Sympy polynomials with `mpfr` coefficients?

Question

I want to use Sympy's polynomials, but I also want to use higher-precision coefficients.

Just Doing It seems to give me polynomials with sympy.core.numbers.float coefficients.

import sympy
from sympy import Poly
from sympy.abc import x
from gmpy2 import mpfr, get_context

get_context().precision = 150

#float64 can't tell this from 1.0
one_and_change = mpfr('1.0000000000000000000000000000000000001')
#mpfr('1.0000000000000000000000000000000000001000000005',150)

p = [one_and_change]
px = Poly(p, x)

print(px)
# Poly(1.0, x, domain='RR')
print(px.is_one)
# True
print(type(px.all_coeffs()[0]))
# <class 'sympy.core.numbers.Float'>

I've also tried sympy.mpmath.mpf, with the same results.

This also didn't work:[1]

domain = sympy.polys.domains.realfield.RealField(150)
px = Poly(p, x, domain=domain)
print(type(px.all_coeffs()[0]))
# <class 'sympy.core.numbers.Float'>

I don't think so. `Float` is Python-sized fixed-width IEEE floating point, isn't it? — leewz, Feb 27 '15 at 20:39
No, Float is a wrapper around mpmath.mpf, which is arbitrary precision. — asmeurer, Feb 27 '15 at 20:52
Alright, I figured it out thanks to looking for a way to set its precision. — leewz, Feb 27 '15 at 22:29

score 0 · Accepted Answer · answered Feb 27 '15 at 22:48

There are a few obstacles:

gmpy.mpfr has no ._sympy_ method, so it will be converted to float in an intermediate step.
sympy.Poly, by default, uses sympy.polys.domain.RR for floating point coefficients, and will use it to convert.
RR, when it loads, uses 53 as its precision, and ignores mpmath.mp.precision.
When converting, RR uses RR.precision and ignores the argument's precision.

Solution:

Coefficients must be a Sympy type (e.g. sympy.Float, which has extended precision).
For the domain, one of the following:
- Set sympy.polys.domain.RR._context.prec = my_precision.
- Pass domain='EX', which doesn't do conversion.
- Pass in a custom domain (such as sympy.polys.domains.realfield.RealField(150)).

Glad you figured it out. Most of these should be considered bugs. — asmeurer, Mar 02 '15 at 17:26
I consider the first an obvious missing feature. Second is fine, except that it leads to the others. Not sure about the third. I think the fourth should be considered a bug, but maybe there's a reason for it. — leewz, Mar 07 '15 at 08:37

Sympy polynomials with `mpfr` coefficients?

1 Answers1