U —9%e=]ã@shddlmZddlmZmZmZddlm Z m Z m Z m Z ddl mZmZmZddlmZddlmZe dddd \ZZZZZe d d d \ZZd d„Zdd„Zdd„Zdd„Z dd„Z!dd„Z"dd„Z#dd„Z$dd„Z%dd „Z&d!d"„Z'd#d$„Z(d%d&„Z)d'd(„Z*d)d*„Z+d+d,„Z,d-d.„Z-d/d0„Z.d1d2„Z/d3d4„Z0d5d6„Z1d7d8„Z2d9d:„Z3d;d<„Z4d=d>„Z5d?d@„Z6dAdB„Z7dCS)Dé)ÚSum)Ú deltaproductÚdeltasummationÚ_extract_delta)ÚEqÚSÚsymbolsÚoo)ÚKroneckerDeltaÚ PiecewiseÚpiecewise_fold)ÚAnd)Úraisesz i j k l mT)ÚintegerZfinitezx yF)Z commutativecCstttddfƒdkst‚tttddfƒtdks4t‚ttttddfƒttdksXt‚ttttddfƒttdks|t‚ttttƒtddfƒtttƒks t‚tttttƒtddfƒtdtttƒksÐt‚ttttttƒtddfƒttdtttƒks t‚dS©Néré)ÚdpÚxÚjÚAssertionErrorÚyÚKDÚiÚk©rrú^/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/concrete/tests/test_delta.pyÚtest_deltaproduct_trivial s$$$0rcCs<ttttƒtddfƒdkst‚ttttƒtddfƒttdƒksBt‚ttttƒtddfƒttdƒksft‚ttttƒtddfƒttdƒksŠt‚ttttƒtdtfƒttdƒttdƒttdƒksÂt‚ttttƒttdfƒttdƒttdƒttdƒksút‚ttttƒtttfƒtttƒtttƒtttdƒks8t‚dS©Nrrréé)rrrrrrÚlrrrrÚtest_deltaproduct_basics$$$88r"cCsrtttttƒtddfƒdks"t‚tttttƒtddfƒtttdƒksNt‚tttttƒtddfƒtttdƒkszt‚tttttƒtddfƒtttdƒks¦t‚tttttƒtdtfƒtttdƒttdƒttdƒksæt‚tttttƒttdfƒtttdƒttdƒttdƒks(t‚tttttƒtttfƒttttƒtttƒtttdƒksnt‚dSr)rrrrrrrr!rrrrÚtest_deltaproduct_mul_x_kd s",,,@Br#cCs¨ttttttƒtddfƒdks&t‚ttttttƒtddfƒttttdƒksZt‚ttttttƒtddfƒttttdƒksŽt‚ttttttƒtddfƒttttdƒksÂt‚ttttttƒtdtfƒttttdƒttdƒttdƒks t‚ttttttƒttdfƒttttdƒttdƒttdƒksVt‚ttttttƒtttfƒtttttƒtttƒtttdƒks¤t‚dSr) rrrrrrrrr!rrrrÚ test_deltaproduct_mul_add_x_y_kd*s&444$ÿ $ÿ (ÿr$cCs¤ttttƒtttƒtddfƒdks(t‚ttttƒtttƒtddfƒttdƒttdƒks`t‚ttttƒtttƒtddfƒttdƒttdƒks˜t‚ttttƒtttƒtddfƒttdƒttdƒksÐt‚ttttƒtttƒtdtfƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒksdt‚ttttƒtttƒttdfƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒttdƒksøt‚ttttƒtttƒtttfƒtttdƒtttƒtttƒtttƒtttƒtttƒtttdƒtttdƒtttdƒtttƒtttdƒks t‚dSr)rrrrrrr!ÚmrrrrÚtest_deltaproduct_add_kd_kd7s>(888&ÿÿþþ &ÿÿþþ *ÿÿ$þ$þr&cCstttttƒtttƒtddfƒdks,t‚tttttƒtttƒtddfƒtttdƒttdƒkslt‚tttttƒtttƒtddfƒtttdƒttdƒks¬t‚tttttƒtttƒtddfƒtttdƒttdƒksìt‚tttttƒtttƒtdtfƒttdƒtttdƒttdƒtttdƒttdƒtdttdƒttdƒttdƒtdttdƒttdƒttdƒksœt‚tttttƒtttƒttdfƒttdƒtttdƒttdƒtttdƒttdƒtdttdƒttdƒttdƒtdttdƒttdƒttdƒksLt‚tttttƒtttƒtttfƒtttdƒttttƒtttƒttttƒtttƒtdtttdƒtttƒtttdƒtdtttƒtttdƒtttdƒkst‚dSr) rrrrrrrr!r%rrrrÚ!test_deltaproduct_mul_x_add_kd_kdGs>,@@@*ÿÿ$þ$þ *ÿÿ$þ$þ .