U Ч9%e@у@s<ddlmZddlmZmZmZddlmZddlm Z ddl mZddlm Z ddlmZddlmZmZmZmZmZmZdd lmZmZmZmZdd lmZddlmZm Z m!Z!ddl"m#Z#dd l$m%Z%m&Z&ddДZ'ddДZ(ddДZ)ddДZ*ddДZ+ddДZ,ddДZ-ddДZ.ddДZ/d d!ДZ0d"d#ДZ1d$d%ДZ2d&d'ДZ3d(S))щ)┌Basic)┌I┌Rational┌piй┌evaluate)┌S)┌Symbol)┌sympify)┌sqrt)┌Line┌Point┌Point2D┌Point3D┌Line3D┌Plane)┌rotate┌scale┌ translate┌GeometryEntity)┌Matrix)┌subsets┌permutations┌cartes)┌Undecidable)┌raises┌warnsc sЖ tdddН}tdddН}tdddН}tdddН}tdddН}tdddН}tj}t||ГЙt||Г}td d ГЙtd d Г}td d Г} ttd d Гd dНЙИИksЮtВИ|ksкtВ|j|ks╕tВИ||ks╚tВ|Иt||||ГksцtВ|t||Гks■tВttdd ДГtt dd ДГtt dd ДГtt dd ДГtt dd ДГtdt dГГttddГt dГГkРsltВtаИ|бt||ГkРsИtВtаИ|бt||||||ГkРs┤tВtа||б|kРs╩tВ|а|б|kРs▐tВИj td d ГkРsЇtВtаИ|бt dГkРstВtаИИбd kРs$tВtаИ|бt |jd|jdГkРsNtВttЗfdd ДГttЗfdd ДГИаИбИаИбkРsМtВ|аИбИа|бkРsжtВtа|ИбdkРs╝tВtа|| бd kРs╥tВtt Зfdd ДГt||ГЙt||Г} t|d |Г}tаИбРstВttddНП tаИtИddНбРs>tВW5QRXИабРsVtВtаИ|бРshtВtаИ|И| бРs~tВtаИ|И|бdkРsШtВtаИИ|| бdkРs▓tВttЗfdd ДГttЗЗfdd ДГИаtd d ГбИgkРsЇtВИа|бgkРstВИаИбgkРstВttddНП4tаtd d d Гtd d Гбtd d d ГgkРsXtВW5QRXtddd Н}t|d Г} td |Г}t|d Г}td |Г}t|d!Г}tа| бРs┤tВtа| |бРs╞tВtа| |||бРs▄tВt| |||fГD]}tj|ОdkРsьtВРqьtа||d|dбdkРs(tВtd d Гаd"d#d$бdkРsFtВtаtd d d d Гtd d d d Гtd d d d Гtd d d d ГбdkРsИtВИаИбРsШtВИаdИбРsмtВИа|бРr╝tВtаtd d Гd%бРs╘tВtаtd d Гd&бРsьtВttd'd ДГtd d Гjtd d ГkРstВtd d Гjtd d ГkРs2tВИjdkРsBtВИjРsNtВ|jdkРs^tВИjdkРsntВИjdkРs~tВ|jРsКtВ|аddбtddГkРsжtВИаddбИkРs╝tВ|аttd(d(ГбИkРs╪tВИа |бИа|баddбkРs·tВИа!|бИа|баddбkРstВ|d!td!d!ГkРs6tВ|d!td)d)ГkРsNtВd!|td!d!ГkРsftВtt d*d ДГt||d |Гt|d||d Гtd d+ГkРsмtВtjtd dГ}}t||Га"dбt|а#dб|а#dбdd,НkРsюtВtt d-d ДГtа$d.d/бtd d ГkРstВtа$d"d/бtd d ГkРs4tВtt Зfd0d ДГtd d ГЙИаtdбtd d ГkРsntВИаtdИбИkРsИtВtd d ГЙИаddбtddГkРsоtВИа%d dбtddГkРs╩tВИа%d бtdd ГkРsфtВИj%d d1Нtd dГkР stВИj%Иj&ОtddГkР stВtt Зfd2d ДГtt Зfd3d ДГd td d d d ГkР sXtВd td d d d ГkР sptВtа'бd+kР sВtВdS)4N┌xTй┌real┌y┌x1┌x2┌y1┌y2rщ)ZslopecSstdГSйNr%йr