+ i/< Rt^RIHtHt^RIHtHtHtHtH t H t ^RI H t H t Ht^RIHtHtHtHtHt^RIHtHtHtHtHtHtHtHt^RIHtH t ^RI!H"t"^RI#H$t$^R I%H&t&H't'H(t(H)t)H*t*H+t+H,t,H-t-H.t.H/t/H0t0R t1]&Pd!]4R 4t3]&Pd!]4R 4t3]&Pd!]4R 4t3]&Pd!]4R4t3]&Pd!] 4R4t3]&Ph!]]4R4t3]&Pd!]4R4t3]'Pd!]4R4t3]'Pd!]4R4t3](Pd!]4R4t3](Pd!]4R4t3](Pd!]4R4t3](Pd!]4R4t3](Pd!] 4R4t3](Pd!]4R4t3](Pd!]4R4t3])Pd!]4R4t3])Pd!]4R4t3])Pd!]4R4t3]*Pd!]4R4t3]*Pd!]4R4t3R t5]+Pd!]4R!4t3]+Pd!]4R"4t3]+Pd!]4R#4t3]+Pd!]4R$4t3]+Pd!] 4R%4t3]+Pd!]4R&4t3]+Pd!]4R'4t3]+Pd!]4R(4t3]+Pd!]4R)4t3]+Pd!]4R*4t3]+Pd!] 4R+4t3]+Pd!]4R,4t3]+Pd!]"4R-4t3]+Pd!]4R.4t3]+Pd!]4R/4t3]+Pd!]4R04t3]+Pd!]4R14t3]+Pd!]4R24t3],Pd!]64R34t3]0Pd!]64R44t3]/Pd!]64R54t3].Pd!]64R64t3]-Pd!]64R74t3R8#)9z? Handlers related to order relations: positive, negative, etc. )Qask)AddBasicExprMulPowS) fuzzy_not fuzzy_andfuzzy_or)E ImaginaryUnitNaNIpi)Absacosacotasinatanexp factoriallog) DeterminantTrace) MatrixElement)MDNotImplementedError) NegativePredicateNonNegativePredicateNonZeroPredicate ZeroPredicateNonPositivePredicatePositivePredicateExtendedNegativePredicateExtendedNonNegativePredicateExtendedNonPositivePredicateExtendedNonZeroPredicateExtendedPositivePredicatecVP4wr#V\P8XgV\P8XdR#V'g*VP^4pVP^8wdV^8#R#VP^4pVP^8wd3V^8wdR#VP^4pVP^8wdV^8#R#R#NF) as_real_imagr revalf_precexpr assumptionsris&& ^/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/assumptions/handlers/order.py_NegativePredicate_numberr4s    DAAEEzQ!%%Z GGAJ 77a<q5L  GGAJ 77a<Av Aww!|1u  c@VP'd \W4#R#N) is_numberr4r/r0s&&r3_r:/ ~~~(;;r5c2VPpVf\hV#r7) is_negativerr/r0rets&& r3r:r:4   C {## Jr5cVP'd \W4#\\P!V4V4pVRJdV#^pVP FYp\\P !V4V4RJgK)\\P!V4V4RJd V^, pKXR# V\VP 48dR#R#)zB Positive + Positive -> Positive, Negative + Negative -> Negative TFN) r8r4rrrealargsnegativepositivelen)r/r0r1nonposargs&& r3r:r:;s  ~~~(;; AFF4L+&A} Fyy qzz# ,D 81::c?K0E9!   C N " #r5c&VP'd \W4#RpVPFapVfRp\\P !V4V4'd V'*pK8\\P !V4V4'dK`R# V#r*)r8r4rCrrrDrEr/r0resultrHs&& r3r:r:Ssq ~~~(;; Fyy >F qzz# , ,ZF C+ . .   