a Ямd:d;ДZ?dd?ДZAd@dAДZBdBdCДZCdDdEДZDdFdGДZEdHdIДZFdJdKДZGdLdMДZHdNdOДZIdPdQДZJdRdSДZKdTdUДZLdVdWДZMdXdYДZNdZd[ДZOd\d]ДZPd^d_ДZQd`daДZRdbdcДZSdddeДZTdfdgДZUdhdiДZVdjdkДZWdldmДZXdndoДZYdpdqДZZdrdsДZ[dtduДZ\dvdwДZ]dxdyДZ^dzd{ДZ_d|d}ДZ`d~dДZadАdБДZbdВdГДZcdДdЕДZddЖdЗДZedИdЙДZfdКdЛДZgdМS)НzTest sparse polynomials. щ)┌reduce)┌add┌mul)┌ring┌xring┌sring┌PolyRing┌PolyElement)┌field┌ FracField)┌ZZ┌QQ┌RR┌FF┌EX)┌lex┌grlex)┌GeneratorsError┌ExactQuotientFailed┌MultivariatePolynomialError┌CoercionFailed)┌raises)┌Symbol┌symbols)┌oo┌pi)┌exp)┌sqrtcCsttdГ\}}}}ttdttГjГdks,JВtt|ttГjГdksFJВttdttГjГdks`JВtt|||fttГjГdksАJВttdttГjГdksЪJВttgttГjГdks┤JВttdd ДГtd t|tГj t|ksрJВtd dtГj t|ks·JВtd tdttГtГj t|kРsJВttd d ДГtdГ}td ttГj tkРsLJВtd t|Гj tkРsdJВtd tdГj tkРs|JВtdttГ}tdttГ}tdttГ}|j|jdkРs╢JВ|j|jdkРs╠JВ|j|jkРs▐JВ|j|jkРsЁJВ|j|jkРsJВ|j|jkРsJВdS)NZxyzt·x,y,zщщ)┌x┌y┌z┌rcSstdttГSйNrйrrrйr'r'·l/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/polys/tests/test_rings.py┌єz(test_PolyRing___init__..r!zZZ[t]┌tcSstdtdttГtГS)Nr!r&r'r'r'r(r)$r*r·x,y) ┌mapr┌lenrrr┌gensrr┌domain┌orderr!r")r!r"r#r+Z_lexZR1ZR2ZR3r'r'r(┌test_PolyRing___init__s2 $r2cCs"tdtГ\}}}}t|ГsJВdSйNrйrr ┌hashй┌Rr!r"r#r'r'r(┌test_PolyRing___hash__6sr8cCsJtdtГdtdtГdks JВtdtГdtdtГdus@JВtdtГdtdtГdks`JВtdtГdtdtГdusАJВtdtГdtdtГdksаJВtdtГdtdtГdus└JВtdtГdtdtГdksрJВtdtГdtdtГduРsJВtdtГdtdtГdkРs$JВtdtГdtdtГduРsFJВdS)Nrrr,)rr rr'r'r'r(┌test_PolyRing___eq__:s ""r9c CstdtГ\}}}}|аdб|dГks(JВ|аd|||бd|||ksRJВ|dd||d|d|dd|d}|аdggdgdgggd вggб|ks░JВ|аddddddd Ьб|ks╨JВ|аgdвб|ksцJВtdtГ\}|аd gб|dГkРsJВdS)Nrщщrщщщr )r<r=r>)йr;rrйr r rйr rrйrrr;йrrr йrrr))r?r )r@r;)rAr)rBr<)rCr=)rDr>r$)r'r:)rr Zring_new)r7r!r"r#┌fr'r'r(┌test_PolyRing_ring_newJs*4* rFcsZtdtГ\ЙЙЙ}ИаИбtdttГks,JВИаИбtdttГksFJВИа|бtdttГks`JВИаdбtdttГkszJВИаdбаdбtdttГksЪJВИаdбаdбаdбtks╕JВИаdбtdttГks╥JВИаdбtdttГksьJВИаdбаdбtd ttГkРsJВИаdбаdбаdбtkРs.JВttЗfd dДГttЗЗЗfddДГdS) Nr·y,zzx,zr,rr#r r;r!cs ИаdбSйNrй┌dropr'йr7r'r(r)jr*z$test_PolyRing_drop..csИаИбаИбSйNrIr'йr7r!r"r'r(r)kr*)rrrJrrr┌ ValueErrorйr#r'rMr(┌test_PolyRing_dropYs " rPcCs~tdtГ\}}}}|ddЕtdttГks.JВ|ddЕtdttГksJJВ|ddЕtdttГksfJВ|ddЕtkszJВdS)Nrrr rGr;r#r)rrrrr6r'r'r(┌test_PolyRing___getitem__ms rQcCs|tdttГ}|jdusJВ|jdus(JВtdttГ}|jdusBJВ|jdusPJВtdttГ}|jdusjJВ|jdusxJВdS)Nr!TFrr$)rr rZ is_univariateZis_multivariaterKr'r'r(┌test_PolyRing_is_usrRcs|tdtГ\}ЙЗfddДtdГDГ}|а|бtt|ГkrPdИddksVnJВtdtГ\}|аgdвбd ksxJВdS) Nr!cs