assume doesn't interact well with solve

[robertwb]

This has been brought up several times on the mailing lists. As a specific example

sage: assume(x>0)
sage: solve([x^2-1],x)
[x == -1, x == 1]

At the very least, we could probably filter out the "solutions" that violate the assumptions.

sage: [all(a.subs(s) for a in assumptions()) for s in solve(x^2-1==0, x)]
[False, True]

[kcrisman]

It sounds like Maxima (intentionally?) doesn't use assumptions in solve, see for instance ​http://www.math.utexas.edu/pipermail/maxima/2008/013152.html and other similar threads. The above solution seems reasonable.

[kcrisman]

Update: the solution above works well for single equations in one variable, but is tricky to implement for multiple equations (you can't subs x+y==3, for instance). Also, one has to keep in mind how to check assumptions like 'x is Integer', which can't be subs'ed in.

[robertwb]

It doesn't catch everything, but is better than what we have now.

[burcin]

minor documentation fixes

[burcin]

The patch looks good and doctests pass. There is one minor problem, the line

sage: GenericDeclaration(x, 'rational').contradicts(y==pi)

is repeated several times in the doctest for sage.symbolic.assumptions.GenericDeclaration.contradicts().

I attached a patch to change these lines and add an INPUT field to the docstring. Can you look over my patch and change the status to positive_review if you agree with the changes?

[robertwb]

Thanks for looking at this. Nice catches, I approve of your changes.

[mpatel]

For the record: Applying the patch to 4.3.2 + ​a long queue gives

applying 6515-solve-assume.patch
patching file sage/symbolic/expression.pyx
Hunk #2 succeeded at 5952 with fuzz 2 (offset 40 lines).
Hunk #3 succeeded at 6037 with fuzz 1 (offset 83 lines).

Please let us know (via sage-devel) about the best order in which to apply the symbolics and calculus patches.

[mpatel]

The first patch is missing a Mercurial header and the ticket number. I've applied a refreshed patch to 4.3.3.alpha0.