a >> from sympy import refine, sqrt, Q >>> from sympy.abc import x >>> refine(sqrt(x**2), Q.real(x)) Abs(x) >>> refine(sqrt(x**2), Q.positive(x)) x >>> refine(Q.real(x), Q.positive(x)) True >>> refine(Q.positive(x), Q.real(x)) Q.positive(x) See Also ======== sympy.simplify.simplify.simplify : Structural simplification without assumptions. sympy.assumptions.ask.ask : Query for boolean expressions using assumptions. csg|]}t|qS)refine).0arg assumptionsrh/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/assumptions/refine.py 3zrefine.. _eval_refineN) isinstancerZis_Atomargsfunchasattrr __class____name__ handlers_dictgetrr)exprrrZref_exprnamehandlerZnew_exprrrrr s&%       rcsddlm}|jd}tt|r>ttt|r>|Stt|rT| St|t rfdd|jD}g}g}|D]*}t||r| |jdq~| |q~t ||t |SdS)aF Handler for the absolute value. Examples ======== >>> from sympy import Q, Abs >>> from sympy.assumptions.refine import refine_abs >>> from sympy.abc import x >>> refine_abs(Abs(x), Q.real(x)) >>> refine_abs(Abs(x), Q.positive(x)) x >>> refine_abs(Abs(x), Q.negative(x)) -x rAbscsg|]}tt|qSr)rabs)rarrrrarzrefine_abs..N) $sympy.functions.elementary.complexesr%rr rrealr negativerrappend)r!rr%rrZnon_absZin_absirrr refine_absFs"     r.cCsddlm}ddlm}t|j|r`tt|jj d|r`tt |j |r`|jj d|j Stt|j|r|jj rtt |j |rt |j|j Stt|j |r||jt |j|j St|j trt|jtrt |jj|jj |j S|jtjur|j jr|}|j \}}t|}t}t}t|} |D]@} tt | |rh|| ntt| |rF|| qF||8}t|dr||8}|tjd} n||8}|d} | |kst|| kr|| |jt|}d|j } tt | |r&| r&| |j9} | jr| \} }|jr|jtjurtt|j |r| dd} tt | |r|j|j Stt| |r|j|j dS|j|j | S||kr|SdS)as Handler for instances of Pow. Examples ======== >>> from sympy import Q >>> from sympy.assumptions.refine import refine_Pow >>> from sympy.abc import x,y,z >>> refine_Pow((-1)**x, Q.real(x)) >>> refine_Pow((-1)**x, Q.even(x)) 1 >>> refine_Pow((-1)**x, Q.odd(x)) -1 For powers of -1, even parts of the exponent can be simplified: >>> refine_Pow((-1)**(x+y), Q.even(x)) (-1)**y >>> refine_Pow((-1)**(x+y+z), Q.odd(x) & Q.odd(z)) (-1)**y >>> refine_Pow((-1)**(x+y+2), Q.odd(x)) (-1)**(y + 1) >>> refine_Pow((-1)**(x+3), True) (-1)**(x + 1) rr$)signN)r(r%Zsympy.functionsr/rbaser rr)rZevenexpZ is_numberr&Zoddr r r NegativeOneZis_AddZ as_coeff_addsetlenaddOnercould_extract_minus_signZ as_two_termsZis_Powinteger)r!rr%r/oldZcoeffZtermsZ even_termsZ odd_termsZinitial_number_of_termstZ new_coeffe2r-prrr refine_Powlsl               r?cCs*ddlm}|j\}}tt|t|@|r<|||Stt|t|@|rh|||tj Stt|t|@|r|||tj Stt |t|@|rtj Stt|t |@|rtj dStt|t |@|rtj dStt |t |@|r"tj S|SdS)a Handler for the atan2 function. Examples ======== >>> from sympy import Q, atan2 >>> from sympy.assumptions.refine import refine_atan2 >>> from sympy.abc import x, y >>> refine_atan2(atan2(y,x), Q.real(y) & Q.positive(x)) atan(y/x) >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.negative(x)) atan(y/x) - pi >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.negative(x)) atan(y/x) + pi >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.negative(x)) pi >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.zero(x)) pi/2 >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.zero(x)) -pi/2 >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.zero(x)) nan r)atanr0N) Z(sympy.functions.elementary.trigonometricr@rr rr)positiver*rPizeroNaN)r!rr@yxrrr refine_atan2s"     rGcCs>|jd}tt||r|Stt||r4tjSt||S)a  Handler for real part. Examples ======== >>> from sympy.assumptions.refine import refine_re >>> from sympy import Q, re >>> from sympy.abc import x >>> refine_re(re(x), Q.real(x)) x >>> refine_re(re(x), Q.imaginary(x)) 0 r)rr rr) imaginaryrZero _refine_reimr!rrrrr refine_res  rLcCsF|jd}tt||r tjStt||r>> from sympy.assumptions.refine import refine_im >>> from sympy import Q, im >>> from sympy.abc import x >>> refine_im(im(x), Q.real(x)) 0 >>> refine_im(im(x), Q.imaginary(x)) -I*x r) rr rr)rrIrH ImaginaryUnitrJrKrrr refine_ims   rNcCs:|jd}tt||r tjStt||r6tjSdS)a" Handler for complex argument Explanation =========== >>> from sympy.assumptions.refine import refine_arg >>> from sympy import Q, arg >>> from sympy.abc import x >>> refine_arg(arg(x), Q.positive(x)) 0 >>> refine_arg(arg(x), Q.negative(x)) pi rN)rr rrArrIr*rB)r!rZrgrrr refine_arg*s  rOcCs.|jdd}||kr*t||}||kr*|SdS)NT)complex)expandr)r!rZexpandedZrefinedrrrrJAs   rJcCs|jd}tt||r tjStt|rZtt||rDtjStt ||rZtj Stt |r| \}}tt||rtj Stt ||rtj S|S)a* Handler for sign. Examples ======== >>> from sympy.assumptions.refine import refine_sign >>> from sympy import Symbol, Q, sign, im >>> x = Symbol('x', real = True) >>> expr = sign(x) >>> refine_sign(expr, Q.positive(x) & Q.nonzero(x)) 1 >>> refine_sign(expr, Q.negative(x) & Q.nonzero(x)) -1 >>> refine_sign(expr, Q.zero(x)) 0 >>> y = Symbol('y', imaginary = True) >>> expr = sign(y) >>> refine_sign(expr, Q.positive(im(y))) I >>> refine_sign(expr, Q.negative(im(y))) -I r)rr rrCrrIr)rAr8r*r4rHZ as_real_imagrM)r!rrZarg_reZarg_imrrr refine_signLs  rRcCsHddlm}|j\}}}tt||rD||r8|S||||SdS)aU Handler for symmetric part. Examples ======== >>> from sympy.assumptions.refine import refine_matrixelement >>> from sympy import MatrixSymbol, Q >>> X = MatrixSymbol('X', 3, 3) >>> refine_matrixelement(X[0, 1], Q.symmetric(X)) X[0, 1] >>> refine_matrixelement(X[1, 0], Q.symmetric(X)) X[0, 1] r) MatrixElementN)Z"sympy.matrices.expressions.matexprrSrr rZ symmetricr9)r!rrSZmatrixr-jrrrrefine_matrixelementus    rU)r%r atan2reZimrr/rSN)T)typingrZtDictrZ sympy.corerrrrrr r Zsympy.core.logicr Zsympy.logic.boolalgr Zsympy.assumptionsr rrr.r?rGrLrNrOrJrRrUrrrrrs.$   <&d- )