improve documentation of 'solve()'

[sagetrac-jakobkroeker]

Even if it is expectable that in some cases solve() may not return all solutions, it should be explicitly pointed out; especially it should be stated that an empty list does not necessarily imply there are no solutions.

See also the discussion at https://groups.google.com/d/msg/sage-support/cg7QYw_1ncg/VKdH3CX4qYsJ

Example from that thread:

solve(5^( x -1) == (1/25)^(2*x), x)
# []
solve(5^( x -1) == (1/25)^(2*x), x,to_poly_solve=True)
#[x == (2*I*pi*z41 + log(5))/log(3125)]

Component: documentation

Branch/Commit: u/jakobkroeker/ticket/17412 @ 2d75747

Issue created by migration from https://trac.sagemath.org/ticket/17412

[sagetrac-jakobkroeker]

Branch: u/jakobkroeker/ticket/17412

[sagetrac-jakobkroeker]

Commit: 2d75747

[sagetrac-jakobkroeker]

comment:2

What is about

 solve_mod()
 solve_ineq_univar()
 solve_ineq_fourier()
 solve_ineq()

may they also fail in some cases to return all solutions?
Which other routines need an explicit statement, that an empty result does not imply
that there are no solutions?

---

New commits:

2d75747

explicitly state that solve may not obtain all existing solutions and that an empty result does not imply there are no solutions

[sagetrac-tmonteil]

comment:3

I think you should also give an explicit example in the doc. However, the one you provide does not work for me (on 6.5.beta0):

sage: solve(5^( x -1) == (1/25)^(2*x), x)
...
NotImplementedError: non-integral exponents not supported

[rwst]

comment:4

Replying to @sagetrac-tmonteil:

I think you should also give an explicit example in the doc. However, the one you provide does not work for me (on 6.5.beta0):

sage: solve(5^( x -1) == (1/25)^(2*x), x)
...
NotImplementedError: non-integral exponents not supported

Returns empty list on 6.5beta1. Is x already initialized?

[sagetrac-tmonteil]

comment:5

Uh my bad, i was using the wrong sage console where i used polynomials before. Sorry for the noise.

That said, adding an example showing explicitly the problem (e.g. that particular example, since it works) could be good to make things explicit. The existing example are somehow too optimistic, and we should point what does not work as well.