r6r6r7Útest_4ps*zŽ€ffRœä”þþô<€$ûrKcCs  tdƒtttdƒtdƒttdƒttƒttdƒtdƒtdƒtttƒttdƒtdƒtdƒtttdƒtdƒttdƒttƒttdƒtdƒttdƒttƒttdƒttƒtgtdƒttdƒtdƒtdƒttdƒtdƒttdƒttƒttdƒtƒttdƒtƒgtdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒttdƒtƒ ttdƒtƒgttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒtttttttdƒtdƒttttdƒtdƒtdƒtdƒtttttdƒtdƒttttdƒtdƒtdƒtdƒttdƒtdƒttdƒtdƒtttƒttttƒttƒttttƒƒtdƒtd ƒttdƒttdƒtttttƒttttƒgtdƒttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒtttttttdƒtdƒttttdƒtdƒtdƒtdƒtttdƒttdƒttttƒttttƒgtdƒttdƒtdƒtdƒ ttdƒtdƒttdƒtdƒ tdƒttdƒtdƒtƒtdƒtdƒtdƒttdƒtdƒttdƒ tƒtdƒtdƒttdƒtƒttdƒ tƒgtdƒttttƒtt ttttƒttdƒtdƒt ttƒttttƒtt ttttƒƒtttƒgtdƒtt tttd ƒtdƒtt tttdƒtdƒttdƒtdƒ tdƒt tt tttdƒtdƒttdƒtt tttdƒtdƒgttttdƒtttttt ttdƒtdƒ ttdƒttttttdƒt tttdƒt tdƒtttttttdƒt tttdƒtdƒt ttttttdƒt tttdƒtdƒt gttttdƒtttttdƒtdƒtdƒttttttttdƒttdƒtdƒtdƒtttttdƒttdƒgttttttttdƒttttdƒtdƒttttttdƒtdƒtdƒttttdƒgttttdƒtttttdƒttttttdƒtttdƒtdƒtdƒtttttdƒttttdƒttdƒtdƒtdƒtttttdƒttttdƒttdƒtdƒtdƒttttttttdƒttdƒtdƒtdƒttttdƒttttttdƒt tttƒttdƒgtttttttdƒttdƒtdƒtdƒttttdƒttttttttdƒgttttdƒttttdƒtdƒttdƒtdƒ tdƒtttttdƒttttdƒtdƒttdƒtdƒttttttdƒttttdƒtdƒttdƒtd ƒtd ƒttdƒtttttdƒttttd ƒtdƒttdƒtd ƒtd ƒttdƒtttttdƒttttd ƒtdƒttdƒtd ƒtdƒttdƒttttttttdƒtdƒttdƒtdƒtdƒttdƒttttdƒtdƒttdƒgttttdƒtdƒttttdƒttdƒt t ttƒttttƒtttttƒƒttdƒtdƒtttttƒttttƒttttgg}|D]C}t |d|dƒ}t|ƒdkr¼t||d|ddddsºt||d|ddddsºJ‚qŠt||d|ddddsÌJ‚qŠdS)Nr"rrr(r%rCrr'ér&ér9r;r=r<rTr))rr.r,r rJrHr?r0rIr>rrGrrr1rr2r6r6r7Útest_5‡s8Þfhþ˜æÚ‚°þšzþ€nþþ(´ñ<€$ûrNc!Cstdƒtttdƒtdƒttdƒttƒttdƒtdƒtdƒtttƒttdƒtdƒtdƒtttdƒtdƒttdƒttƒttdƒtdƒttdƒttƒttdƒttƒtgtdƒttdƒtdƒtdƒttdƒtdƒttdƒttƒttdƒtƒttdƒtƒgtdƒtdƒttdƒtdƒtdƒttdƒtdƒttdƒttdƒtƒ ttdƒtƒgttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒtttttttdƒtdƒttttdƒtdƒtdƒtdƒtttttdƒtdƒttttdƒtdƒtdƒtdƒttdƒtdƒttdƒtdƒtttƒttttƒttƒttttƒƒtdƒtd