Symbolics code passes ungrammatical expressions to maxima

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sage: find_maximum_on_interval(-x^2 + 9*x, 4.4, 8)
RuntimeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

A little investigation with pdb.pm() shows that the error occurs in sage.interfaces.maxima_lib line 420

if statement: result = ((result + '\n') if result else '') + max_to_string(maxima_eval("#$%s$"%statement))

where statement has the value

'is (-20.247454751128636=-20.249999999999996<=-20.199549540424666)'

which is not a valid Maxima expression. The real error is in the code that causes this to happen.

The function maxima_eval is an ECL function, so its parameter gets converted by ECL-lib, outside maxima_lib's control. The string contains a #$...$ reader-macro, which causes the maxima-parser to handle the string. It finds the syntax error and signals it by throwing an uncaught "catch".

Invoking maxima_eval this way isn't particularly wrong, but one should ensure that the expression passed in is at least syntactically correct. If an error condition arises when evaluating the expression using maxima_eval, errors are caught more gracefully.

Digging a little deeper shows that find_maximum should not be called with symbolic arguments, so this particular error could be caught earlier. However, I think the symptom shows that the symbolics code should vet its expression a little better before passing it to maxima: The expression isn't accepted by maxima as grammatical.

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/12032

Yes, that's a bug. Something goes wrong in what gets fed to the function: def f(z): v = sin(x)(x=z) print "evaluating sin(%s)=%s"%(z,v) return vsage: find_maximum_on_interval(f,0,2) evaluating sin(0.7639320225)=0.691766183638 evaluating sin(1.2360679775)=0.944499585162 evaluating sin(1.527864045)=0.999078551136 evaluating sin(1.59062900282 == 1.58711797464)=sin(1.59062900282 == 1.58711797464) As you see, for some reason the evaluation point becomes an equality relation. From that point it is of course just a question *which* piece of code throws an error. These routines use scipy.optimize.fminbound. This doesn't act too nicely with the SymbolicRing. In the source, we find the following lines: ... si = numpy.sign(xm-xf) + ((xm-xf)==0) ... si = numpy.sign(rat) + (rat == 0) x = xf + si*max([abs(rat), tol1]) ... What they need is: .... si = numpy.sign(xm-xf) if si == 0: si = 1 ... si = numpy.sign(rat) if si == 0: si = 1 x = xf + si*max([abs(rat), tol1]) ... Their assumption that numpy.sign(rat) == 0 iff (rat == 0) evaluates to 1 and that (rat == 0) evaluates to 0 otherwise is not unreasonable in their world. The above code is of course a little more robust, but I doubt scipy is willing to change it just because sage's SR acts funny. So the fix: sage should interface a little more carefully with scipy and take care no SR objects leak into it. The problem comes from the fact that the symbolic ring is quite conservative in deciding whether floats are equal to zero and has the habit of returning something that is not readily 0 or 1: sage: 1.1 == 0 False sage: SR(1.1) == 0 1.10000000000000 == 0 So at the least, the sage interface prepares input to scipy that doesn't behave as scipy expects. It may also be that the scipy implementation is suspect. The nasty error comes from the fact that the syntactically invalid expression sin(1.59062900282 == 1.58711797464) doesn't get rejected upon construction.

sagemath / sage

Symbolics code passes ungrammatical expressions to maxima #12032