o *╬оcР0у@s<ddlmZddlmZmZmZmZddlmZddl m Z mZddlm Z mZmZmZmZddlmZddlmZddlmZmZmZmZmZmZdd lmZdd lm Z ddl!m"Z"ddl#m$Z$dd l%m&Z&edГ\Z'Z(Z)Z*edГZ+ddДZ,ddДZ-ddДZ.ddДZ/ddДZ0ddДZ1ddДZ2ddДZ3d d!ДZ4d"d#ДZ5d$S)%щ)┌diff)┌E┌I┌Rational┌pi)┌S)┌Symbol┌symbols)┌Abs┌ conjugate┌im┌re┌sign)┌log)┌sqrt)┌acos┌asin┌cos┌sin┌atan2┌atan)┌ integrate)┌Matrix)┌trigsimp)┌ Quaternion)┌raiseszw:z┌phic s8tttttГ}||tdtdtdtdtГksJВtаtdГdtdГdtdГdfttddГб}|tt j t j t j t j ГksEJВttt Гtt Гdgtt Гtt ГdggdвgГ}ttа|бГ}|ttdГttt ГdГdddtddtt ГГttt ГГdГksЛJВtdddНЙttЗfd d ДГdS)Nщщrйrrщr ┌ncFй┌commutativecstttИtГSйN)r┌w┌x┌zййr!r(·K/tmp/pip-target-vg8gfxp4/lib/python/sympy/algebras/tests/test_quaternion.py┌ sz.test_quaternion_construction..)rr%r&┌yr'┌from_axis_anglerrrr┌Halfrrrrr┌from_rotation_matrixrrr┌ ValueError)┌q┌q2┌M┌q3r(r)r*┌test_quaternion_constructions*$ 0Nr5cCsddtdtdГdtdГdddffdtdtdГddtdГddffdtdtdГdddtdГdffdtdfdtdfdtd fd tddtdГdtdГdtdГfftdГdtdГdtdГdftddtjtjtjtjffg }|D]\}}}tа||бt|ОksЛJВqzdS) N)йr rrr)r rrrr6rr)rr rr)rr rrйrrr rйrrrr йr r r r r)rrrr.rr-)┌ test_data┌axis┌angle┌expectedr(r(r*┌test_quaternion_axis_angle#s$$$(>ў r>cCsдtаdtdГб}|jttdГdГksJВ|jtdГttdГdГdks(JВ|jtdГttdГdГdks;JВ|j dtdГttdГdГdksPJВdS)N)r rrщrщщr) rr-r┌ar┌brr┌c┌d)┌resultr(r(r*┌)test_quaternion_axis_angle_simplification5s &&.rGc sАtdddН}tdddН}tdddНЙtttttГЙ|Иttt|Гtt|ГttГks.JВd Иtd ttttГks=JВtИttd tttГksLJВ|Иtt|tttГks[JВt t ЗЗfd dДГt t ЗЗfddДГt t ЗЗfd dДГИtttttГksЙJВtddtddtdddtddН}td dddГ}|ddttddtddtdddtГks┬JВ|ddttddddГks╙JВ|ddttddtddtddtddtdddtddtГkРsJВ|ddttddddГkРsJВtd dddГ}tddddГ}|||kРs,JВ|||kРs5JВ|||kРs>JВdS)NrBTй┌complexrCй┌realrDFr"r csИИSr$r(r(йrDr1r(r*r+Gєz7test_quaternion_complex_real_addition..csИИSr$r(r(rLr(r*r+HrMcsИИSr$r(r(rLr(r*r+IrMrr?rщrrAщй┌ real_fieldiЎ щщ&щ√ )r rr%r&r,r'r rrrr0)rBrC┌q1r2┌q0r(rLr*┌%test_quaternion_complex_real_addition<s2* *:"H $rWcCsМttdГddtdГГабttdГабddtdГабГksJВtdtdГdddtdГГабtdtdГабdddtdГабГksDJВdS)Nrrrr )rr┌evalfr(r(r(r*┌test_quaternion_evalf]sJВtdГЙttЗЗfddДГtdddНЙttЗЗfddДГtddddГабdkРsjJВtttttГабtkРsxJВtddddГабtddddГkРsЛJВtttttГабtdtttГkРsЮJВИа бtddtdГddtdГddtdГdГkРs╛JВИа ба dбtddddГkРs╧JВИа бабdkРs┌JВ|а бtdtttdtdtdГtttdtdtdГtttdtdtdГГkРsJВИа!бdkРsJВИа!бd kРs$JВtddddГа!бdkРs2JВtddd!dГа!бdkРs@JВttdd!dГа!бdkРsNJВИа"бt#tdГГkРs[JВ|а"бt$ttdtdtdГtГkРssJВtа%Иtddd"dГбdkРsГJВtа%Иtdd d#d$ГбdkРsУJВtа%Иtddd%d&ГбdkРsгJВtа%ИtddddГбdkРs│JВtа%Иttdd"dГбdkРs├JВtа%ИtddddГбd kРs╙JВtа%ИtttttГбdkРsуJВttЗЗfd'dДГtа&tddd%d&Гtddd"dГtddddГбdkРsJВtа&tddddГtddd"dГtddddГбdkРs#JВtа&tdddd"Гtddd"d"ГtddddГбd kРs>JВtа&tddddГtddtd"Гtdd"ddГбdkРsYJВttЗЗfd(dДГtddddГа'tdddd"ГбdkРswJВtddddГа'tdddd"Гбd kРsЛJВtddddГа'ttttd"ГбdkРsЯJВttЗЗfd)dДГtddddГа(tdd ddГбdkРs╜JВtddddГа(tdddd"Гбd kРs╤JВtddddГа(ttttd"ГбdkРsхJВttЗЗfd*dДГИа)бtddtd+Гddtd+Гddtd+ГdГkРsJВtddd,dГа)бtddd,dГkРs"JВtddd,dГа*бttd-ГГkРs4JВtddddГа*бttdГГkРsFJВИа+бdkРsOJВИа+бd kРsXJВttdddГа+бdkРsfJВdS).Nr rrr?rщ csИабSr$)┌inverser(йrVr(r*r+lrMz+test_quaternion_functions..