move pexpect-maxima code to maxima_lib

[rwst]

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 speed up Maxima computations by using more of maxima_calculus.eval() #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() (Extend normalize() and use it instead of Maxima in simplify_rational() #21335), simplify_log(), expand_log(), factor() (Replace Maxima with Pynac/Singular in Expression.factor() #23835), solve(), sum()
• symbolic/maxima_wrapper.py: *
• calculus/calculus.py: symbolic_expression_from_maxima_string() called by factor() (Replace Maxima with Pynac/Singular in Expression.factor() #23835) and indirectly by solve()

Already done:

• Expression.coefficients() and poly(): (both rewrite buggy Expression.coefficients() without Maxima #20455)
• functions/orthogonal_polys.py (Replace all pexpect-maxima calls in function/orthogonal-polys #22325): hermite() (ECL crash with Hermite polynomials #20297), jacobi_P() (Jacobi P polynomials without pexpect-maxima #22326), laguerre() (symbolic Laguerre / associated Laguerre polynomials #17151), legendre_P/Q() (symbolic Legendre / associated Legendre functions / polynomials #16813), ultraspherical() (crash with ultraspherical polynomials #20428)
• functions/special.py: SphericalHarmonic._eval_() (Fix crash and remove pexpect-Maxima usage in Y(m,n) #20939)
• combinat/combinat.py: euler_number() (see Euler numbers revamp #17770 and Euler numbers via flint #20763)
• geometry/lattice_polytope.py: positive_integer_relations() avoid using maxima simplex algo in lattice_polytope #20766

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

Component: interfaces

Issue created by migration from https://trac.sagemath.org/ticket/17753

[dimpase]

comment:17

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

[rwst]

comment:18

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]

comment:20

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.