Mr5cVP\8Xd5\\P!VP 4V4'dR#R#VP 'd \W4#\\P!VP4V4'd\\P!VP4V4'd3\\P!VP 4V4'dR#\\P!VP 4V4'dR#\\P!VP 4V4'd+\\P!VP4V4#R#R#)za Real ** Even -> NonNegative Real ** Odd -> same_as_base NonNegative ** Positive -> NonNegative FN) baser rrrBrr8r4rEevenoddrDr9s&&r3r:r:cs yyA~ qvvdhh - - ~~~(;; 166$)) k** qzz$))$k 2 2166$((#[11 qvvdhh - - quuTXX , ,qzz$)),k: : - +r5cR#Fr9s&&r3r:r:{ r5cr\\P!VP4V4'dR#\hrQ)rrrBrrr9s&&r3r:r:s% 166$(( [)) r5cVP'd?\\W44pV'd!\\P !V4V4#V#R#r7)r8r r4rrrB)r/r0 notnegatives&& r3r:r:> ~~~ 9$ LM qvvd|[1 1  r5c2VPpVf\hV#r7)is_nonnegativerr>s&& r3r:r:   C {## Jr5c2VPpVf\hV#r7) is_nonzerorr>s&& r3r:r:s //C {## Jr5ca\\P!V44RJdR#VP'd8VP ^4pRo\ V3RlVP 444#R#)Fc2VP^8wdV^8g#R#)N)r-)r2s&r3nonz_..nonzsww!|Av r5c34<"TF pS!V4xK R#5ir7rR).0r2r`s& r3 _..s:)9AQ)9sN)rrrBr8r,r r+)r/r0r2r`s&& @r3r:r:sU 166$<E! ~~~ JJqM :)9::: r5c\a\;QJd)V3RlVP4F 'dK RM RM!V3RlVP44'gU\;QJd)V3RlVP4F 'dK RM RM!V3RlVP44'dR#R#)c3d<"TF%p\\P!V4S4xK' R#5ir7)rrrErcxr0s& r3rdres# >Iq3qzz!}k * *I-0FTc3d<"TF%p\\P!V4S4xK' R#5ir7)rrrDrhs& r3rdres#FIq3qzz!}k22IrjN)allrCr9s&fr3r:r:s^ s >DII >sss >DII >>>sFDIIFsssFDIIFFFGr5cVPF/p\\P!V4V4pV'dK-Vu# R#)T)rCrrnonzero)r/r0rHrKs&& r3r:r:s4yyQYYs^[1    r5cV\\P!VP4V4#r7)rrrnrMr9s&&r3r:r:s qyy#[ 11r5cd\\P!VP^,4V4#)rrrnrCr9s&&r3r:r:s qyy1& 44r5cR#r7rRr9s&&r3r:r: r5c2VPpVf\hV#r7)is_zerorr>s&& r3r:r:s ,,C {## Jr5c \\\\P!V4V44\\P !V4V4.4#r7)r r rrrnrBr9s&&r3r:r:s< iAIIdO[ AB AFF4L+&( ))r5cBa\V3RlVP44#)c3d<"TF%p\\P!V4S4xK' R#5ir7)rrzero)rcrHr0s& r3rdres#GYcCs [11Yrj)r rCr9s&fr3r:r:s GTYYG GGr5c2VPpVf\hV#r7)is_nonpositiverr>s&& r3r:r:rZr5cVP'd?\\W44pV'd!\\P !V4V4#V#R#r7)r8r _PositivePredicate_numberrrrB)r/r0 notpositives&& r3r:r:rWr5c4VP4wr#V'g*VP^4pVP^8wdV^8#R#VP^4pVP^8wd3V^8wdR#VP^4pVP^8wdV^8#R#R#)FN)r+r,r-r.s&& r3r~r~s    DA GGAJ 77a<q5L  GGAJ 77a<Av Aww!