g|]}Иdd|dСqSйr;rr'й┌.0┌iйr!r'r(┌ Зr*z%test_PolyRing_add..r<r;щr$)r;r=r:щ)rr┌rangerrйr7┌Fr'rWr(┌test_PolyRing_addЕs 2r^csЬtdtГ\}ЙЗfddДtdГDГ}|а|бtt|ГkrpИddИddИdd Иd dksvnJВtdtГ\}|аgd вбdksШJВdS)Nr!cs g|]}Иdd|dСqSrSr'rTrWr'r(rXСr*z%test_PolyRing_mul..r<щrYr>щ╬iшr;i▒r$)r;rr=щ)rrr[rrr\r'rWr(┌test_PolyRing_mulПs RrbcCsаtdГ\}}}}tdttГ}t|d|d|Г||jd|jd|jfksVJВtdttГ}t|d||dГ||jd|j|jdfksЬJВt|d||dgГ||jd|j|jdgfks╥JВtdttГ}td|tГ}t|d||d|d||||Г||jd|j |jd|j d|jfkРsHJВtdttГ}td|tГ}t|||d|d|d|||Г||j|j |jd|j d|jdfkРs╛JВt dttГ}td|tГ}t|d|||d|d|||Г||jd|j|j |j d|jdfkРs4JВtdГtdГ}t|ddН\}}|jtа tdГtdГбkРsvJВ|jdkРsЖJВ||jа|бkРsЬJВdS) N·x,y,z,trr;rr+T)┌ extensionr')rrrrrr!r"r#r r+rrr0┌algebraic_fieldr/Z from_sympy)r!r"r#r+r7┌Rt┌r┌ar'r'r(┌ test_sringЩs(::6^^^"ricCs*tdtГ\}}}}t|||Гs&JВdSr3r4r6r'r'r(┌test_PolyElement___hash__╡srjcCstdttГ\}}}||d||dkdks2JВ||d||d||kdksZJВd||d||kdkszJВd||||d||kdksвJВ||||dkdks╛JВd||||kdks┌JВ||||dkdksЎJВd||||kdkРsJВ||||dkdkРs2JВd||||kdkРsPJВ||d||dkdkРsrJВ||d||d||kdkРsЬJВd||d||kdkРs╛JВd||||d||kdkРsшJВ||||dkdkРsJВd||||kdkРs$JВ||||dkdkРsBJВd||||kdkРs`JВ|jtddГkРrВ|jkРsИnJВ|jdkРrд|jkРsкnJВtdtГ\}}td|Г\}}}|d |||d kdkРsъJВ|d |||d kdkРsJВdS)Nr,r=r>FTrr r+rr<)rrrZoner )r7r!r"rfr+r'r'r(┌test_PolyElement___eq__╣s2 ( ("*"*(""rkcCs╘tdtГ\}}}|dГ|kr:|dkr:|dks@nJВ|dГ|krj|dkrj|dkspnJВ|d|dkrЪ|krЪ|dГksаnJВ|d|dkr╩|kr╩|dГks╨nJВdS)Nr,r r;r)rrrMr'r'r(┌test_PolyElement__lt_le_gt_ge__▐s 000rlcCsNtdtГ\}}}}||d|}|аб}||ks6JВd|d<||ksJJВdS)Nrrr:йr r r )rr┌copy)r7r!r"r#rE┌gr'r'r(┌test_PolyElement_copyчsrpcs(tdtГ\}}}}d|d||||d|ddЙ|j\Й}}dИd|И||d|dd}И|ksВJВИаб|ksТJВtdГ\Й}}dИd|И||d|dd}И|ks╪JВИаИ||б|ksюJВttЗЗfddДГtdtГ\}|dГабdkРs$JВdS) Nrrr;r:r cs ИаИбSrL)┌as_exprr'й┌XrEr'r(r)r*z*test_PolyElement_as_expr..r$)rrrrqrrN)r7r!r"r#┌Y┌Zror'rrr(┌test_PolyElement_as_exprёs,,,rvcs■tdГ\Й}}tИ||ftГ\Й}}}Иаdб}|dkrDt|ИjГsHJВИаИб}||krft|ИjГsjJВИаИ||б}||||krШt|ИjГsЬJВИаИ||И|Иб}|||||||krтt|ИjГsцJВИаИd||Иd|ddб}||d|||d|ddkРrHt|ИjГРsLJВttdГgГ\}}|аtdГб}||dkРrИt||jГРsМJВtt ЗЗfddДГtt ЗЗfd dДГtt ЗЗfd dДГtdtГ\ЙИаdб}|dkРrЎt|ИjГРs·JВdS)Nrr rr;r:rcsИаdИбS)Nr й┌ from_exprr'йr7r!r'r(r)r*z,test_PolyElement_from_expr..csИаdИбSйNr;rwr'ryr'r(r)r*csИаdИtdГбS)Nr:r;)rxrr'ryr'r(r)r*r$) rrrrx┌ isinstance┌dtyperrrrN)r"r#rsrtrurErgr]r'ryr(┌test_PolyElement_from_exprs* ,*< r}cCsЎtdtГ\}}}}|dГабtus(JВ|dГабdksJВ|dГабdkРsTJВdSr~)rrZtail_degreerr6r'r'r(┌test_PolyElement_tail_degreeHs8$$(((0((0((0rАcCsrtdtГ\}}}}|dГабtttfks2JВ|dГабdksFJВ|d||d|dабdksnJВdS)Nrrr