I am a newbie in Sage. I would like to do complex-expand (Mathematica command) in Sage. Please tell me how to implement? Say, there is a function like (1/(a+b.I)), I wish to symbolical output (a-b.I)/(a^2+b^2). Here, we regard a and b as real numbers. thanks in advance for help
Use z.simplify_rectform(None).factor():
sage: a, b = var('a b', domain='real')
sage: z = 1/(a + I*b)
sage: z.simplify_rectform(None)
a/(a^2 + b^2) - I*b/(a^2 + b^2)
sage: z.simplify_rectform(None).factor()
(a - I*b)/(a^2 + b^2)
Note that z.simplify_rectform(None) is a shortcut for z.simplify_rectform(complexity_measure=None). Type z.simplify_rectform? for more details.
Hi, welcome. Don't know how far the next works, but while nobody answers, consider:
var('x,y',domain=RR)
def csimp(complex_poly):
if type(imag_part(denominator(complex_poly))) == sage.symbolic.expression.Expression:
return numerator(complex_poly)\
*(conjugate(denominator(complex_poly)))/(norm(denominator(complex_poly))^2)
else:
return (complex_poly)
csimp(1/z) # (x - I*y)/(x^2 + y^2)^2
Running :
var("a, b", domain="real")
z=1/(a+I*b)
(z.real()+I*z.imag()).factor()
prints :
(a - I*b)/(a^2 + b^2)
HTH,
Asked: 2024-07-10 00:17:06 +0100
Seen: 170 times
Last updated: Jul 10
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