CallableSymbolicExpressionRing over subrings of SR

[mkoeppe]

1. Currently, CallableSymbolicExpressionRing allows meaningless operations such as the following.

sage: f(t) = t
sage: f
t |--> t
sage: f * t
t |--> t^2

This should be changed so it gives:

_dummy |--> _dummy * t

f currently is an element of a CallableSymbolicExpressionRing, a ring over the base SR (the only allowed base for this class).

2. The design of CallableSymbolicExpressionRing has another critical flaw pointed out in Meta-ticket: Callable symbolic expressions #28434 (Syntax for callable symbolic expressions causes too much confusion) as "7. Addition confusion":

sage: f(x) = x^2
sage: g(x) = x^2
sage: var('t')
sage: h(t) = t^2
sage: f+g
x |--> 2*x^2
sage: f+h
(t, x) |--> t^2 + x^2

In this ticket:

• We remove the distinction between the CallableSymbolicExpressionRing instances based on the names of the argument variable names. Instead, they will be unique by number of arguments, and the set of non-argument symbols that appear in the definition.
• The element constructor substitutes the arguments in the expression by dummy variables, i.e., unique internal symbols that are only used for this purpose. The argument names are substituted back only in _repr_ and when converted into SR by SymbolicRing._element_constructor_
• We extend the class to support base rings that are subrings of SR. Then we change the default base ring of a callable expression to be the subring of SR that rejects all dummy variables.

Related:

• comparison of symbolic functions #18259 (comparison of symbolic functions)
• composition of symbolic subring functors #19949 (composition of symbolic subring functors)

CC: @rburing @slel @egourgoulhon @tscrim @dkrenn

Component: symbolics

Branch/Commit: u/mkoeppe/callablesymbolicexpressionring_over_subrings_of_sr @ f71de5b

Issue created by migration from https://trac.sagemath.org/ticket/32008

[mkoeppe]

Branch: u/mkoeppe/callablesymbolicexpressionring_over_subrings_of_sr

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b5a0bbe	Expression.function: Pass parent to CallableSymbolicExpressionRing as base ring
f71de5b	WIP coercion

[sagetrac-git]

Commit: f71de5b

[mkoeppe]

comment:4

With this version, we get:

sage: var('a b c')
(a, b, c)
sage: (a*b*c).function(a, b)
(a, b) |--> a*b*c
sage: _.parent()
Callable function ring with arguments (a, b) over Symbolic Subring rejecting the variables a, b
sage: (a*b*c).function(a, b) * b
TypeError: unsupported operand parent(s) for *: 'Callable function ring with arguments (a, b) over Symbolic Subring rejecting the variables a, b' and 'Symbolic Ring'
sage: (a*b*c).function(a, b) * SR.subring([x])(x)
(a, b) |--> a*b*c*x