rDr;r)rr r;)rr┌degreesrr6r'r'r(┌test_PolyElement_degreesks rВcCsrtdtГ\}}}}|dГабtttfks2JВ|dГабdksFJВ|d||d|dабdksnJВdS)Nrrr rDr;rr?)rrZtail_degreesrr6r'r'r(┌test_PolyElement_tail_degreesrs rГcsNtdttГ\}ЙЙЙdИdИИИИdИddЙИаdбdksRJВttЗfddДГИаИбd ksvJВИаИбd ksИJВИаИбd ksЪJВИаИdИбdks┤JВИаИИИбd ks╬JВИаИdбdksфJВttЗЗЗfddДГttЗЗЗЗfddДГttЗЗfd dДГtdtГ\}|dГаdбdkРsJJВdS)Nrrr;r:щr cs ИаdбSrHй┌coeffr'йrEr'r(r)~r*z(test_PolyElement_coeff..rщ csИаdИdИбS)Nrr;rЕr'йrEr!r"r'r(r)Иr*csИаИИИбSrLrЕr'йrEr!r"r#r'r(r)Йr*csИаdИdбS)Nr:rrЕr')rEr#r'r(r)Кr*r$)rrrrЖrrNrKr'rКr(┌test_PolyElement_coeffys,rЛcCsztdttГ\}}}|dГjtdГks(JВtddГ|jtddГksFJВtddГ||tddГ|jtddГksvJВdSйNr,rr r;r<)rr rZLCrMr'r'r(┌test_PolyElement_LCПsrНcCsjtdttГ\}}}|dГjdks$JВtddГ|jdks.rЪcCsАtdtГ\}}}}|dd|dd|ddаб}|gdвksJJВtdttГ\}}}||dd|d|d}|аб|аtбkrо|аd бkrоd dgks┤nJВ|аtб|аdбkr╪dd gks▐nJВtdttГ\}}}||dd|d|d}|аб|аtбkРrH|аdбkРrHdd gkРsNnJВ|аtб|аd бkРrvd dgkРs|nJВdS) Nrr;rr<r=)r?rЦrЧr,r:rrSrШr)rr ┌monomsrrr)r7r!r"r#rЫrEr'r'r(┌test_PolyElement_monoms┼s( 8* >rЬcCsФtdtГ\}}}}|dd|dd|ddаб}|tddГtddГtddГgks^JВtdttГ\}}}||dd|d|d}|аб|аtбkr┬|аd бkr┬ddgks╚nJВ|аtб|аd бkrьddgksЄnJВtdttГ\}}}||dd|d|d}|аб|аtбkРr\|аd бkРr\ddgkРsbnJВ|аtб|аd бkРrКddgkРsРnJВdS)Nrr;rr<r=r r,r:rr)rr ┌coeffsrrr)r7r!r"r#rЭrEr'r'r(┌test_PolyElement_coeffs╓s($ 8* >rЮcs╪tdtГ\}ЙtdtГ\}Й}td|Г\}Й}}tИd|ГdddЬksNJВtИИГtИИГkrxdИdЬks~nJВtИИ|ГtИ|ИГkr░dИdЬks╢nJВtИИ||ГtИ||ИГkrЄddИd Ьks°nJВtИИИГtИИИГkРr0d ИdikРs6nJВtИИИ|ГtИ|ИИГkРrtdИdЬkРsznJВtИИИ||ГtИ||ИИГkРr┬ddИdЬkРs╚nJВttЗЗfd dДГttЗЗfddДГttЗЗfddДГttЗЗfddДГtdtГ\}Й}td|Г\}Й}}tИИГtИИГkРrhdИdЬkРsnnJВtdtГ\}Й}}tttГИ||ГtИ||ttГГkРr╬tdГttГdЬkРs╘nJВdS)Nr+·u,vrrr йrAйrr rйrArDйr@rDйr@rCrDrAйr@rAйr@rCrAcsИИSrLr'r'йr+r!r'r(r)Ўr*z*test_PolyElement___add__..csИИSrLr'r'rзr'r(r)ўr*csИИSrLr'r'йr+┌ur'r(r)°r*csИИSrLr'r'rиr'r(r)∙r*йrmrDйrr┌dictr┌ TypeErrorr rrйrf┌Ruv┌v┌Rxyzr"r#┌Fuvr'йr+rйr!r(┌test_PolyElement___add__чs&08B>DN4r┤cs№tdtГ\}ЙtdtГ\}Й}td|Г\}Й}}tИd|ГdddЬksNJВtИИГtИИГkr|dИdЬksВnJВtИИ|ГtИ|ИГkr╕dИd Ьks╛nJВtИИ||ГtИ||ИГkРrddИd ЬkРsnJВtИИИГtИИИГkРrDdИdikРsJnJВtИИИ|ГtИ|ИИГkРrМdИdЬkРsТnJВtИИИ||ГtИ||ИИГkРr▐ddИd ЬkРsфnJВttЗЗfddДГttЗЗfddДГttЗЗfddДГttЗЗfddДГtdtГ\}Й}td|Г\}Й}}tИИГtИИГkРrИdИdЬkРsОnJВtdtГ\}Й}}tttГИ||ГtИ||ttГГkРrЄtdГttГdЬkРs°nJВdS)Nr+rЯrrr щ¤ rаrвrгrдrArеrжcsИИSrLr'r'rзr'r(r)r*z*test_PolyElement___sub__..csИИSrLr'r'rзr'r(r)r*csИИSrLr'r'rиr'r(r)r*csИИSrLr'r'rиr'r(r)r*rкrлrоr'r│r(┌test_PolyElement___sub__s&4.csИИИSrLr'r'r╖r'r(r):r*csИИИSrLr'r'йr+rйr#r'r(r);r*csИИИSrLr'r'r╕r'r(r)<r*rmrл)rfrпr░r▒r"r▓r')r+rйr!r#r(┌test_PolyElement___mul__!s4.DDHHPPPPPPPPV2r╣c