Add example with solution_dict and substituting in a matrix

[kcrisman]

See ​this ask.sagemath.org question. The poster wants an example something like

f(x,y)=x^2*y+y^2+y
solutions=solve(list(f.diff()),[x,y])
the_solution=solutions[2]
H=f.diff(2);  # Hessian matrix

but showing this.

sage: solutions=solve(list(f.diff()),[x,y],solution_dict=True)
sage: solutions
[{y: 0, x: -I}, {y: 0, x: I}, {y: -1/2, x: 0}]
sage: H.subs(solutions[2])
[(x, y) |--> -1  (x, y) |--> 0]
[ (x, y) |--> 0  (x, y) |--> 2]
sage: H(x,y).subs(solutions[2])
[-1  0]
[ 0  2]

This seems like a reasonable request.

[tscholl2]

Added two examples in symbolic expressions on:

​http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/relation.html

One is substituting variables into matrices of symbolic functions and the other is solving a multivariate equation and substituting the solution into a matrix.

---

New commits:

​3843197

Added example subtituting values into a matrix of symbolic functions.

[vdelecroix]

Hello,

Could you use A = B instead of A=B? You did it in the first example but not the second. Something like

sage: solutions = solve(list(f.diff()), [x,y], solution_dict=True)

is much easier to read.

Vincent

[git]

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

​b26b327

fixed spacing

[tscholl2]

Thanks for pointing that out!

I added some spacing. Is there anything else you noticed?

[vdelecroix]

That was all!

[vbraun]

Doctest depends on dictionary order of symbolic variables:

sage -t --long src/sage/symbolic/relation.py
**********************************************************************
File "src/sage/symbolic/relation.py", line 158, in sage.symbolic.relation
Failed example:
    solutions
Expected:
    [{y: 0, x: -I}, {y: 0, x: I}, {y: -1/2, x: 0}]
Got:
    [{x: -I, y: 0}, {x: I, y: 0}, {x: 0, y: -1/2}]
**********************************************************************
1 item had failures:
   1 of 131 in sage.symbolic.relation
    [295 tests, 1 failure, 7.50 s]

[git]

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

​97ee2c1

Merge tag '6.9.beta6' into matrix_solution_11541

[tscholl2]

I didn't get that error when I tested the file. I merged in the latest release and I still don't get the error. Do you think it could be my Sage installation? It's a pretty clean version except for an optional package for another branch I was working on. Are other people getting this error?

[vbraun]

The doctest sorts dictionaries, but the sort order of symbolic variables is random (and depends strongly on memory locations / the OS). Just rewrite the test as something that doesn't depend on random orders, e.g.

solutions == [{x: -I, y: 0}, {x: I, y: 0}, {x: 0, y: -1/2}]

[git]

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

​5307163

removed dependency on order of dictionary in doctest

[tscholl2]

Interesting, I had no idea the order of symbolic variables was that random.

I updated the doc test using the equality check instead and it seems to work great. Thanks for the fix!

I noticed there was some other tests not using equality checks like this on lines 136 and 143 (and probably more), which is probably where I copied my test from. Should this be a separate ticket or should I modify it on this branch as well?

[git]

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

​a925d7e

Merge branch 'develop' into 11541

[tscholl2]

I found that the other tests did not rely on multiple variables, so they are fine.

I also brought this branch up to date and checked that the docs still build.

[aly.deines]

The doctests pass and the documentation builds and looks good.