improve documentation for multivariate polynomial ideals

[malb]

After the patch was applied:

SCORE devel/sage-docday2/sage/rings/polynomial/multi_polynomial_ideal.py: 88% (40 of 45)

Missing doctests:
         * redSB(func)
         * wrapper(*args, **kwds)
         * _variety(T, V, v=None)
         * _macaulay2_(self, macaulay2=None)
         * groebner_fan(self, is_groebner_basis=False, symmetry=None, verbose=False)

I cannot write Macaulay2 doctests right now because the optional SPKG fails to install. Groebner fan also has issues.

Old:

----------------------------------------------------------------------
devel/sage-main/sage/rings/polynomial/multi_polynomial_ideal.py
SCORE devel/sage-main/sage/rings/polynomial/multi_polynomial_ideal.py: 68% (32 of 47)

Missing documentation:
         * is_MPolynomialIdeal(x)
         * __enter__(self)
         * __exit__(self, type, value, tb)
         * wrapper(*args, **kwds)
         * f(x,y)
         * _singular_groebner_basis(self)
         * _variety(T, V, v=None)


Missing doctests:
         * __init__(self, singular=singular_default)
         * redSB(func)
         * dimension(self)
         * genus(self)
         * syzygy_module(self)
         * reduced_basis(self)
         * _macaulay2_(self, macaulay2=None)
         * groebner_fan(self, is_groebner_basis=False, symmetry=None, verbose=False)


Possibly wrong (function name doesn't occur in doctests):
         * _magma_groebner_basis(self)
         * _contains_(self, f)
         * _macaulay2_groebner_basis(self)

----------------------------------------------------------------------

This patch does not increase the number of doctests very much but focuses on the quality of the doctests and documentation.

CC: @ncalexan

Component: documentation

Issue created by migration from https://trac.sagemath.org/ticket/2455

[malb]

Attachment: mpoly-ideal-docday.patch.gz

apply against code repository

[malb]

this patch adds a doctest for the groebner_fan method

[malb]

comment:2

Attachment: mpoly-ideal-gfan.patch.gz

[ncalexan]

comment:3

This looks good to me, with one major exception: all the Groebner's were changed to "Gröbner" and it doesn't display correctly for me. I think we should stick to standard transliteration or latex.

I say apply after fixing that Groebner business.

[malb]

comment:5

Replying to @ncalexan:

This looks good to me, with one major exception: all the Groebner's were changed to "Gröbner" and it doesn't display correctly for me. I think we should stick to standard transliteration or latex.

This is a Trac issue. It prints correctly (as "Gröbner") in my shell, in the reference manual PDF and in the Sage notebook.

[ncalexan]

comment:6

I downloaded the patch and it displays wrong in my emacs and in my shell.