s╘tdtГ\}Й}}dИdddИddks6JВdИdddИdksVJВИddаИбИkspJВИdИаИбИdksОJВИddИИИdksоJВИdИИИdks╩JВИdddИИdИddksЎJВИddаdИбdkРsJВИdИИdИdИаИdбkРrPИkРsVnJВtdtГ\}Й}}tИdd|dd|ddабГdkРsЮJВtdtГ\}Й}}tИdd|dd|ddабГdkРsцJВtd tГ\}Йtd tГ\}Й}td|Г\}Й}}tИdИИИГИddЬkРs>JВttЗЗfdd ДГttЗЗfdd ДГttЗЗfdd ДГttЗЗfdd ДГttЗЗfdd ДГtdtГ\}ЙИddИd|dГЙЙtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtdtГ\}Й}И|dИd|dГЙЙtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfdd ДГtt ЗЗfd d ДГtt ЗЗfd!d ДГtdtГ\}ЙИdddИdЙЙ|dГИdd}}Иа ИбtИИГkРrz||fkРsАnJВИаИбИИkРrв|kРsиnJВИаИбИИkРr╩|kРs╨nJВtt ЗЗfd"d ДГdИdИdИddИddИdЙЙ|dГИ}}Иа ИбtИИГkРrP||fkРsVnJВИаИбИИkРrx|kРs~nJВИаИбИИkРrа|kРsжnJВtt ЗЗfd#d ДГdИddИddИddИdИddИdЙЙdИdd$Иd%Иd}}Иа ИбtИИГkРrJ||fkРsPnJВИаИбИИkРrr|kРsxnJВИаИбИИkРrЪ|kРsаnJВtt ЗЗfd&d ДГdИddИddИddИdИИddИdd'ЙЙdИd$d(ИddИdd)Иd*}}Иа ИбtИИГkРr\||fkРsbnJВИаИбИИkРrД|kРsКnJВИаИбИИkРrм|kРs▓nJВtt ЗЗfd+d ДГtdtГ\}ЙИdddИdЙЙИdd|dГ}}Иа ИбtИИГkРr,||fkРs2nJВИаИбИИkРrT|kРsZnJВИаИбИИkРr||kРsВnJВtt ЗЗfd,d ДГdИdИdИddИddИdЙЙtddГИtd-d.Гtd/d.ГИtd0d.Г}}Иа ИбtИИГkР r&||fkР s,nJВИаИбИИkР rN|kР sTnJВИаИбИИkР rv|kР s|nJВtt ЗЗfd1d ДГtdtГ\}Й}Иd|dИ|ЙЙИ||dГ}}Иа ИбtИИГkР rЇ||fkР s·nJВИаИбИИkР r|kР s"nJВИаИбИИkР rD|kР sJnJВИаИб|kР s^JВИd|dИ|ЙЙИ|d|d}}Иа ИбtИИГkР r╢||fkР s╝nJВИаИбИИkР r▐|kР sфnJВИаИбИИkРr|kРsnJВtt ЗЗfd2d ДГИd|dИ|ЙЙИ|d|d}}Иа ИбtИИГkРr|||fkРsВnJВИаИбИИkРrд|kРsкnJВИаИбИИkРr╠|kРs╥nJВtt ЗЗfd3d ДГИd|ddИd|ЙЙ|dГИ}}Иа ИбtИИГkРr>||fkРsDnJВИаИбИИkРrf|kРslnJВИаИбИИkРrО|kРsФnJВtt ЗЗfd4d ДГtdtГ\}Й}Иd|dИ|ЙЙИ||dГ}}Иа ИбtИИГkР r||fkР snJВИаИбИИkР r4|kР s:nJВИаИбИИkР r\|kР sbnJВИаИб|kР svJВИd|dИ|ЙЙИ|d|d}}Иа ИбtИИГkР r╬||fkР s╘nJВИаИбИИkР rЎ|kР s№nJВИаИбИИkРr|kРs$nJВtt ЗЗfd5d ДГИd|dИ|ЙЙИ|d|d}}Иа ИбtИИГkРrФ||fkРsЪnJВИаИбИИkРr╝|kРs┬nJВИаИбИИkРrф|kРsъnJВtt ЗЗfd6d ДГИd|ddИd|ЙЙИd|dd|d}}Иа ИбtИИГkРrf||fkРslnJВИаИбИИkРrО|kРsФnJВИаИбИИkРr╢|kРs╝nJВtt ЗЗfd7d ДГdS)8Nrr;r<rr rИrr=r+rЯrвcsИИdИИSrzr'r')rйr!r'r(r)cr*z.test_PolyElement___truediv__..csИИSrLr'r'rзr'r(r)er*csИИSrLr'r'rзr'r(r)fr*csИИSrLr'r'rиr'r(r)gr*csИИSrLr'r'rиr'r(r)hr*r!cs ИаИбSrLй┌divr'йrEror'r(r)mr*cs tИИГSrLй┌divmodr'r╝r'r(r)nr*cs ИаИбSrLй┌remr'r╝r'r(r)or*csИИSrLr'r'r╝r'r(r)pr*cs ИаИбSrLй┌quor'r╝r'r(r)qr*csИИSrLr'r'r╝r'r(r)rr*cs ИаИбSrLй┌exquor'r╝r'r(r)sr*r,cs ИаИбSrLr║r'r╝r'r(r)xr*cs tИИГSrLr╜r'r╝r'r(r)yr*cs ИаИбSrLr┐r'r╝r'r(r)zr*csИИSrLr'r'r╝r'r(r){r*cs