#13645: better input handling for solve()
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Reporter: llpamies | Owner: burcin
Type: defect | Status: needs_review
Priority: trivial | Milestone: sage-5.9
Component: symbolics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Burcin Erocal | Merged in:
Dependencies: | Stopgaps:
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Comment (by ppurka):
Here is an example code which can convert the polynomial to a symbolic
expression.
{{{
#!python
R.<y,z> = RR[]
a = y^2 + 2 * z^2
is_Polynomial(a) # test for polynomial a
False
is_MPolynomial(a) # test for multinomial a
True
va = a.variables()
vSR = map(SR, va)
aSR = a.subs({_x: _xs for _x,_xs in zip(va, vSR)})
type(aSR)
<type 'sage.symbolic.expression.Expression'>
solve(aSR, *vSR)
([y == -I*sqrt(2)*z, y == I*sqrt(2)*z], [1, 1])
}}}
This can be done internally in the solve function.
There is only one problem to this approach. Polynomial rings can be over
other fields, for instance finite fields, too. The output of solve in this
case doesn't really make much sense because it loses the information that
the elements are in finite fields.
{{{
sage: F.<b> = GF(4)
sage: R.<y,z> = F[]
sage: a = y^2 + b* z^2
sage: type(a)
<type
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
sage: is_MPolynomial(a)
True
sage: va = a.variables()
sage: vSR = map(SR, va)
sage: aSR = a.subs({_x: _xs for _x,_xs in zip(va, vSR)})
sage: type(aSR)
<type 'sage.symbolic.expression.Expression'>
sage: aSR
y^2 + b*z^2
sage: solve(aSR, *vSR)
([y == -sqrt(-b)*z, y == sqrt(-b)*z], [1, 1])
sage: aSR.coeffs(z)
[[y^2, 0], [b, 2]]
sage: type(aSR.coeffs(z)[1][0])
<type 'sage.symbolic.expression.Expression'>
}}}
So, we need some test to check whether the polynomial is defined only over
reals or complexes.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13645#comment:7>
Sage <http://www.sagemath.org>
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