bugs in conversion of variable names from Maxima to Sage

[williamstein]

-----------
sage: from sage.calculus.calculus import symbolic_expression_from_maxima_string
sage: symbolic_expression_from_maxima_string('%i')
I
sage: symbolic_expression_from_maxima_string('i')
I
sage: symbolic_expression_from_maxima_string('%inf')
Inf
-----------

So as you see, we are converting both '%i' and 'i' to  imaginary 'I' !!!!

The ticket should implement a multi word replace and use that on a symtable with additional entries 'e':'_e', 'i':'_i', 'I':'_I'.

We do not want to be surprised when some new Maxima variable starting %i is introduced. At the moment it's really just a string replace from %i to I, without sense of word boundaries.

CC: @robert-marik

Component: calculus

Author: Ralf Stephan

Branch/Commit: 518de3e

Reviewer: Karl-Dieter Crisman

Issue created by migration from https://trac.sagemath.org/ticket/6882

[kcrisman]

comment:1

Here is the relevant discussion.

[kcrisman]

comment:2

This will also happen with %e and e, and any other similar pairs, so a fix should take care of all of them.

[robert-marik]

comment:3

As another consequence, solving of ode y'=c*x is not correct, the free variable is messed up with a parameter, see sage-devel - thanks for
Yuri Karadzhov

[marik@um-bc107 /opt/sage-4.3.4]$ ./sage
----------------------------------------------------------------------
| Sage Version 4.3.4, Release Date: 2010-03-19                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: from sage.calculus.calculus import symbolic_expression_from_maxima_string
sage: symbolic_expression_from_maxima_string('%c')
c
sage: c=var('c'); y=function('y',x); eq=diff(y,x)==c*x; eq
D[0](y)(x) == c*x
sage: desolve(eq,y,ivar=x)
1/2*c*x^2 + c

the answer should be something like 1/2cx^2 + c1

[jasongrout]

comment:4

See #8734 for what I think is a "needs work" solution.

[jasongrout]

comment:5

Actually, I guess the patch at #8734 will help with the solution, but may not totally solve the problem.

[robert-marik]

comment:6

This should fix also #9421.

[kcrisman]

comment:7

Also, in a situation where we don't have the duplication of constants, we get

sage: c
Traceback (click to the left of this block for traceback)
...
NameError: name 'c' is not defined

which isn't good either, though apparently that part of the expression still has type SymbolicExpression.