йr(r(·^/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/geometry/tests/test_point.py┌%єztest_point..cSs tdgГSr&r'r(r(r(r)r*&r+cSs tdtГSйNщйr rr(r(r(r)r*'r+cSstdttГS)Nщr.r(r(r(r)r*(r+cSstdttГSr,r.r(r(r(r)r*)r+чfffffA@r-щйщr/cstаИdбSйNr)r ┌distancer(й┌p1r(r)r*5r+cstаИtГбSйN)r r4rr(r5r(r)r*6r+cstаИИбSr7)r ┌canberra_distancer(й┌p3r(r)r*?r+FйZtest_stacklevelщ)┌dimcs tаИбSr7)r ┌is_collinearr()┌liner(r)r*Nr+cs ИаИбSr7)r>r()r?┌p1_1r(r)r*Or+)Zpositiveщйr%r%)r/r/)r/r%)щ rC)rrCcSs tаttdГtdГГtddГбS)Nzx1%y1zx2%y2rr%)r ┌is_scalar_multipler r(r(r(r)r*lr+gр?чЪЩЩЩЩЩ╔?cSstddГdSйNrщ r'r(r(r(r)r*Гr+rCrcSstddГdSйNr%r/r'r(r(r(r)r*Лr+)rr%)r%rcstаИtddГбSr3)r ┌projectr(r5r(r)r*Рr+)r cs ИаИбSr7й┌ transformr(r9r(r)r*Юr+csИаtddgddggГбSйNr%rйrKrr(й┌pr(r)r*Яr+)(r r┌Halfr r┌AssertionErrorr r┌ TypeError┌ ValueErrorrr┌midpoint┌originr4r┌taxicab_distancer8r>r┌UserWarning┌intersection┌is_concyclicrrDrZorthogonal_direction┌is_zeroZ is_nonzerorrr┌__radd__┌__rsub__┌evalf┌nrIr┌argsZaffine_rank)rr r!r"r#r$┌half┌p2┌p4┌p5┌p1_2┌p1_3Zx_posZp2_1Zp2_2Zp2_3Zp2_4Zp2_5Zpts┌a┌br()r?rOr6r@r:r)┌ test_pointsь (,* $8 B"$8 rhc sиtdddНЙtdddН}tdddН}tdddН}tdddН}tdddН}td ddН}td ddН}tj}t|||Г}t|||Г} tdddГ} tdddГ}tddd Г}||ksоtВ|| ks║tВ| j|ks╚tВ| ||ks╪tВ| |t||||||Гks№tВ| t|||ГkРstВtdtdГГttddГtdГГkРsBtВtа | |бt|||ГkРs`tВtа ||бt|||||||||ГkРsЦtВtа | | б| kРsмtВ| а | б| kРs└tВtа | |бtdГkРs┌tВtа ||бdkРsЁtВtа | | бt| jd | jd | jd ГkРs$tВt|||Г} t|||Г}t|d||Г}tа | бtа | |бРshtВtа | || |бРs~tВtа | || |бdkРsШtВtа | | ||бdkРs▓tВ| аtdddГб| gkРs╨tВ| а|бgkРsфtВ|dtdddГkРs■tВ|dtdddГkРstВd|tdddГkРs2tВttddДГ|j|||fkРsVtВ| j|||fkРsltВ| jdkРs|tВ|jdkРsМtВ|jdkРsЬtВ|jdkРsмtВ|jdkРs╝tВ|jd kРs╠tВtИИd|d ГtИd И|ddГtdddГkРs tВtjtddГtddГ}}}t|||Гаd бt|аd б|аd б|аd бddНkРsbtВttddДГtdddГЙИаd dбtd ddГkРsЪtВИаdd бtd ddГkРs╕tВИаdбtd ddГkРs╘tВИjddНtddd ГkРsЄtВИjИjОtd d d ГkРstВtdddd d!