ƒttdƒttdƒtttttƒttttƒgtdƒttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒtttttttdƒtdƒttttdƒtdƒtdƒtdƒtttdƒttdƒttttƒttttƒgtdƒttdƒtdƒtdƒ ttdƒtdƒttdƒtdƒ tdƒttdƒtdƒtƒtdƒtdƒtdƒttdƒtdƒttdƒ tƒtdƒtdƒttdƒtƒttdƒ tƒgtdƒttttƒtt ttttƒttdƒtdƒt ttƒttttƒtt ttttƒƒtttƒgtdƒtt tttd ƒtdƒtt tttdƒtdƒttdƒtdƒ tdƒt tt tttdƒtdƒttdƒtt tttdƒtdƒgttttdƒtttttt ttdƒtdƒ ttdƒttttttdƒt tttdƒt tdƒtttttttdƒt tttdƒtdƒt ttttttdƒt tttdƒtdƒt gttttdƒtttttdƒtdƒtdƒttttttttdƒttdƒtdƒtdƒtttttdƒttdƒgttttttttdƒttttdƒtdƒttttttdƒtdƒtdƒttttdƒgttttdƒtttttdƒttttttdƒtttdƒtdƒtdƒtttttdƒttttdƒttdƒtdƒtdƒtttttdƒttttdƒttdƒtdƒtdƒttttttttdƒttdƒtdƒtdƒttttdƒttttttdƒt 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ttƒttttƒttƒttttƒƒttdƒtdƒttƒttttƒttttƒtgtdƒttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒttttƒttttttttdƒtdƒtdƒtdƒtttttƒtttttdƒttttƒgtttt ttttdƒtdƒt tdƒtdƒt ttdƒttttdƒt ttdƒtdƒt gtdƒt gt tttttttƒtttttdƒt gttttttdƒtttdƒttdƒtttdƒtdƒtttdƒtdƒtdƒtttdƒtdƒtdƒtttdƒgttttdƒtttdƒttttdƒtdƒ tdƒtttdƒtttttt tƒgg}|D]C}t|d|dƒ}t|ƒdk r´t||d|dddd s²t||d|dddd s²J‚ q‚t||d|dddd sÄJ‚ q‚dS)Nr"rrr(r%rCrr'rLr&rMr9r;r=r<r:rTr))rr.r,r rJrHr?r0rIr>rrGrr/rrr1rr2r6r6r7Útest_6¢sTÞfhþ˜æÚ‚°þšzþ€nþþ(´þ¾þþDÂþÀÄÞšpç<€$ûrOcCs ttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒttttttttdƒtdƒttttdƒtdƒtttdƒtdƒttttdƒtdƒttttdƒtdƒttdƒtdƒtttttdƒttttƒttdƒtdƒttdƒtdƒtdƒtdƒtttttdƒttdƒ ttdƒtdƒttttdƒtdƒttdƒtdƒttttdƒtdƒƒttdƒtdƒttdƒtdƒtdƒtdƒtttttdƒttdƒttdƒƒtdƒttdƒtdƒttttdƒtdƒttdƒtdƒttttdƒtdƒttdƒƒƒttdƒtdƒttdƒtdƒttdƒƒgttttdƒtdƒttttdƒtdƒttdƒtdƒ tdƒttttttttdƒtdƒttttdƒtdƒttdƒtdƒtdƒttttdƒtdƒttttdƒtdƒttdƒtdƒtttttdƒttttƒttdƒtdƒttd ƒtdƒtdƒtdƒtttttdƒttdƒ ttdƒtdƒttttdƒtdƒttdƒtdƒttttdƒtdƒƒttdƒtdƒttd ƒtdƒtdƒtdƒtttttdƒttdƒttdƒƒtdƒttdƒtdƒttttdƒtdƒttdƒtdƒttttdƒtdƒttdƒƒƒttdƒtdƒttd 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