ИаИбSrLr┴r'r╝r'r(r)|r*csИИSrLr'r'r╝r'r(r)}r*cs ИаИбSrLr├r'r╝r'r(r)~r*cs ИаИбSrLr├r'r╝r'r(r)Иr*cs ИаИбSrLr├r'r╝r'r(r)Рr*r>щcs ИаИбSrLr├r'r╝r'r(r)Шr*щ щщ,щ6cs ИаИбSrLr├r'r╝r'r(r)аr*cs ИаИбSrLr├r'r╝r'r(r)кr*rZщщ4щocs ИаИбSrLr├r'r╝r'r(r)▓r*cs ИаИбSrLr├r'r╝r'r(r)─r*cs ИаИбSrLr├r'r╝r'r(r)╠r*cs ИаИбSrLr├r'r╝r'r(r)╘r*cs ИаИбSrLr├r'r╝r'r(r)цr*cs ИаИбSrLr├r'r╝r'r(r)юr*cs ИаИбSrLr├r'r╝r'r(r)Ўr*)rrr┬r.rЩr rмrrн┌ZeroDivisionErrorr╗r╛r└rr─) r7r"r#rfrпr░r▒┌qrgr')rEror+rйr!r(┌test_PolyElement___truediv__Gs$ , @66(.((6.((F".((N2.((.((62.((.((.((.((".((.((.((.((".((r╧cs░tdttГ\}}d|dЙИddks,JВИdИks.rИr<щr╞r_щ$r╔щщщ`щ╪щQr=щ щЁi╨i8i*щєrr>r+i@╘ i, щ1lM┐lА3uЯrZlL]▓Йl@LVщ lAьecl╟FИ l`ФVi░Ы Ii┴ЎW)rrrrrNZ_pow_generic┌_pow_multinomial)r7r!r"r#ror+r'rЗr(┌test_PolyElement___pow__°s<HTfr(Ш:" ■ ■■r▌c Cs<tdttГ\}}|dd|dd}|d}|dd|d}d}|а|gб|g|fksbJВtdttГ\}}|dd|d}|а|d Гgб|gd fksдJВtdttГ\}}|dd|d}|а|dГgбtd dГ|d|d gd fks№JВtdttГ\}}}d|d|d||d|d|d }|а|dГgбd|d|||d||dgd fkРsВJВ|аd|gбd|d|d gd|d fkРs║JВ|d }|d }|а|gбd g|fkРsцJВ||dd }||d |d g}|dg}d}|а|б||fkРs.JВ|d|||d|d}||d |dd g}||d g}||d }|а|б||fkРsЦJВ|dd ||d g}|d |g}d|d }|а|б||fkРs▐JВtdtГ\}|dГа|dГбdkРsJВtdtГ\}|dГа|dГбtddГd fkРs8JВdS)Nr!rr╨r;щ*r╞r╥щЕ r rr,r<r_rИr$)rr)rrrr╗r ) r7r!rEror╬rgr"┌G┌Qr'r'r(┌test_PolyElement_divsJ40D8 rтcCs|tdttГ\}}|dd|dd}|d}d}|а|gб|а|gбdkr\|ksbnJВtdttГ\}}}d |d|d||d |d|d }|а|dГgб|а|dГgбdkr╘dks┌nJВ|аd|gб|аd|gбdkРrd |d kРsnJВ|d}|d}|а|gб|а|gбdkРrX|kРs^nJВ||dd}||d|dg}d}|а|б|а|бdkРrо|kРs┤nJВ|d|||d|d}||d|ddg}||d}|а|б|а|бdkРr |kРs&nJВ|dd||dg}d|d}|а|б|а|бdkРrr|kРsxnJВdS)Nr!rr╨r;r▐r▀r r,r<r_r)rrrr└r╗)r7r!rErorgr"rрr'r'r(┌test_PolyElement_remPs..06B2. .rуcCstdtГ\}}d|dа|dd|ddбdd||dd|dgfksXJВtdtГ\}}}|dГа|dГбdddgfksКJВ|dГа|dГбdddgfksмJВ|dГа|dГбdddgfks╬JВ|dГаd|бddd|gfksЇJВd|аd|бdd|d|gfkРs JВ|dГаd|dбd dd|gfkРsLJВd|dаd|dбd d|d|gfkРsАJВ|d|d|d|d}|d|d |d|d}|а|бd|d|d||d||d ||dgfkРsJВdS)Nr!r;r<r )r;r,rrР)r r;r)r;r )rr┌deflateйr7r!r"rEror'r'r(┌test_PolyElement_deflatevsJ"""&,,4 rцc sюtdtГ\}}}|dГабtdГdfks,JВ|dГабtdГdfksHJВ|tddГГабdksbJВ|tddГГабdks|JВd|d|абdd|d|fksиJВ|dtddГ|абdd|d|fks┌JВtdttГ\}}}tdttГ\Й}}|tdd Г|dtd dГ|dtd dГ|dtddГ|dtddГ|dtddГ|dtddГ|tddГ|dtddГ|dtddГ|dtd dГ|dtd!d"Г|dtd#d"Г|dtd$dГ|dtd%dГ|td&dГg}d'|d(|dd)|dd*|dd+|dd,|dd-|dd.|d/d|dd0|dd|dd1|dd2|dd3|dd4|dd5|d6g}Зfd7d8Д|DГ|kРsъJВdS)9Nr,r r:r)rr:r;zx,tl∙╩O{С]БKХ_╔$э-щ\╖WхK▄.j/%=udLhрL`l:P╖$пG╠ЬвNДA3ЬV▀CДЁcД8RNe]Ж┌lйHНBSW▄~b]"zZДMю} зEю|u└"╒┐K╔2lhБ^%==2■pDu.