Status: Accepted
Owner: smichr
Labels: Type-Defect Priority-Critical
New issue 1556 by smichr: evalf for (a+i*b)*(c+~0i) => ac + ~0i instead of
ac + ibc
http://code.google.com/p/sympy/issues/detail?id=1556
When a complex number multiplies another number that has an insignificant
complex part, the result also has almost no significant imaginary part.
This snippet...
###
from sympy import *
x1,x2,x0=var('x1 x2 x0');
d={x2: (-1)**(S(6)/7), x1: (-1)**(S(4)/7), x0: (-1)**(S(2)/7)};
eq2=(x0*(1 + x1*(1 + x2)));
print x0.subs(d).evalf(),'*',(1 + x1*(1 + x2)).subs(d).evalf(),'='
print eq2.subs(d).expand().evalf(),'after expansion'
print eq2.subs(d).evalf(chop=True),'with chop=True'
print eq2.subs(d).evalf(),'with just evalf()'
###
generates...
(0.623489801858733 + 0.78183148246803*I) * (0.554958132087371 + .0e-23*I)
= 0.346010735815048 + 0.433883739117558*I after expansion
= 0.346010735815048 + 0.433883739117558*I with chop=True
= 0.346010735815048 + .0e+0*I with just evalf()
I wonder if the evalf.cmul routine which multiplies two complex numbers
should stop looking at the re and im parts of the number (picking the
smallest accuracy for each) and instead only look at the overall
uncertainty of each number, picking the smallest uncertainty *there* and
then assign that to the re and im parts of the result.
I can understand losing significance when finding a difference in two
numbers, but when adding (the cross terms of the complex product) you
shouldn't be losing digits.
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