ÿÿ,þ,ýr'cCsnttttttƒtttƒtddfƒdks0t‚ttttttƒtttƒtddfƒttttdƒttdƒksxt‚ttttttƒtttƒtddfƒttttdƒttdƒksÀt‚ttttttƒtttƒtddfƒttttdƒttdƒks t‚ttttttƒtttƒtdtfƒttdƒttttdƒttdƒttttdƒttdƒttdttdƒttdƒttdƒttdttdƒttdƒttdƒksÎt‚ttttttƒtttƒttdfƒttdƒttttdƒttdƒttttdƒttdƒttdttdƒttdƒttdƒttdttdƒttdƒttdƒks’t‚ttttttƒtttƒttt fƒttt dƒttttt ƒttt ƒttttt ƒttt ƒttdttt dƒttt ƒttt dƒttdttt ƒttt dƒttt dƒksjt‚dSr) rrrrrrrrr!r%rrrrÚ'test_deltaproduct_mul_add_x_y_add_kd_kdXsJ0&ÿ&ÿ&ÿ .ÿÿ(þ(ý .ÿÿ(þ(ý 2ÿÿ0þ0ýr(cCsžtttttttƒtddfƒttdtttdttdƒtttttttdƒttdtttdƒks„t‚tttttttƒtddfƒtttttdƒksÀt‚tttttttƒtddfƒtttttdƒksüt‚tttttttƒtddfƒtttttdƒks:t‚tttttttƒtdtfƒtttttttdtttttt dtkttkƒfdƒksªt‚tttttttƒttdfƒttt dttttttttdtt ttktdkƒfdƒks t‚tttttttƒttt fƒttt t dttttttttt tt ttktt kƒfdƒksšt‚dS©Nrrr©rTr ) rrrrrrrrr r r!rrrrÚ&test_deltaproduct_add_mul_x_y_mul_x_kdns8*ÿÿÿ <<>  4þÿ  4þÿ  4þÿr+cCs‚ttttttƒtddfƒttdtttdttdƒtttttttdƒttdtttdƒks€t‚ttttttƒtddfƒttttdƒks´t‚ttttttƒtddfƒttttdƒksèt‚ttttttƒtddfƒttttdƒkst‚ttttttƒtdtfƒtttttttdtttttt dtkttkƒfdƒ  ¡ksŽt‚ttttttƒttdfƒttt dttttttttdtt ttktdkƒfdƒ  ¡kst‚ttttttƒttt fƒttt t dttttttttt tt ttktt kƒfdƒ  ¡ks~t‚dSr)© rrrrrrrrr r Úexpandr!rrrrÚ test_deltaproduct_mul_x_add_y_kd…s8&ÿÿÿ 446 4þÿ 4þÿ 4þÿr.cCsÄtttdtttƒtddfƒttddtttdttdƒdtttttttdƒdttdtttdƒkst‚tttdtttƒtddfƒttdttdƒksÌt‚tttdtttƒtddfƒttdttdƒks t‚tttdtttƒtddfƒttdttdƒksHt‚tttdtttƒtdtfƒttttdtttdtttttt dtkttkƒfdƒ  ¡ksÀt‚tttdtttƒttdfƒttt dtdtttttttdtt ttktdkƒfdƒ  ¡ks>t‚tttdtttƒttt fƒttt t dtdtttttttt tt ttktt kƒfdƒ  ¡ksÀt‚dS)Nrrrr*r r,rrrrÚ#test_deltaproduct_mul_x_add_y_twokdœs8*ÿ ÿÿ <>>  8þÿ  8þÿ  8þÿr/cCsXtttttttƒtddfƒtttdtttttdttdƒtttttdtttdƒtttdttttdƒks t‚tttttttƒtddfƒtttttdƒksÜt‚tttttttƒtddfƒtttttdƒkst‚tttttttƒtddfƒtttttdƒksXt‚tttttttƒtdtfƒttttttttdtttttttttttttt tdkttk@fdƒksðt‚tttttttƒttdfƒtttdtttt ttttttttt