sagemathgh-40265: Migrate from Maxima pexpect interface to ECL interface
    
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<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
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Fixes sagemath#17753 and fixes sagemath#30071 by
migrating the last usages of the pexpect interface to `maxima_lib`.

### 📝 Checklist

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- [ ] The title is concise and informative.
- [ ] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: sagemath#40265
Reported by: Tobias Diez
Reviewer(s): Dima Pasechnik, nbruin, Tobias Diez, user202729, Vincent Macri

Author: Release Manager

src/doc/en/constructions/plotting.rst

@@ -214,7 +214,7 @@ Terminal application.)
 ::
 
     sage: maxima.eval('load("plotdf");')
-    '".../share/maxima.../share/dynamics/plotdf.lisp"'
+    .../share/maxima.../share/dynamics/plotdf.lisp...
     sage: maxima.eval('plotdf(x+y,[trajectory_at,2,-0.1]); ')  # not tested
 
 This plots a direction field (the plotdf Maxima package was also

src/doc/en/developer/coding_basics.rst

@@ -186,14 +186,6 @@ included in one of the following places:
   :func:`importlib.resources.as_file`. It should be imported in the
   same way as shown above.
 
-- Older code in the Sage library accesses
-  the package data in more direct ways. For example,
-  :sage_root:`src/sage/interfaces/maxima.py` uses the file
-  :sage_root:`src/sage/interfaces/maxima.lisp` at runtime, so it
-  refers to it as::
-
-    os.path.join(os.path.dirname(__file__), 'sage-maxima.lisp')
-
 - In an appropriate subdirectory of :sage_root:`src/sage/ext_data/`.
   (At runtime, it is then available in the directory indicated by
   ``SAGE_EXTCODE``).  For example, if ``file`` is placed in

src/doc/en/reference/calculus/index.rst

@@ -56,7 +56,6 @@ Internal functionality supporting calculus
 - :doc:`sage/symbolic/expression_conversions`
 - :doc:`sage/symbolic/benchmark`
 - :doc:`sage/symbolic/random_tests`
-- :doc:`sage/symbolic/maxima_wrapper`
 - :doc:`External integrators <sage/symbolic/integration/external>`
 - :doc:`External interpolators <sage/calculus/interpolators>`
 
@@ -94,7 +93,6 @@ Internal functionality supporting calculus
    sage/calculus/interpolators
    sage/calculus/functions
    sage/calculus/var
-   sage/symbolic/maxima_wrapper
    sage/symbolic/operators
    sage/symbolic/benchmark
    sage/symbolic/random_tests

src/sage/calculus/calculus.py

@@ -349,6 +349,10 @@
 Note that ``x`` is still ``x``, since the
 maxima used by the calculus package is different than the one in
 the interactive interpreter.
+Clear the maxima variables to avoid interference with other tests::
+
+    sage: maxima('kill(x,y)')
+    done
 
 Check to see that the problem with the variables method mentioned
 in :issue:`3779` is actually fixed::
@@ -395,7 +399,7 @@
 Check if maxima has redundant variables defined after initialization,
 see :issue:`9538`::
 
-    sage: maxima = sage.interfaces.maxima.maxima
+    sage: maxima = sage.interfaces.maxima_lib.maxima
     sage: maxima('f1')
     f1
     sage: sage.calculus.calculus.maxima('f1')
@@ -419,26 +423,23 @@
 """
 
