abs(a+b)^2 == (a+b)^2

[sagetrac-jan]

sage: version()
'Sage Version 4.7, Release Date: 2011-05-23'
sage: var('a b', domain='real');
sage: A = abs((a+i*b))^2
sage: A
abs(a + I*b)^2
sage: imag(A)
0
sage: A.simplify_full()
a^2 + 2*I*a*b - b^2
sage: imag(A.simplify_full())
2*a*b

The last result is clearly wrong. abs() is real by definition. simplify_full() doesn't handle abs() correctly.

Demo Notebook: http://demo.sagenb.org/home/pub/181/

CC: @kcrisman @orlitzky

Component: symbolics

Keywords: maxima abs

Author: Karl-Dieter Crisman

Reviewer: Michael Orlitzky

Merged: sage-5.11.beta3

Issue created by migration from https://trac.sagemath.org/ticket/11668

[kcrisman]

comment:2

The exact place is

sage: A.simplify_radical()
a^2 + 2*I*a*b - b^2

This is how radcan in Maxima does this over the real domain, which simplify_radical temporarily makes us in.

I'm not sure what the best thing to do here is. Two ideas:

• Change so that we stay in domain:complex in Maxima, sort of missing the point of simplify_radical
• Give lots of warnings not to trust simplification because (like most simplification) it is not always true, but useful. (Sort of like how \sqrt{x^2}\neq x but sometimes it's useful to simplify it that way.)

I do not think we pass the domain information from the (Pynac) variables in any case, or if that would be very easy to do.

[kcrisman]

comment:3

This has been fixed by #12780.

sage: var('a b')
(a, b)
sage: A = abs((a+i*b))^2
sage: A.simplify_radical()
abs(a + I*b)^2
sage: imag(A)
0
sage: imag(A.simplify_full())
0

Patch probably coming up. This would also be dealt with by #12737, but that is orthogonal to having fixed the domain issues.

[kcrisman]

Author: Karl-Dieter Crisman

[orlitzky]

comment:5

Two minor things, can you use a,b = SR.var('a,b') to create the variables? That will eliminate one line of unrelated output. And just a style preference, since sage outputs the complex unit as I, I think it's a tiny bit more consistent to use that for input as well, but I'll take it either way.

[kcrisman]

Attachment: trac_11668.patch.gz

Based on 5.10.rc1

[kcrisman]

comment:6

Two minor things

Sure, no problem. I put the i instead of I just because I copied from the original example in the ticket, but that is unimportant. Thanks!

[orlitzky]

Reviewer: Michael Orlitzky

[jdemeyer]

Merged: sage-5.11.beta3