conversion of Symbolic Ring to FriCAS Expression Integer

[mantepse]

This ticket modifies the FriCAS interface so that symbolic ring elements are always converted to FriCAS Expression Integer or Expression Complex Integer, depending on whether the complex unit appears. Doing so, we fix the failure below.

see ​https://ask.sagemath.org/question/48431/why-this-integral-fail-using-fricas-algorithm/

for the original bug report:

integrate(sqrt(2)*x^2 + 2*x,x, algorithm="fricas")

[mantepse]

New commits:

​4c672a0

make sagemath SR convert to FriCAS EXPR INT

[tmonteil]

Possible collision with #28641 which refers to the same ask.sagemath.org question.

[mantepse]

Replying to tmonteil:

Possible collision with #28641 which refers to the same ask.sagemath.org question.

Yes, but the solutions are orthogonal to each other. In other words: after applying this branch, #28641 solves a different problem.

[chapoton]

some failing doctests in src/sage/functions/generalized.py and src/sage/functions/exp_integral.py

[mantepse]

There are unfortunately more problems. In particular, fricas(I) calls FriCASConverter.pyobject(I, I) (as it should). But this now returns I instead of %i.

[mantepse]

I'm afraid my approach won't work, because FriCAS distinguishes between Expression Integer and Expression Complex Integer.

Put differently, the complex unit I is not an element of Expression Integer, but would have to be expressed as sqrt(-1). I see the following options:

1. rewrite I as sqrt(-1),
2. always use Expression Complex Integer,
3. detect whether I appears and distinguish accordingly,
4. somehow let FriCAS decide

I tend towards option 1., but I am not sure at all.

[mantepse]

help appreciated

[git]

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

​8948d38

try to fix conversion of complex expressions to fricas

[mantepse]

I think I have to make an exception for the conversion of symbols, because otherwise fricas.integrate(ex, x) won't work anymore.

[git]

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

​8601700	fix doctests
​4205759	Merge branch 'u/mantepse/conversion_of_symbolic_ring_to_fricas_expression_integer' of git://trac.sagemath.org/sage into t/28647/conversion_of_symbolic_ring_to_fricas_expression_integer
​d1b4490	Merge branch 'develop' into t/28647/conversion_of_symbolic_ring_to_fricas_expression_integer

[git]

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

​b95f2a4

make an exception for symbols

[git]

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

​09bee26

fix doctests

[embray]

Ticket retargeted after milestone closed

[mkoeppe]

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.