 import re
+from types import FunctionType
+
 from sage.arith.misc import algebraic_dependency
+from sage.interfaces.maxima_lib import maxima
+from sage.misc.latex import latex
+from sage.misc.parser import LookupNameMaker, Parser
+from sage.rings.cc import CC
 from sage.rings.integer import Integer
 from sage.rings.rational_field import QQ
 from sage.rings.real_double import RealDoubleElement
 from sage.rings.real_mpfr import RR, create_RealNumber
-from sage.rings.cc import CC
-
-from sage.misc.latex import latex
-from sage.misc.parser import Parser, LookupNameMaker
 from sage.structure.element import Expression
-from sage.symbolic.ring import var, SR
-from sage.symbolic.symbols import symbol_table
 from sage.symbolic.function import Function
 from sage.symbolic.function_factory import function_factory
-from sage.symbolic.integration.integral import (indefinite_integral,
-        definite_integral)
-
-from sage.misc.lazy_import import lazy_import
-lazy_import('sage.interfaces.maxima_lib', 'maxima')
-from types import FunctionType
+from sage.symbolic.integration.integral import definite_integral, indefinite_integral
+from sage.symbolic.ring import SR, var
+from sage.symbolic.symbols import symbol_table
 
 
 ########################################################
@@ -667,6 +668,7 @@ def symbolic_sum(expression, v, a, b, algorithm='maxima', hold=False):
     elif algorithm == 'sympy':
         expression,v,a,b = (expr._sympy_() for expr in (expression, v, a, b))
         from sympy import summation
+
         from sage.interfaces.sympy import sympy_init
         sympy_init()
         result = summation(expression, (v, a, b))
@@ -920,6 +922,7 @@ def symbolic_product(expression, v, a, b, algorithm='maxima', hold=False):
     elif algorithm == 'sympy':
         expression,v,a,b = (expr._sympy_() for expr in (expression, v, a, b))
         from sympy import product as sproduct
+
         from sage.interfaces.sympy import sympy_init
         sympy_init()
         result = sproduct(expression, (v, a, b))
@@ -1674,7 +1677,11 @@ def mma_free_limit(expression, v, a, dir=None):
         sage: mma_free_limit(e^(-x), x, a=oo) # optional - internet
         0
     """
-    from sage.interfaces.mathematica import request_wolfram_alpha, parse_moutput_from_json, symbolic_expression_from_mathematica_string
+    from sage.interfaces.mathematica import (
+        parse_moutput_from_json,
+        request_wolfram_alpha,
+        symbolic_expression_from_mathematica_string,
+    )
     dir_plus = ['plus', '+', 'above', 'right']
     dir_minus = ['minus', '-', 'below', 'left']
     math_expr = expression._mathematica_init_()
@@ -1915,6 +1922,7 @@ def laplace(ex, t, s, algorithm='maxima'):
     elif algorithm == 'sympy':
         ex_sy, t, s = (expr._sympy_() for expr in (ex, t, s))
         from sympy import laplace_transform
+
         from sage.interfaces.sympy import sympy_init
         sympy_init()
         result = laplace_transform(ex_sy, t, s)
@@ -2100,6 +2108,7 @@ def inverse_laplace(ex, s, t, algorithm='maxima'):
     elif algorithm == 'sympy':
         ex_sy, s, t = (expr._sympy_() for expr in (ex, s, t))
         from sympy import inverse_laplace_transform
+
         from sage.interfaces.sympy import sympy_init
         sympy_init()
         result = inverse_laplace_transform(ex_sy, s, t)
@@ -2460,10 +2469,12 @@ def symbolic_expression_from_maxima_string(x, equals_sub=False, maxima=maxima):
 
     Make sure that we don't accidentally pick up variables in the maxima namespace (:issue:`8734`)::
 
-        sage: sage.calculus.calculus.maxima('my_new_var : 2')
+        sage: maxima('my_new_var : 2')
         2
         sage: var('my_new_var').full_simplify()
         my_new_var
+        sage: maxima('kill(my_new_var)')
+        done
 
     ODE solution constants are treated differently (:issue:`16007`)::
 

src/sage/calculus/desolvers.py

@@ -71,19 +71,15 @@
 #                  https://www.gnu.org/licenses/
 ##########################################################################
 
