Sympy-conversion of complex numbers

[mwageringel]

This ticket implements conversions to Sympy of elements of ComplexField, CDF and QuadraticNumberField(-1). This solves some inconsistencies with the unicode art of symbolic expressions involving complex numbers.

Most symbolic expressions use the Sympy symbol ⅈ for the unicode art of the imaginary unit, but some do not:

sage: unicode_art(sqrt(3) * I)  # correct
√3⋅ⅈ
sage: unicode_art(I)  # should use symbol ⅈ
I
sage: unicode_art(cos(I)), cos(I)  # should render the same
(1.54308063481524, cosh(1))
sage: unicode_art(SR(CC(1/3 + I)))  # should use symbol ⅈ
0.333333333333333 + 1.00000000000000*I
sage: unicode_art(SR(CDF(1/3 + I)))  # should use symbol ⅈ
0.3333333333333333 + 1.0*I

The underlying problem is that these complex numbers cannot be converted to Sympy, currently, which is what the unicode_art method of symbolic expressions would need. In that case, the fallback is the usual string representation, which does not use the symbol ⅈ. Hence, this is solved by implementing the conversions above.

Additionally, this ticket improves the conversion to Sympy of elements of RealField by taking into account the precision of the field.

sage: a = SR(RealField(100)(1/3))
sage: a, unicode_art(a)  # unicode art loses precision
(0.33333333333333333333333333333, 0.333333333333333)

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Note that other implementations of complex numbers (QQbar, CIF, CBF), that cannot meaningfully by converted to Sympy in general, are not affected by this ticket. For example, the following symbolic expressions still render the same:

sage: unicode_art(SR(QQbar(1 + I)))
I + 1
sage: unicode_art(SR(CBF(1/3 + I)))
[0.3333333333333333 +/- 7.04e-17] + 1.000000000000000*I

Depends on #28891

Component: symbolics

Keywords: sympy, unicode_art

Author: Markus Wageringel

Branch/Commit: a6ed554

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28903

[mwageringel]

Dependencies: #28891

[mwageringel]

Branch: u/gh-mwageringel/28903

[mwageringel]

comment:1

This branch is based on #28891 to avoid a merge conflict.

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New commits:

8bdd72d	28891: character art/sympy-conversion of symbolic series
7e7d3d3	28903: unicode_art/sympy-conversion of (symbolic) complex numbers

[mwageringel]

Author: Markus Wageringel

[mwageringel]

Commit: 7e7d3d3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

a6ed554

28903: unicode_art/sympy-conversion of (symbolic) complex numbers

[sagetrac-git]

Changed commit from 7e7d3d3 to a6ed554

[mwageringel]

comment:3

I added another test case:

sage: (10.0^400)._sympy_()  # used to be `inf`
1.00000000000000e+400

[tscrim]

comment:4

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[fchapoton]

comment:5

9.0 is out

[vbraun]

Changed branch from u/gh-mwageringel/28903 to a6ed554