tttttdtttt ttktdk@fdƒksœt‚tttttttƒttt fƒttttttt tttt ttttttttt tttttt tttt ttktt k@fdƒksTt‚dS©Nrrréÿÿÿÿr*r ) rrrrrrrrr r!rrrrÚ&test_deltaproduct_mul_add_x_y_add_y_kd³sn. ÿ$þ ý <>> 0ÿÿÿþÿ   ÿÿ ÿÿÿÿþþÿ  .2ÿÿÿþÿr2cCs>tttttƒttttƒtddfƒttdƒtttƒttttƒttdttdƒtttƒtttttƒtdtttdƒtttƒttdtttƒttttƒttdksÐt‚tttttƒttttƒtddfƒttttƒtttdƒkst‚tttttƒttttƒtddfƒttttƒtttdƒksdt‚tttttƒttttƒtddfƒttttƒtttdƒks®t‚tttttƒttttƒtdtfƒtttƒtttttttƒttdtttƒttttttƒttttƒttttttƒttt tdkttk@fdƒkspt‚tttttƒttttƒttdfƒtttƒttdtttƒttt ttttƒttttttƒttt tttƒttttƒttdtttƒttt ttktdk@fdƒksLt‚tttttƒttttƒttt fƒtttƒtttttƒttt tttƒttt ttttƒttttttƒttt tttƒttttƒttt tttƒttt ttktt k@fdƒks:t‚dSr0) rrrrrrrrr r!rrrrÚ'test_deltaproduct_mul_add_x_kd_add_y_kdÉs¢&,0ÿ,þýÿ&ÿ &ÿ &ÿ &8ÿÿÿÿýÿ &ÿÿ4ÿÿÿþýÿ & ÿÿÿÿ"ÿÿ ÿÿ ÿÿÿþþþr3cCstttddfƒdkst‚tttddfƒdtks4t‚ttttddfƒdttksXt‚ttttddfƒdttks|t‚ttttƒtddfƒdtttƒks¤t‚tttttƒtddfƒdttttƒksÔt‚ttttttƒtddfƒdtttttƒkst‚dSr)ÚdsrrrrrrrrrrrÚtest_deltasummation_trivialæs$$(0r5cCs@tdddd}tt|dƒ|ddfƒdks,t‚tttdtdƒtt tfƒtttdtdƒtt tfƒkspt‚tttt ƒt dtktdkƒfdƒttttƒttt ƒtddfƒkrÚtttt ƒtttƒtddfƒksànt‚tttt ƒt t tfƒdkst‚tttt ƒt dtfƒtdt j tkfdƒks2t‚tttt ƒt ddfƒtdt dtktdkƒfdƒksjt‚tt tttƒttt ƒt t tfƒttttƒks¤t‚tttttƒtt tfƒtksÊt‚tttttƒtt tfƒtksðt‚tt tddfƒdt kst‚ttttttƒtt tfƒdtksrrrrÚ#test_deltasummation_mul_x_add_kd_kddsF$ÿÿ $ÿÿ $ÿÿ $ÿÿ $ÿÿ $ÿÿ $ÿÿr@c Csîttttttƒtttƒtddfƒttttt dtktdkƒfdƒtttt dtktdkƒfdƒƒkspt ‚ttttttƒtttƒtddfƒttttt tdƒfdƒtttt tdƒfdƒƒksÐt ‚ttttttƒtttƒtddfƒttttt tdƒfdƒtttt tdƒfdƒƒks2t ‚ttttttƒtttƒtddfƒttttt tdƒfdƒtttt tdƒfdƒƒks”t ‚ttttttƒtttƒtdt fƒttttt dtktt kƒfdƒtttt dtktt kƒfdƒƒkst ‚ttttttƒtttƒtt dfƒttttt t tktdkƒfdƒtttt t tktdkƒfdƒƒksxt ‚ttttttƒtttƒtt t fƒttttt t tktt kƒfdƒtttt t tktt kƒfdƒƒksêt ‚dSr8)r4rrrrrrr r r rrr!r%rrrrÚ)test_deltasummation_mul_add_x_y_add_kd_kd|sF(ÿÿ (ÿÿ (ÿÿ (ÿÿ (ÿÿ (ÿÿ (ÿÿrAcCsjtttttttƒtddfƒtdttttdtktdkƒfdttdfƒksZt‚tttttttƒtddfƒttttt tdƒfttdfƒks¤t‚tttttttƒtddfƒttttt tdƒfttdfƒksît‚tttttttƒtddfƒttttt tdƒfttdfƒks:t‚tttttttƒtdt fƒtt ttttdtktt kƒft ttdfƒks–t‚tttttttƒtt dfƒtdt ttttt tktdkƒfdt