Refine¶
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sympy.assumptions.refine.
refine
(expr, assumptions=True)[source]¶ Simplify an expression using assumptions.
Gives the form of expr that would be obtained if symbols in it were replaced by explicit numerical expressions satisfying the assumptions.
Examples
>>> 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
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sympy.assumptions.refine.
refine_Pow
(expr, assumptions)[source]¶ Handler for instances of Pow.
>>> from sympy import Symbol, 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)
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sympy.assumptions.refine.
refine_Relational
(expr, assumptions)[source]¶ Handler for Relational
>>> from sympy.assumptions.refine import refine_Relational >>> from sympy.assumptions.ask import Q >>> from sympy.abc import x >>> refine_Relational(x<0, ~Q.is_true(x<0)) False
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sympy.assumptions.refine.
refine_abs
(expr, assumptions)[source]¶ Handler for the absolute value.
Examples
>>> from sympy import Symbol, Q, refine, 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
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sympy.assumptions.refine.
refine_atan2
(expr, assumptions)[source]¶ Handler for the atan2 function
Examples
>>> from sympy import Symbol, Q, refine, 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