move pexpect-maxima code to maxima_lib

[rws]

This metaticket tracks efforts to remove the usage of pexpect for calling maxima, either by using maxima_lib or replacing it altogether. Code that is dependent on the maxima expect interface is in:

• doc/ and other places using maxima.eval() (see #30071)
• calculus/desolvers.py: desolve_*()
• functions/piecewise.py: piecewise.convolution()
• matrix/matrix1.pyx: Matrix._maxima_init_()
• matrix/matrix_symbolic_dense.pyx: Matrix_symbolic_dense.exp()
• structure/sage_object.pyx: SageObject._maxima_(), _maxima_init_()
• symbolic/assumptions.py: GenericDeclaration.assume()
• symbolic/expression.pyx: Ex.assume(), forget(), assume_str(), assert(), expand_trig(), reduce_trig(), maxima_methods(), rectform(), simplify(), simplify_real(), simplify_rational() (#21335), simplify_log(), expand_log(), factor() (#23835), solve(), sum()
• symbolic/maxima_wrapper.py: *
• calculus/calculus.py: symbolic_expression_from_maxima_string() called by factor() (#23835) and indirectly by solve()

Already done:

• Expression.coefficients() and poly(): (both #20455)
• functions/orthogonal_polys.py (#22325): hermite() (#20297), jacobi_P() (#22326), laguerre() (#17151), legendre_P/Q() (#16813), ultraspherical() (#20428)
• functions/special.py: SphericalHarmonic._eval_() (#20939)
• combinat/combinat.py: euler_number() (see #17770 and #20763)
• geometry/lattice_polytope.py: positive_integer_relations() #20766

This can be considered part of the metaticket #16688. See also ​http://trac.sagemath.org/wiki/symbolics/maxima

[dimpase]

I am confused about the meaning of Absolute vs Optional dependencies mentioned on the wiki, could you elaborate?

[rws]

As far as I recall, I named that code optional that I thought is only executed when certain non-default keywords are given. Looking at the three items,

• symbolic_expression_from_maxima_string is only used in doctests of calculs.py but is absolutely imported by ex.factor() and in relation.py:string_to_list_of_solutions() which is used by solve() so the assessment was wrong
• stirling_number2 in combinat/combinat.py: default is not Maxima, okay
• integration/*: certainly Maxima is called, so it's wrong

Thanks for asking, I'm changing it.

[dimpase]

there are places where maxima.eval instead of considerably faster maxima_calculus.eval is used for no good reason, e.g. in src/doc, see #30071.