#11513: add _is_numerically_zero() method to symbolic expressions
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Reporter: burcin | Owner: burcin
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.8
Component: symbolics | Keywords: sd35.5
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by burcin):
Replying to [comment:7 zimmerma]:
> I'm puzzled about this ticket. Why doesn't the {{{is_zero}}} method
suffice? As said by Karl-Dieter,
> for general expressions the problem is undecidable, thus if you want to
check expressions that
> *reduce* to zero, the name of the method should reflect the fact that
there could be false
> negatives.
Hi Paul, I wanted to ask you about this in Warwick. I got caught up in the
linear algebra stuff and this slipped my mind.
`is_zero()` usually ends up calling maxima, which is very slow especially
in the context of automatic evaluation of symbolic functions.
At the moment, many symbolic functions (see
`sage/functions/generalized.py` for example) use code similar to the
following to test if an argument is zero within a reasonable time: (BTW,
this code should not initialize `CIF` on every call.)
{{{
try:
approx_x = ComplexIntervalField()(x)
if bool(approx_x.imag() == 0): # x is real
if bool(approx_x.real() == 0): # x is zero
return None
else:
return 0
except: # x is symbolic
pass
}}}
The reason for this ticket was to move this to a separate function to
avoid code duplication. If this function can detect `pi + (pi - 1)*pi -
pi^2 == 0` or `(pi - 1)*x - pi*x + x == 0` it would be even better. In
this context, false negatives are not a problem. We should just avoid
false positives. It's also OK if this test is not purely numeric. Any
suggestions for a better name for this function is also welcome of course.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11513#comment:8>
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