Шq┤~Д@|`С:*w ╠hr>l┘[_Х+Jъ[╝kэPОuф=\L=кI┼GS{,Ё▓c.\) olP=Kzzd№aЙъ$\0ci}=$?&°@#uTn0ШQ r=lCN║VO&ilo?еuTvBпp5║yН\ $lй$╓aP╤-NCRlHi)Sbx|5eS6O--:ЛQRb V.rП?1lЦWr<lMГ[S¤╡ hl┘є<▌M╧6╛>ЗPР|oPo╘Dug═el╨[дWGfNQNB┴3N╓oCBxcBR'х.Cml├.wSKП-нGуб+~96nzLwGD╔═0I эBг,Iu!Ш|чJ┌=y┬9╢-l@╣VєT╫ry![t╘ пRdl°CHjЄ\LмLЗf:'l0┼%ТH8[J▌/@)\LMё3B\_>■mxwr)l╫$ф><JkЁtGl│+o▀g╞Kрz╖╔eXBOЖНRвFlД`%C!+[OЗ;RY.▓{└;й░gW!▌o^@*▀>r_l`(Уsўx┤]Yli╜4&фm:l└,8 y'X^l▒е:╒W]lk ╠B`l ─Oк<тpф{l;7>ЬrмI░l``6]jЧ_{l@хo;b╔|?lTї=Ц-╔l╩lЛFORl RtJ)1~M▓CйMgK▌bиqл∙c├L╢eлl┴r¤a2╚U!JП'B\KW4Du+┴%B:оN'М/|,ч3D`Nl >C_ї=DшmbgrVJ5n,╗O {О-[8╖Dю/7╩"▓l*╫uцQ!є3'╔; ─Pt╡Sфo"_;Н2g0PZwg l└з.ыSЎ[_i║ксk 8CЪn|# v*Тu0HtЦSбl5Сu3▄j┴xШ]L*Я(¤IIyL┌1iCй┬oзlat╓1:'╔6(lPнg ];meVК╬q╠ц'О%░op╣Z"╝Mmtф:%63lP*71}<U1q╒q,╝+╝'╘cэX0rVvQa;ЇpA9l@irЫ0ъ@Г>/3,лF%*┴;W@ {=5|o&р(╦c_46l`k-╖@\K'l4C| ,YdmlLo 5зRоsl "#?╟Vql@otc?cltв-JOlSъz(Gчcsg|]}|абdаИбСqS)r )┌clear_denomsZset_ring)rUrEйZrZZr'r(rX╜r*z1test_PolyElement_clear_denoms..)rr rчrr) r7r!r"ZrQQr+rs┌Tr]rрr'rшr(┌test_PolyElement_clear_denomsКsШ,2 ■¤№√·∙ ■¤№√·∙° ■ ¤ № √ ·∙° ■ ¤ № √ ·∙°ўrъc CsАtdtГ\}}}|dГ|dГ}}|а|бdks4JВ|dГ|dГ}}|а|бdksXJВ|dГ|dГ}}|а|бdks|JВ|dГ|dГ}}|а|бdksаJВ|dГd|d }}|а|бd|d dd fks╓JВd|d |dГ}}|а|бd|d d dfkРsJВ|dГ|dГ}}|а|бdkРs4JВ|dГ|dГ}}|а|бdkРsZJВ|dГ|dГ}}|а|бd kРsАJВ|dГ|dГ}}|а|бdkРsжJВ|dd|d |d Г}}|а|бd |dd|d d fkРsюJВ|dd|d |dГ}}|а|бd |dd|d dfkРs6JВd|dd |d|dГ}}|а|бd|dd|d d fkРsВJВ|dГd|dd |d}}|а|бdd |dd|d fkРs╬JВd|dd |d|d }}|а|б|d d|dd fkРsJВ|d d|dd |d}}|а|б|d d d|dfkРs^JВtdtГ\}}}}}|dd|d d|d}}|а|б|d |d dfkРs╢JВ|d|dd|d||d||||dd|d }}|d |d||d||d }}} |а|б||| fkРsFJВ|а|б|| |fkРs`JВtdtГ\}}}td dГ|d|td dГ}td dГ|td dГ}|d }|а|б||td dГfkРs╨JВ|а|б|td dГ|fkРsЁJВtdtГ\}}}d||dd||d|}d|d}d|}|а|б|||||fkРsZJВ|а|б|||||fkРs|JВdS)Nr,rrDr;)r;r rщ■ )r;rИr)r;rrИr<r )r;r r )r;rИr )r;r rИ)r;rИrИrcg═╠╠╠╠╠@rgЁ?)rrZ cofactorsr r) r7r!r"rEror#r+┌hZcff┌cfgr'r'r(┌test_PolyElement_cofactors┐sh "**"*"*"&"&""J, $"rюcCsbtdtГ\}}}tddГ|d|tddГ}tddГ|tddГ}|а|б|dks^JВdS)Nr,r r;)rr ┌gcdrхr'r'r(┌test_PolyElement_gcds rЁc CsтtdtГ\}}}d|dd|dd|}d|dd|}d|d}d}|а|б||fksjJВ|а|б||fksДJВ|а|б||fksЮJВtdtГ\}}}tddГ|d|dtddГ|}tddГ|dtddГ|}d|d}d}|а|б||fkРsJВ|а|б||fkРs:JВ|а|б||fkРsVJВtdtГ\}}td|Г\}} |ddd| }| d|ddd}|а|б|dd| d| dd|ddfkРs▐JВdS)Nr,r;rr<r r!r+)rr┌cancelr r ) r7r!r"rEror]rрZFxrfr+r'r'r(┌test_PolyElement_cancels* ( rЄcCshtdtГ\}}}|dГабdks$JВ|dГабdks8JВ|dd|dd|dабdksdJВdS)Nr,rr rr<r;)rrZmax_normrMr'r'r(┌test_PolyElement_max_norm9srєcCshtdtГ\}}}|dГабdks$JВ|dГабdks8JВ|dd|dd|dабdksdJВdS)Nr,rr