ttdfƒksút‚tttttttƒtt t fƒtt t dttttt tktt kƒft t dttdfƒksft‚dS©NrrTrr r;rrrrÚ(test_deltasummation_add_mul_x_y_mul_x_kd”s, 2ÿ "ÿ "ÿ "ÿ  2ÿ  :ÿ "(ÿrCcCsNttttttƒtddfƒtdttttdtktdkƒfdttdfƒksVt‚ttttttƒtddfƒttttt tdƒfttdfƒksœt‚ttttttƒtddfƒttttt tdƒfttdfƒksât‚ttttttƒtddfƒttttt tdƒfttdfƒks*t‚ttttttƒtdt fƒtt ttttdtktt kƒft ttdfƒks‚t‚ttttttƒtt dfƒtdt ttttt tktdkƒfdt ttdfƒksât‚ttttttƒtt t fƒtt t dttttt tktt kƒft t dttdfƒksJt‚dSrBr;rrrrÚ"test_deltasummation_mul_x_add_y_kd¥s,2ÿ"ÿ"ÿ"ÿ 2ÿ :ÿ (ÿrDcCs†tttdtttƒtddfƒtdttdttdtktdkƒfdttdfƒks^t‚tttdtttƒtddfƒtttdtt tdƒfttdfƒks¬t‚tttdtttƒtddfƒtttdtt tdƒfttdfƒksút‚tttdtttƒtddfƒtttdtt tdƒfttdfƒksJt‚tttdtttƒtdt fƒtt ttdttdtktt kƒft ttdfƒksªt‚tttdtttƒtt dfƒtdt ttdttt tktdkƒfdt ttdfƒkst‚tttdtttƒtt t fƒtt t dttdttt tktt kƒft t dttdfƒks‚t‚dS)NrrrTr r;rrrrÚ%test_deltasummation_mul_x_add_y_twokd¶s. 6ÿ &ÿ &ÿ &ÿ  6ÿ "(ÿ ",ÿrEcCsÀtttttttƒtddfƒtdttttttdtktdkƒfdtttdfƒksft‚tttttttƒtddfƒttttttt tdƒftttdfƒks¼t‚tttttttƒtddfƒttttttt tdƒftttdfƒkst‚tttttttƒtddfƒttttttt tdƒftttdfƒkslt‚tttttttƒtdt fƒtt ttttttdtktt kƒft tttdfƒksÔt‚tttttttƒtt dfƒtdt ttttttt tktdkƒfdt tttdfƒksDt‚tttttttƒtt t fƒtt t dttttttt tktt kƒft t dtttdfƒks¼t‚dSrBr;rrrrÚ(test_deltasummation_mul_add_x_y_add_y_kdÇs2"(ÿ  .ÿ .ÿ  .ÿ "(ÿ ",þ "0þrFcCsêtttttƒttttƒtddfƒtttttƒtt dtktdkƒfdƒdtttƒttƒkslt ‚tttttƒttttƒtddfƒtttttƒtt tdƒfdƒtttƒttƒksÌt ‚tttttƒttttƒtddfƒtttttƒtt tdƒfdƒtttƒttƒks.t ‚tttttƒttttƒtddfƒtttttƒtt tdƒfdƒtttƒttƒkst ‚tttttƒttttƒtdtfƒtttttƒtt dtkttkƒfdƒttttƒttƒksþt ‚tttttƒttttƒttdfƒtttttƒtt ttktdkƒfdƒdttttƒttƒkspt ‚tttttƒttttƒttt fƒtttttƒtt ttktt kƒfdƒt tdtttƒttƒksæt ‚dS)Nrrr*rr ) r4rrrrrrr r r rrr!rrrrÚ)test_deltasummation_mul_add_x_kd_add_y_kdÚsF($ÿÿ (ÿÿ (ÿÿ (ÿÿ ($ÿÿ ($ÿÿ ($ÿÿrGcCsttdd„ƒdS)NcSsttttƒtttƒtƒS)N)rrrrrr!rrrrÚóóz$test_extract_delta..)rÚ ValueErrorrrrrÚtest_extract_deltaòsrKN)8Zsympy.concreterZsympy.concrete.deltarrrr4rZ sympy.corerrrr Zsympy.functionsr rr r Z sympy.logicr Zsympy.testing.pytestrrrrr!r%rrrr"r#r$r&r'r(r+r.r/r2r3r5r7r9r:r<r=r?r@rArCrDrErFrGrKrrrrÚsD