НjdjРs.tВИjdkРs>tВ| jdkРsNtВ|jdkРs^tВttЗЗfd"dДГtабРsАtВtаd#d#d$бРsФtВtаd#d%бРsжtВttdd&НПttd'dДГW5QRXtаd#d%бРs▐tВtаdd(dd)бdkРs°tВtdddГ}tdddГ}tаИ||бdkРs(tВtаИ||| бdkРsBtВtаИ|бРsTtВtddd Г}tdddГ}tаИ||бРsАtВtd)d*d+ГЙtjЗfd,d-ДtdГDГОРsоtВtаtИ|ГtИИ|Гt|Иd ГбdkРsрtВ|аtИ|Гбtddd ГgkРstВ|аdddб|kРstВ|аd d d |бtdddГkРs>tВ|аddd| б|kРsXtВt ddddgddddgddddgddddggГ}Иа!|бИkРsЬtВt ddddgddddgddddgddddggГ}Иа!|бtd d d ГkРsшtВttЗfd.dДГttЗfd/dДГИа"|бdkРs tВtddddГ}ttdd&НП"И|tddddГkРsXtВW5QRXtddddГ}ttdd&НП"И|tddddГkРsЪtВW5QRXdS)0NrTrr r!r"┌x3r#r$┌y3rr%r/r0r-r1r2FrArEcSstdddГdSrFйrr(r(r(r)r*▄r+ztest_point3D..)rrr)r%r%r%)rr%r/rCr<rcSstdddГdS)Nr%r/r-rkr(r(r(r)r*яr+)┌zчЪЩЩЩЩЩ╣?┌ignore)r┌on_morphcstаИИбSr7)r┌ are_collinearr()rOrr(r)r*r+)r%r/r)r%r-rйr%r/r-r;cSstаddбS)Nйr%r/rq)r┌are_coplanarr(r(r(r)r* r+)r%r%r)r%r/r%)r/r%r)r-r%r/csg|]}Иаd||fбСqS)rC)Z projectionй┌.0┌i)┌planer(r)┌ sz test_point3D..cs ИаИбSr7rJr(rNr(r)r*'r+csИаtddgddggГбSrLrMr(rNr(r)r*(r+)#r rrPrrQr r rrrTr4rrlrprXrrS┌coordinatesr]r^rrr_┌is_Float┌lengthrRrsrrWr┌rangerrrK┌equals)r r!r"rir#r$rjr`r6rar:rbrcr@rdrerfrg┌cZplanar2Zplanar3┌identityZtransZp_4dZp_4d3dr()rOrwrr)┌test_point3Dйs╘$( 4 * "2$"00&rАcCs╞tddГ}tddГ}d}|а|бtdГdks2tВ|а|бtdГdksLtВ|jdksZtВ|jdkshtВ|jdksvtВ|jtdГdksМtВ|jd ksЪtВ|jdtdГdfks┤tВ|jd ks┬tВdS)Nr%rAr<g@)щr-щ=r/щ)r%rA)r%rAr%rA) rr4rrQrr rryZboundsйr6rar:r(r(r)┌test_Point2D6s rЕcCs>tdddГ}tdddГ}tdddГ}tа|||бdks:tВdS) Nr<щ■ rБr%r/r-щF)rrprQrДr(r(r)┌test_issue_9214JsrИc CsHtdddГ}tddГ}ttddНП|а|бtdГks:tВW5QRXdS)Nr%rr/Fr;rA)rrrrWr4rrQйr6rar(r(r)┌test_issue_11617Rs rКcCsмtddГ}|аttdГбtddГks*tВ|аtddГбtddГksHtВ|аtddГбtddГksftВtddГаdddбtddГksИtВtddГаdd бtd d ГksиtВdS)Nr%r/rCr-)r<rArЖi∙ r<rArБ)r rKrrrQrrrNr(r(r)┌test_transformZs rЛcCsVtddГtddГ}}tddГtddГ}}tа|||бs>tВtа||||бrRtВdS)NrCrr%r/)r rYrQ)r6rar:rbr(r(r)┌test_concyclic_doctest_bugesrМc CsdddgtddГf}dddgtddГf}t||Г}tddГ}ddddgtdddГf}t|dГ}tdddГ}dddddgtddddГf}t|dГ}tddddГ} d d ddd ddddg } ddg}|D]}t|Гq└| D]} |D]}t|| Г|Гq┌q╥|D]} |D]}t|| Г|Оq№qЇdg}|D]}t|ГРq| D] } |D]}t|| Г|ГРq8Рq0|D] } |D]}t|| Г|ОРq^РqVdg}|D]}t|ГРqВ| D] } |D]}t| | Г|ГРqЮРqЦ|D] } |D]}t| | Г|ОРq─Рq╝tdГ}tddГ}|d|ftdd|ddНkРstВtddГ}|dtddddНkРs:tВtddГ}|dtddddНkРs`tВtddddН}t|dddН}|jdkРsМtВt dd Д|jd!dЕDГГРsоtВt d"d Дt|ГjDГГРs╠tВtdd#dНРs▐tВt td$d%ДГt td&d%ДГt td'd%ДГd!S)(zЗFunctions accepting `Point` objects in `geometry` should also accept tuples and lists and automatically convert them to points.rrr%r/)r%r-r-rq)r%r/r-r<r<r4rDrVrTrX┌dotr}┌__add__┌__sub__rYr>rrrmFrg$@grErnйr=ro)rmrErrcss|]}|jVqdSr7йrzrtr(r(r)┌ лsz!test_arguments..Ncss|]}|jVqdSr7rСrtr(r(r)rТнs┌errorcSstdddddНS)Nr%r-rУrРr'r(r(r(r)r*│r+z test_arguments..cSstdddddНS)Nr%r-┌unknownrРr'r(r(r(r)r*╡r+cSsttГtГГSr7)r rr(r(r(r)r*╖r+) r rrrr┌getattrr rQr_┌allrrSrR)Z singles2dZ singles2d2Z doubles2dZp2dZ singles3dZ doubles3dZp3dZ singles4dZ doubles4dZp4dZtest_singleZtest_doublerO┌funcrrf┌uZu4r(r(r)┌test_argumentslsl $ "rЩcCs.tddГjttdГdtdГdГks*tВdSrH)r ┌unitrrQr(r(r(r)┌ test_unit╣srЫcCsttddДГdS)NcSstddГаtddГбS)Nr%r/)rrrB)r rНrr(r(r(r)r*╛r+ztest_dot..)rrRr(r(r(r)┌test_dot╜srЬcCsntаtddГtddГбtddГtddГgks0tВtjtddГtdddГddНtdddГtdddГgksjtВdS)Nr%r/r-r<rrn)ro)r Z_normalize_dimensionrQr(r(r(r)┌test__normalize_dimension┴s rЭc Cs"tdГПtddГW5QRXdS)NFr%r/)rr r(r(r(r)┌test_issue_22684╔s rЮcCstdddГ}tdddГ}|аtdddГбdddgks8tВ|аtdddГбdddgksXtВ|аtddtГбdddgksxtВ|аtdddГбdddgksШtВ|аtdtdГdГбdddgks╝tВ|аtdddГбdddgks▄tВ|аtdddГбtdГdtdГddgkРstВ|аtdddГбtdГdtdГdtdГdgkРsHtВ|аtddГбd td Гd dtd Гd dgkРsАtВ|аtdddГбtdГdtdГdtdГdgkРs└tВ|аtdddГбdddgkРsтtВ|аtdddГбtdГddtdГdgkРstВdS) Nrr%rAr-g333333@r/iЇ iё щ№ щ)щ√ щ)rZdirection_cosinerQrrrЙr(r(r)┌test_direction_cosine╧s $ 2:8@"rгN)4Zsympy.core.basicrZsympy.core.numbersrrrZsympy.core.parametersrZsympy.core.singletonrZsympy.core.symbolr Zsympy.core.sympifyr Z(sympy.functions.elementary.miscellaneousrZsympy.geometryrr rrrrZsympy.geometry.entityrrrrZsympy.matricesrZsympy.utilities.iterablesrrrZsympy.utilities.miscrZsympy.testing.pytestrrrhrАrЕrИrКrЛrМrЩrЫrЬrЭrЮrгr(r(r(r)┌s6 M