-import shutil
 import os
+import shutil
 
-from sage.interfaces.maxima import Maxima
+from sage.calculus.functional import diff
+from sage.interfaces.maxima_lib import maxima
 from sage.misc.functional import N
 from sage.rings.real_mpfr import RealField
 from sage.structure.element import Expression
 
-from .functional import diff
-
-
-maxima = Maxima()
-
 
 def fricas_desolve(de, dvar, ics, ivar):
     r"""
@@ -156,8 +152,8 @@ def fricas_desolve_system(des, dvars, ics, ivar):
         [x(t) == cos(t)^2 + sin(t)^2 + 2*sin(t), y(t) == -2*cos(t) + 1]
     """
     from sage.interfaces.fricas import fricas
-    from sage.symbolic.ring import SR
     from sage.symbolic.relation import solve
+    from sage.symbolic.ring import SR
     ops = [dvar.operator() for dvar in dvars]
     y = fricas(des).solve(ops, ivar).sage()
     basis = y["basis"]
@@ -1364,9 +1360,9 @@ def desolve_rk4_inner(de, dvar):
             return plot_slope_field(de, (ivar, XMIN, XMAX), (dvar, YMIN, YMAX)) + R
 
     if not (isinstance(dvar, Expression) and dvar.is_symbol()):
-        from sage.symbolic.ring import SR
         from sage.calculus.functional import diff
         from sage.symbolic.relation import solve
+        from sage.symbolic.ring import SR
         if isinstance(de, Expression) and de.is_relational():
             de = de.lhs() - de.rhs()
         # consider to add warning if the solution is not unique
@@ -1614,8 +1610,9 @@ def desolve_odeint(des, ics, times, dvars, ivar=None, compute_jac=False, args=()
     """
 
     from scipy.integrate import odeint
-    from sage.ext.fast_eval import fast_float
+
     from sage.calculus.functions import jacobian
+    from sage.ext.fast_eval import fast_float
 
     def desolve_odeint_inner(ivar):
         # one-dimensional systems:
@@ -1838,9 +1835,9 @@ def desolve_tides_mpfr(f, ics, initial, final, delta, tolrel=1e-16, tolabs=1e-16
     import subprocess
     if subprocess.call('command -v gcc', shell=True, stdout=subprocess.PIPE, stderr=subprocess.PIPE):
         raise RuntimeError('Unable to run because gcc cannot be found')
-    from sage.interfaces.tides import genfiles_mpfr
-    from sage.functions.other import ceil
     from sage.functions.log import log
+    from sage.functions.other import ceil
+    from sage.interfaces.tides import genfiles_mpfr
     from sage.misc.temporary_file import tmp_dir
     tempdir = tmp_dir()
     intfile = os.path.join(tempdir, 'integrator.c')

src/sage/categories/pushout.py

@@ -3936,6 +3936,7 @@ def __init__(self, box):
         TESTS::
 
             sage: from sage.categories.pushout import BlackBoxConstructionFunctor
+            sage: from sage.interfaces.maxima_lib import maxima
             sage: FG = BlackBoxConstructionFunctor(gap)
             sage: FM = BlackBoxConstructionFunctor(maxima)                              # needs sage.symbolic
             sage: FM == FG                                                              # needs sage.libs.gap sage.symbolic
@@ -3967,6 +3968,7 @@ def __eq__(self, other):
         TESTS::
 
             sage: from sage.categories.pushout import BlackBoxConstructionFunctor
+            sage: from sage.interfaces.maxima_lib import maxima
             sage: FG = BlackBoxConstructionFunctor(gap)
             sage: FM = BlackBoxConstructionFunctor(maxima)                              # needs sage.symbolic
             sage: FM == FG       # indirect doctest                                     # needs sage.libs.gap sage.symbolic
@@ -3986,6 +3988,7 @@ def __ne__(self, other):
         EXAMPLES::
 