|1u  r5c2VPpVf\hV#r7) is_positiverr>s&& r3r:r:r@r5c@VP'd \W4#R#r7)r8r~r9s&&r3r:r: r;r5cVP'd \W4#RpVPF]p\\P !V4V4'dK+\\P !V4V4'd VR, pK\R# V#TN)r8r~rCrrrErDrJs&& r3r:r:si ~~~(;; Fyy qzz# , ,  C+ . .d]F   Mr5cVP'd \W4#\\P!V4V4pVRJdV#^pVP FYp\\P !V4V4RJgK)\\P!V4V4RJd V^, pKXR# V\VP 48dR#R#)TFN) r8r~rrrBrCrErDrF)r/r0r1nonnegrHs&& r3r:r: s ~~~(;; AFF4L+&A} Fyy qzz# ,D 81::c?K0E9!   C N " #r5cVP\8Xd\\P!VP 4V4'dR#\\P !VP 4V4'dA\\P!VP \\,, 4V4#R#VP'd \W4#\\P!VP4V4'd3\\P!VP 4V4'dR#\\P!VP4V4'dg\\P!VP 4V4'dR#\\P!VP 4V4'dR#R#R#)TNF)rMr rrrBr imaginaryrNrrr8r~rErDrOr9s&&r3r:r:4s yyA~ qvvdhh - - q{{488$k 2 2qvvdhh"o. < < ~~~(;; 1::dii +.. qvvdhh - - 1::dii +.. qvvdhh - - quuTXX , , -/r5cJ\\P!VP4V4'dR#\\P!VP4V4'dA\\P !VP\ \,, 4V4#R#r)rrrBrrrNrrr9s&&r3r:r:Hs` 166$(( [)) 1;;txx +..166$((AbD/*K88/r5cx\\P!VP^,4V4pVRJdV#\\P!VP^,^, 4V4'dR#\\P !VP^,^, 4V4'dR#R#rrTFN)rrrBrCrErD)r/r0r1s&& r3r:r:Os| AFF499Q< +.A} 1::diilQ& '55 1::diilQ& '556r5cVP^,p\\P!V4\P!V4,V4'dR#R#rrTN)rCrrintegerrEr/r0ris&& r3r:r:Ys9 ! A 199Qr5cVP^,p\\P!V^, 4\P!V^,4,V4'dR#R#r)rCrrrrrs&& r3r:r:sD ! A 1==Q !--A"6 6 DDEr5cd\\P!VP^,4V4#rq)rrrBrCr9s&&r3r:r:s qvvdiil#[ 11r5cR#r7rRr9s&&r3r:r:rtr5cx\\P!V4\P!V4,V4#r7)rrrDnegative_infiniter9s&&r3r:r:( qzz$!"5"5d";;[ IIr5cx\\P!V4\P!V4,V4#r7)rrrEpositive_infiniter9s&&r3r:r:rr5c\\P!V4\P!V4,\P!V4,\P !V4,V4#r7)rrrrDrErr9s&&r3r:r:sM  D!AJJt$44qzz$7GG!J]J]^bJcc r5c\\P!V4\P!V4,\P!V4,V4#r7)rrrrDrzr9s&&r3r:r:s;  D!AJJt$44qvvd|C r5c\\P!V4\P!V4,\P!V4,V4#r7)rrrzrErr9s&&r3r:r:s;  t qzz$''!*=*=d*CC r5N)7__doc__sympy.assumptionsrr sympy.corerrrrrr sympy.core.logicr r r sympy.core.numbersr rrrrsympy.functionsrrrrrrrrsympy.matricesrr"sympy.matrices.expressions.matexprrsympy.multipledispatchrpredicates.orderrrr r!r"r#r$r%r&r'r(r4registerr: register_manyr~objectrRr5r3rs%44;;;;LLL-<8    .E"<#<D!" C !.C  ! C ;!;.  m45C  ! u%&t$%4 ! 5! ;" ;3  3 32 235 53   ))HHt$% u%&&D!" E"<#<C  ! C !&C !&C 9!9 C !I&' M*+C -!-E"#K()M*+ D!6"6D!"D!" D!2"2C ! ##F+J,J ##F+J,J ""6*+&&v./&&v./r5