a Эм єz.test_quaternion_construction..)rr"r#┌yr$┌from_axis_anglerrrr┌HalfrrrrrZfrom_rotation_matrixrrr┌ ValueError)┌q┌q2┌M┌q3r%r&r'┌test_quaternion_constructions*$ 0Pr2cCsddtdtdГdtdГdddffdtdtdГddtdГddffdtdtdГdddtdГdffdtdfdtdfdtd fd tddtdГdtdГdtdГfftdГdtdГdtdГdftddtjtjtjtjffg }|D]"\}}}tа||бt|ОksЇJВqЇdS) N)йrrrr)rrrrr3rr)rrrr)rrrrйrrrrйrrrrйrrrrr)rrrr,rr+)Z test_data┌axis┌angle┌expectedr%r%r'┌test_quaternion_axis_angle#s$$$(>ўr:cCsдtаdtdГб}|jttdГdГks*JВ|jtdГttdГdГdksPJВ|jtdГttdГdГdksvJВ|j dtdГttdГdГdksаJВdS)N)rrrщrщщr) rr+r┌ar┌brr┌c┌d)┌resultr%r%r'┌)test_quaternion_axis_angle_simplification5s &&rCc sЖtdddН}tdddН}tdddНЙtttttГЙ|Иttt|Гtt|ГttГks\JВd Иtd ttttГkszJВtИttd tttГksШJВ|Иtt|tttГks╢JВt t ЗЗfd dДГt t ЗЗfddДГt t ЗЗfd dДГИtttttГkРsJВtddtddtdddtddН}td dddГ}|ddttddtddtdddtГkРsИJВ|ddttddddГkРsмJВ|ddttddtddtddtddtdddtddtГkРsJВ|ddttddddГkРs0JВtd dddГ}tddddГ}|||kРs^JВ|||kРspJВ|||kРsВJВdS)Nr>Tй┌complexr?й┌realr@Fr rcsИИSr!r%r%йr@r.r%r'r(Gr)z7test_quaternion_complex_real_addition..csИИSr!r%r%rHr%r'r(Hr)csИИSr!r%r%rHr%r'r(Ir)rr;rщrr=щйZ real_fieldiЎ щщ&щ√ )r rr"r#r*r$r rrrr-)r>r?┌q1r/┌q0r%rHr'┌%test_quaternion_complex_real_addition<s2*"*<$H $rQcCsМttdГddtdГГабttdГабddtdГабГks.щ■ i∙ щсщЦчр┐csИdS)NrYr%r%)rOr%r'r(rr)щщщ<щZщxr6rIr=┌ncsИИSr!r%r%йr_rOr%r'r(Мr)T)┌integercsИИSr!r%r%r`r%r'r(Оr))rr"r#r*r$rZnormr┌ normalizerT┌powrr-r┌NotImplemented┌ TypeError┌exprrrZ_lnrrZpow_cos_sinrr┌rotate_pointr┌Onerйr.r%)r_rPrOr'┌test_quaternion_functionsbsZ 0>@RP64¤ ¤ &&&¤ (, *rjc CsntddddГ}|абdtdГddtdГddtdГdfdttdГdГfks\JВ|абttddГtddГtd dГgtddГtd dГtddГgtddГtddГtddГggГks╛JВ|аdбttddГtddГtd dГtdd ГgtddГtd dГtddГtjgtddГtddГtddГtdd Гgtjtjtjtj ggГkРsJJВt dddН}tt|dГddt|dГГ}t |абГtt|Гt|Гdgt|Гt|ГdggdвgГkРs╢JВ|абddt|dГtt|dГГfdtt|dГГfkРs·JВt |аdбГtt|Гt|Гdt|Гt|Гdgt|Гt|Гdt|Гt|ГdggdвgdвgГkРsjJВdS)Nrrrr;rZr[rVщrLrSr<r6rI┌thetaTrFrrr4r5)r┌ to_axis_anglerr┌to_rotation_matrixrrrZZerorhr rrrr )rOrlr/r%r%r'┌test_quaternion_conversionsСs@■¤ "■,"¤¤& $$№rocCsbtttdГttdГddГ}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 rrr3N)rrrrrrnrrir%r%r'┌ test_quaternion_rotation_iss1593┤s ¤rpcCs\tddtddtdddtdd Н}td dddГ}td d d tГ}tаdd бdksZJВtаd|бtddtdd tdddtГksРJВ|аdбtddddГksмJВ|а|бtdtddtdddttdГksфJВ|а|б||ks·JВtdddН}tt|Гt|ГddГ}ttdddНО}||||kРsBJВ||||kРsXJВdS)Nrr;rrIrr=rJFrKrщщщщщ щщ rNщ r$TrDzq:4rF)rrr*Z_generic_mul┌mulr r r)rOr/r1r$Zz_quatr.r%r%r'┌test_quaternion_multiplication─s*68rzcs└tddddГЙttЗfddДГtddddГ}|аб\}}tаd||fбtjd dtd Гd fksfJВtddddГ}tdГdtdГdtdГdf}dtd}||f|абks╝JВdS)NrcsdИS)Nrr%r%rUr%r'r(┌r)z"test_issue_16318..rrrr;r6rIr=rS) rrr-rmrgrrhrr)r.r7r8r%rUr'┌test_issue_16318╫s,(r{N)4Zsympy.core.functionrZsympy.core.numbersrrrrZsympy.core.singletonrZsympy.core.symbolrr Z$sympy.functions.elementary.complexesr rrr rZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrZ(sympy.functions.elementary.trigonometricrrrrZsympy.integrals.integralsrZsympy.matrices.denserZsympy.simplify.trigsimprZsympy.algebras.quaternionrZsympy.testing.pytestrr"r#r*r$rr2r:rCrQrRrjrorprzr{r%r%r%r'┌s0!/#