             sage: from sage.categories.pushout import BlackBoxConstructionFunctor
+            sage: from sage.interfaces.maxima_lib import maxima
             sage: FG = BlackBoxConstructionFunctor(gap)
             sage: FM = BlackBoxConstructionFunctor(maxima)                              # needs sage.symbolic
             sage: FM != FG       # indirect doctest                                     # needs sage.libs.gap sage.symbolic

src/sage/features/sagemath.py

@@ -1116,7 +1116,6 @@ def __init__(self):
                               PythonModule('sage.interfaces.maple'),
                               PythonModule('sage.interfaces.mathematica'),
                               PythonModule('sage.interfaces.mathics'),
-                              PythonModule('sage.interfaces.maxima'),
                               PythonModule('sage.interfaces.maxima_abstract'),
                               PythonModule('sage.interfaces.maxima_lib'),
                               PythonModule('sage.interfaces.qepcad'),

src/sage/functions/orthogonal_polys.py

@@ -396,13 +396,12 @@
 import warnings
 
 import sage.rings.abc
-
 from sage.arith.misc import rising_factorial
 from sage.misc.lazy_import import lazy_import
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.symbolic.function import BuiltinFunction, GinacFunction
 from sage.structure.element import Expression, parent
+from sage.symbolic.function import BuiltinFunction, GinacFunction
 
 lazy_import('sage.functions.other', ['factorial', 'binomial'])
 
@@ -2444,8 +2443,8 @@ def _eval_(self, n, x, *args, **kwds):
             sage: laguerre(-9,2)                                                        # needs sage.symbolic
             66769/315*e^2
         """
-        from sage.rings.integer import Integer
         from sage.functions.log import exp
+        from sage.rings.integer import Integer
         ret = self._eval_special_values_(n, x)
         if ret is not None:
             return ret
@@ -2558,14 +2557,15 @@ def __init__(self):
 
         EXAMPLES::
 
+            sage: from sage.interfaces.maxima_lib import maxima
             sage: # needs sage.symbolic
             sage: a, n, x = var('a, n, x')
             sage: gen_laguerre(x, x, x)._sympy_()                                       # needs sympy
             assoc_laguerre(x, x, x)
             sage: maxima(gen_laguerre(1, 2, x, hold=True))
             3*(1-_SAGE_VAR_x/3)
             sage: maxima(gen_laguerre(n, a, gen_laguerre(n, a, x)))
-            gen_laguerre(_SAGE_VAR_n,_SAGE_VAR_a, gen_laguerre(_SAGE_VAR_n,_SAGE_VAR_a,_SAGE_VAR_x))
+            gen_laguerre(_SAGE_VAR_n,_SAGE_VAR_a,gen_laguerre(_SAGE_VAR_n,_SAGE_VAR_a,_SAGE_VAR_x))
 
         TESTS::
 
@@ -2914,8 +2914,8 @@ def _eval_(self, n, x, b, c, *args, **kwds):
         if kwds.get('hold', False):
             return None
         if n not in ZZ or n < 0:
-            from sage.functions.hypergeometric import hypergeometric
             from sage.functions.gamma import gamma
+            from sage.functions.hypergeometric import hypergeometric
             return gamma(b + n) / gamma(b) * hypergeometric([-n, -x], [b], 1 - 1/c)
         try:
             return self.eval_formula(n, x, b, c)

src/sage/interfaces/all.py

@@ -1,14 +1,8 @@
 # interfaces to other interpreters
 
-# import problems
-try:
-    # from maxima_lib import maxima_lib
-    from sage.interfaces.maxima import maxima, Maxima
-except ImportError:
-    pass
-
 from sage.misc.lazy_import import lazy_import
 
+lazy_import('sage.interfaces.maxima', 'maxima')
 lazy_import('sage.interfaces.sage0', ['sage0', 'sage0_version', 'Sage'])
 lazy_import('sage.interfaces.axiom', ['Axiom', 'axiom'])
 lazy_import('sage.interfaces.ecm', ['ECM', 'ecm'])