щ■ i∙ щсщЦчр┐csИdS)Nr`r(r()rUr(r*r+rrMщщщ<щZщxr9rNrA┌ncєИИSr$r(r(йrfrUr(r*r+МrMT)┌integercrgr$r(r(rhr(r*r+ОrMщщщ7rOFщ щщ¤ щ№ щщcstаИИбSr$)r┌arc_coplanarr(йrVrUr(r*r+лscstаИtddddГИбS)Nrr?rnrO)r┌vector_coplanarr(rtr(r*r+▒scє ИаИбSr$)┌parallelr(rtr(r*r+╢є crvr$)┌ orthogonalr(rtr(r*r+╗rxifщ щz),rr%r&r,r'r┌normr┌ normalizer[┌powrr0r┌NotImplemented┌ TypeError┌exprrr┌_lnrr┌pow_cos_sinrr┌rotate_pointr┌Oner┌scalar_part┌vector_partr;┌is_purer<rrrsrurwry┌index_vector┌mensor┌is_zero_quaternionйr1r()rfrVrUr*┌test_quaternion_functionsbs░ 0>@PN44¤ ¤ &&&¤ (, *&&@"p0 6666((((((@&$$ rНc CshtddddГ}|абdtdГddtdГddtdГdfdttdГdГfks.JВ|абttddГtddГtd dГgtddГtd dГtddГgtddГtddГtddГggГks_JВ|аdбttddГtddГtd dГtdd ГgtddГtd dГtddГtjgtddГtddГtddГtdd Гgtjtjtjtj ggГksдJВt dddН}tt|dГddt|dГГ}t |абГtt|Гt|Гdgt|Гt|ГdggdвgГks┘JВ|абddt|dГtt|dГГfdtt|dГГfks·JВt |аdбГtt|Гt|Гdt|Гt|Гdgt|Гt|Гdt|Гt|ГdggdвgdвgГkРs2JВdS)Nr rrr?rarbr]щrRrZr@r9rN┌thetaTrJrrr7r8)r┌ to_axis_anglerr┌to_rotation_matrixrrr┌ZerorЕr rrrr )rUrПr2r(r(r*┌test_quaternion_conversions╟s@■ ¤"■,"¤¤& $$№rУcCsbtttdГttdГddГ}t|абГtgdвdttГttГgdttГttГggГks/JВdS)a3 There was a sign mistake in the definition, of the rotation matrix. This tests that particular sign mistake. See issue 1593 for reference. See wikipedia https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix for the correct definition rrr6N)rrrrrrСrrМr(r(r*┌ test_quaternion_rotation_iss1593ъs ¤rФcCsbtddtddtdddtdd Н}td dddГ}td d d tГ}tаtdГtjбdks0JВtаtdГ|бtddtdd tdddtГksMJВ|аdбtddddГks[JВ|а|бtdtddtdddttdГkswJВ|а|б||ksВJВtdddН}tt|Гt |ГddГ}ttdddНО}||||ksеJВ||||ksпJВdS)Nrr?rrNrrArOFrPr rqrrщщщ rnrmrTrzr'TrHzq:4rJ) rrr,┌_generic_mulrrЕ┌mulr r r)rUr2r4r'┌z_quatr1r(r(r*┌test_quaternion_multiplication·s*:8rЫcs└tddddГЙttЗfddДГtddddГ}|аб\}}tаd||fбtjd dtd Гd fks3JВtddddГ}tdГdtdГdtdГdf}dtd}||f|абks^JВdS)NrcsdИS)Nr r(r(r\r(r*r+rMz"test_issue_16318..r rrr?r9rNrArZ) rrr0rРrДrrЕrr)r1r;r<r(r\r*┌test_issue_16318 s,(rЬN)6┌sympy.core.functionr┌sympy.core.numbersrrrr┌sympy.core.singletonr┌sympy.core.symbolrr ┌$sympy.functions.elementary.complexesr rrr r┌&sympy.functions.elementary.exponentialr┌(sympy.functions.elementary.miscellaneousr┌(sympy.functions.elementary.trigonometricrrrrrr┌sympy.integrals.integralsr┌sympy.matrices.denser┌sympy.simplify.trigsimpr┌sympy.algebras.quaternionr┌sympy.testing.pytestrr%r&r,r'rr5r>rGrWrYrНrУrФrЫrЬr(r(r(r*┌s2 !e#