rr<r;r█)rrZl1_normrMr'r'r(┌test_PolyElement_l1_normAsrЇcCs╥tdtГ\}}tddГ|dd|dd|dd |d dd|dd|dd |dd d|ddd|dd}|а|dбtddГ|dd |dd|dd |d dd|d|dd |dd d|dkРsJВ|а|dбtddГ|dd|dd|dd|d dd|dd|dd |ddkРsДJВ|а|d бtddГ|dd|dd|dd |d kРs╬JВdS)Nzx:11i r=rr_r r>r<rr█r;i r:r╙i`rYщ@)rr ┌diff)r7rsrEr'r'r(┌test_PolyElement_diffIs В~vrўcsTtdtГ\}}d|dЙИdГdks*JВИdГdks:JВttЗfddДГttЗfddДГttЗfd dДГtd tГ\}}}d||ddЙИddГdksжJВИddГd ks╕JВ|а|б}ИdГ|jddks▄JВИdГ|jddksЎJВttЗfddДГttЗfddДГttЗfddДГttЗfddДГttЗfddДГdS)Nr!rr rr<csИГSrLr'r'rЗr'r(r)Yr*z+test_PolyElement___call__..cs ИddГS)Nrr r'r'rЗr'r(r)Zr*csИtddГГSйNr r:йr r'rЗr'r(r)\r*r,r;r:щ5csИГSrLr'r'rЗr'r(r)ir*csИdddГS)Nrr r;r'r'rЗr'r(r)jr*csИdtddГГSr°r∙r'rЗr'r(r)lr*csИtddГdГSr°r∙r'rЗr'r(r)mr*csИtddГtddГГSr°r∙r'rЗr'r(r)nr*)rrrrNrrJr")r7r!r"ZRyr'rЗr(┌test_PolyElement___call__Rs& r√csъtdtГ\}ЙИddИddИdЙИаИdб}|dkrLt|tГrPJВttЗЗfddДГtdtГ\}ЙЙ}ИИddИИddИИdЙИаИdб}|dkr╚t||аИбjГs╠JВИаИdfИdfgб}|dkРrt||аИИбjГРsJВИаИdб}|dkРr0t||аИбjГРs4JВИаИdfИdfgб}|dkРrjt||аИИбjГРsnJВИаИdfИdf|dfgб}|dkРrаt|tГРrдJВttЗЗЗfd dДГttЗЗЗfd dДГttЗЗЗfddДГdS)Nr!rr<r;rcsИаИtddГбSr°й┌evaluater r'йrEr!r'r(r)wr*z+test_PolyElement_evaluate..rcsИаИdfИtddГfgбSr°r№r'rЙr'r(r)Иr*csИаИtddГfИdfgбSr°r№r'rЙr'r(r)Йr*cs"ИаИtddГfИtddГfgбSr°r№r'rЙr'r(r)Кr*) rrr¤r{r rrrJr|йr7rgr#r'rЙr(┌test_PolyElement_evaluateps( ,$"$rcs0tdtГ\}ЙИddИddИdЙИаИdб}|dkrNt||jГsRJВttЗЗfddДГtdtГ\}ЙЙ}ИddИddИdЙИаИdб}|dkr╕t||jГs╝JВИаИdfИdfgб}|dkrцt||jГsъJВttЗЗЗfd dДГttЗЗЗfd dДГttЗЗЗfddДГdS)Nr!rr<r;rcsИаИtddГбSr°й┌subsr r'r■r'r(r)Уr*z'test_PolyElement_subs..rcsИаИdfИtddГfgбSr°rr'rЙr'r(r)Эr*csИаИtddГfИdfgбSr°rr'rЙr'r(r)Юr*cs"ИаИtddГfИtddГfgбSr°rr'rЙr'r(r)Яr*)rrrr{r|rrr r'rЙr(┌test_PolyElement_subsМs rcsцtdtГ\}ЙИddИddИdЙИаИdб}|dkrNt||jГsRJВИаИИбИksfJВИаИИdбИddИddИddksЮJВttЗЗfddДГtd tГ\}Й}}ИddИddИdЙИаИdб}|dkРrt||jГРsJВИаИdf|dfgб}|dkРr:t||jГРs>JВИddИddИ||dаИ||dd б}||dd dd||dd dd||dd ||d}||kРr▐t||jГРsтJВdS)Nr!rr<r;rr>csИаИtddГбSr°)┌composer r'r■r'r(r)лr*z*test_PolyElement_compose..rr )rrrr{r|rr)r7rgr"r#r╬r'r■r(┌test_PolyElement_composeбs 8 csИjSrL)┌ is_cyclotomicr'rWr'r(r)¤r*z&test_PolyElement_is_..r$)rr Zis_generatorZ is_groundZis_monomialZis_term┌is_zeroZis_oneZis_monicZis_primitiveZ is_linearZis_quadraticZ is_squarefreeZis_irreduciblerrrrr)r7r"r#┌_r+rйrEr'rWr(┌test_PolyElement_is_╣sh $0r csкtdtГ\}Й}Й|dГаdбjtdttГks2JВ|dГаdбаdбjtdttГksXJВt|dГаdбаdбаdб|jГdusВJВttЗfddДГttЗfd dДГdS) Nrr rrGr#FcsИаdбаdбаdбSr%rIr'rOr'r(r) r*z'test_PolyElement_drop..cs