symbolic_expression: Better handling of vectors and matrices

[kcrisman]

sage: symbolic_expression(vector([1,2]))
<boom>
TypeError:

This is pretty uninformative, esp. when it is in the midst of a larger computation.

Instead of working on the error message, we add some code to handle vector and matrix inputs.

Depends on #14270

CC: @tscrim

Component: symbolics

Author: Matthias Koeppe

Branch/Commit: 0623d79

Reviewer: Karl-Dieter Crisman, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/16761

[mkoeppe]

Dependencies: #32103

[mkoeppe]

Branch: u/mkoeppe/error_message_bad_when_trying_to_make_vector_symbolic_expression

[mkoeppe]

New commits:

e523ac0	sage.calculus.all.symbolic_expression: Handle callables
d2e8c8f	symbolic_expression: Update doctest output
0b9408e	Merge #32103
5e3e34f	symbolic_expression: Handle vectors and matrices; fix result parent for list/tuple of length 0

[mkoeppe]

Description changed:

--- 
+++ 
@@ -6,9 +6,5 @@
 ```
 This is pretty uninformative, esp. when it is in [the midst of a larger computation](http://ask.sagemath.org/question/23690/how-to-fit-data-to-an-arrhenius-equation/).
 
-I'm not suggesting we make a vector a symbolic expression, though of course 
+Instead of working on the error message, we add some code to handle vector and matrix inputs.
 
-```
-sage: vector([x,2*x])
-```
-works so we could go that way.

[mkoeppe]

Commit: 5e3e34f

[mkoeppe]

Author: Matthias Koeppe

[kcrisman]

comment:5

It's always so great to wake up to someone working on a ticket from seven years ago :-)

I agree that this is the preferred way to handle it, and on a first pass the code looks good for it. I do have two usage questions.

sage: f = symbolic_expression(lambda z: z^2 + 1); f

Am I correct that this does not inject z into the global namespace? This seems to be how you constructed it with SR.var.

Also, I'm not familiar with SR.subring(no_variables=True), which is presumably what generates the "Symbolic Constants Subring". If someone later wanted to take something like symbolic_expression(vector(QQ, 0)) and then add it to another (zero-dimensional) vector, how would that behave? Would it complain because it has a different base ring? Or would it do the "obvious" thing in any of these degenerate cases? I don't know if there is a "right" answer here (for degenerate cases), but I wanted to ask.

Finally, it could be fun to exemplify the recursive nature of the code by having a vector composed of vector functions or something. Though I doubt that would be a real use case; this ticket is more to make sure that if people insist on making everything "symbolic" that nothing goes boom.

[mkoeppe]

comment:6

Replying to @kcrisman:

sage: f = symbolic_expression(lambda z: z^2 + 1); f

Am I correct that this does not inject z into the global namespace? This seems to be how you constructed it with SR.var.

That's right. (Note this is from #32103, not the present ticket.)

[mkoeppe]

comment:7

Replying to @kcrisman:

Also, I'm not familiar with SR.subring(no_variables=True), which is presumably what generates the "Symbolic Constants Subring". If someone later wanted to take something like symbolic_expression(vector(QQ, 0)) and then add it to another (zero-dimensional) vector, how would that behave?

The coercion system takes care of it:

sage: vector(SR.subring(no_variables=True), 0) + vector(SR, 0) + vector(ZZ, 0)
()
sage: _.parent()
Vector space of dimension 0 over Symbolic Ring