ИаdбSr%rIr'rWr'r(r)r*) rrrJrrr{r|rrN)r7r"r')r!r#r(┌test_PolyElement_drops &*rcCsИtdtГ\}}}|d|d||}}||d}}|а|б||fksNJВ|а|б|ks`JВ|а|б|ksrJВ|а|б|ksДJВdS)Nr,r;r)rrZpdivZpremZpquoZpexquo)r r!r"rEror╬rgr'r'r(┌test_PolyElement_pdiv srcCsrtdtГ\}}d||dd}}|dtddГd}}}|а|б||fksVJВ|а|б|||fksnJВdS)Nr!r;r╙r╫r )rr Z half_gcdexZgcdex)r r!rEro┌sr+rьr'r'r(┌test_PolyElement_gcdexs rcCsZtdtГ\}}|dd|d|ddd|d}}}|а|б|||gksVJВdSйNr!r;r )rrZ subresultantsйr r!rErorьr'r'r(┌test_PolyElement_subresultants!s0rcCsLtdtГ\}}|dd|d|ddd}}}|а|б|ksHJВdS)Nr!r;r r)rrZ resultantrr'r'r(┌test_PolyElement_resultant's(rcCsжtdtГ\}}|dd|dd|dd}}|аб|ksDJВtdtГ\}}}}td|Г\}}||d||||dd||}}|аб|ksвJВdS) Nr!rr;r╞щ ip╥ za,b,cr<)rrZdiscriminant)r r!rEror]rh┌b┌cr'r'r(┌test_PolyElement_discriminant-s&.rcCsоtdtГ\}}|dd|dd|dd|dd |d d|dd|d }|d d|d }|dd|}|а||б|ksЦJВ|аб||gksкJВdS)Nr!r╨r┼r█щЦr_iЇr>щqr<r;rr╞r=)rrrZ decomposerr'r'r(┌test_PolyElement_decompose:sPrcCsDtdtГ\}}|dd|dаdб|dd|dks@JВdSr)rr┌shift)r r!r'r'r(┌test_PolyElement_shiftDsrc CshtdtГ\}}td|Г\}}dd|d|ddd|d|d d d|d |ddd|d |d |dГd||dГd}|аб|dd|d |d d|d|d dd|d d||d d|d d|dГd|d|d dd|dd|dd|d d|dd|d dgkРsdJВdS) Nr+r!ii =r_r=irr<r╫rщАr;r i$Їщdщ@r╩r╙щ╚r╘i Nr╞щiў r╨i╚пl i rїiжl^_)r rrZsturm)r]r+r r!rEr'r'r(┌test_PolyElement_sturmHs|2,>№r!cCs╠tdtГ\}}|dd|d|dd|d}|аб|df|ddfgksVJВ||dd|dd|dd|d}|аб|dd|ddf|dd|ddf|dfgks╚JВdS)Nr!r=r;r<rr )rrZgff_list)r r!rEr'r'r(┌test_PolyElement_gff_listUs ( 0r"cCs▄tdtаtdГбГ\}}|абj}|ddабd|ddtdГ|d|dd|ddfkslJВtdtаtdГбГ\}}|абj}|ddабd|ddtdГ|d|dd|ddfks╪JВdS)Nr!rr;r r<r█)rr rerZ to_groundr!Zsqf_norm)r7r!rsr'r'r(┌test_PolyElement_sqf_norm^s J r#cCsЮtdtГ\}}|d|d|dd}|dd|dd|d}|d}|d|d|d}|аб|kszJВ|абd|df|dfgfksЪJВdS)Nr!r=rr;r r<)rrZsqf_partZsqf_list)r r!rErorь┌pr'r'r(┌test_PolyElement_sqf_listis r%cCsttdtГ\}}|d|d|dd}|d}|d}|d|d}|абd|df|df|dfgfkspJВdS)Nr!r=rr;r )rrZfactor_list)r r!rErйr░┌wr'r'r(┌test_PolyElement_factor_listtsr'cCsltdtdГГ\}}|d|d|d|dd}|аdб|d|d |d |ddkshJВdS)Nr!r;r>r=r<rr rYr┼r╙r╨)rrr▄)r7r!r$r'r'r(┌test_issue_21410Аs$r(N)h┌__doc__┌ functoolsr┌operatorrrZsympy.polys.ringsrrrrr Zsympy.polys.fieldsr rZsympy.polys.domainsrr rrrZsympy.polys.orderingsrrZsympy.polys.polyerrorsrrrrZsympy.testing.pytestrZ sympy.corerrZsympy.core.numbersrrZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrr2r8r9rFrPrQrRr^rbrirjrkrlrprvr}rrАrВrГrЛrНrСrУrФrХrЪrЬrЮr┤r╢r╣r╧r▌rтrуrцrъrюrЁrЄrєrЇrўr√rrrr rrrrrrrrr!r"r#r%r'r(r'r'r'r(┌sШ" % ## &2;&5Q! J