Add more conversions from giac

[mforets]

A "conversion" is a dictionary entry which maps object names in an interface (e.g. Maxima, Mathematica, Giac, ...) to corresponding objects with a different name in Sage.

Some conversions relevant to the Giac interface are missing:

• Derivatives of Dirac delta, as in Dirac(t, 1).
• Special function names at /functions/orthogonal_polys.py.

See also:

• In the file: local/share/giac/doc/aide_cas, lines starting by # are keywords followed by synonyms, next lines are for small doc and see also. Full doc can be found in: Symbolic algebra and Mathematics with Xcas

• sage.libs.pynac.pynac.register_symbol can be used to register new symbols in the symbols_table, as in register_symbol(heaviside,{'giac':'Heaviside'}).

• for BuiltIn functions which exist in giac with a different name, it is sufficient to update the conversions dictionary for the corresponding __init__ method.

Depends on #22422

CC: @paulmasson @frederichan-IMJPRG

Component: interfaces

Keywords: giac, special functions

Author: Paul Masson, Marcelo Forets

Branch: 350316f

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/22706

[mforets]

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 Some conversions relevant to the Giac interface are missing:
 
-- Dirac delta with support different from 0, as in `Dirac(t, 1)`.
+- Derivatives of Dirac delta, as in `Dirac(t, 1)`.
 - Special function names at `/functions/orthogonal_polys.py`.
 
 See also: 

[mforets]

Description changed:

--- 
+++ 
@@ -7,6 +7,6 @@
 
 See also: 
 
-- In the file: `local/share/giac/doc/aide_cas`, lines starting by # are keywords followed by synonyms, next lines are for small doc and see also. Full doc it is here: [Symbolic algebra and Mathematics with Xcas](http://www-fourier.ujf-grenoble.fr/~parisse/giac/doc/en/cascmd_en/cascmd_en.html)
+- In the file: `local/share/giac/doc/aide_cas`, lines starting by # are keywords followed by synonyms, next lines are for small doc and see also. Full doc can be found in: [Symbolic algebra and Mathematics with Xcas](http://www-fourier.ujf-grenoble.fr/~parisse/giac/doc/en/cascmd_en/cascmd_en.html)
 
 - `sage.libs.pynac.pynac.register_symbol` can be used to register new symbols in the `symbols_table`, as in `register_symbol(heaviside,{'giac':'Heaviside'})`.

[mforets]

Description changed:

--- 
+++ 
@@ -10,3 +10,5 @@
 - In the file: `local/share/giac/doc/aide_cas`, lines starting by # are keywords followed by synonyms, next lines are for small doc and see also. Full doc can be found in: [Symbolic algebra and Mathematics with Xcas](http://www-fourier.ujf-grenoble.fr/~parisse/giac/doc/en/cascmd_en/cascmd_en.html)
 
 - `sage.libs.pynac.pynac.register_symbol` can be used to register new symbols in the `symbols_table`, as in `register_symbol(heaviside,{'giac':'Heaviside'})`.
+
+- for BuiltIn functions which exist in giac with a different name, it is sufficient to update the `conversions` dictionary from the corresponding `__init__` method. 

[mforets]

Description changed:

--- 
+++ 
@@ -11,4 +11,4 @@
 
 - `sage.libs.pynac.pynac.register_symbol` can be used to register new symbols in the `symbols_table`, as in `register_symbol(heaviside,{'giac':'Heaviside'})`.
 
-- for BuiltIn functions which exist in giac with a different name, it is sufficient to update the `conversions` dictionary from the corresponding `__init__` method. 
+- for `BuiltIn` functions which exist in giac with a different name, it is sufficient to update the `conversions` dictionary for the corresponding `__init__` method. 

[frederichan-IMJPRG]

comment:5

This one doesn't look easy. Any idea to deal with rootof?

sage: giac.simplify((exp(2*i*pi/3)+exp(2*i*pi/15))^3)
((-768*i)*(-1)^(2/15)*sqrt(3)-768*(-1)^(2/15)+768*i*(-1)^(4/15)*sqrt(3)-768*(-1)^(4/15)+rootof([[16-16*i,-16+16*i,-400+528*i,144+240*i],[1,0,-30,-40,5]]))/512

do we need to chose a name for the variable in the extention field? (if yes then how? (or what would be a good name))

[mforets]

Dependencies: #22422

[paulmasson]

Branch: u/paulmasson/22706

[paulmasson]

comment:9

I went through the files in sage/functions to add as many conversions for special functions as possible, but could only find ten that were different from Sage.

The Giac exponential integrals Ei, Si and Ci have existing Sage aliases, so there shouldn't be a problem with those.

The orthogonal polynomials hermite and laguerre have the same names in Giac and Sage. Same for erf and a pending erfc, as well as binomial and factorial.

The Giac function Psi has is a different name from Sage psi, but the order of the arguments is reversed so I didn't add it now.

---

New commits:

0e337ef	Add Giac conversions and cleanup
ffba36a	Add Giac conversions and cleanup
e1a63ed	Add Giac conversions and cleanup
3a3d079	Add Giac conversion
bdc2807	Add Giac conversions and cleanup

[paulmasson]

Author: Paul Masson

[paulmasson]

Commit: bdc2807

[paulmasson]

comment:10

Considering the derivatives of delta functions, I think we'll have to do a string replacement using a regular expression similar to how Maxima conversions are handled starting here. Perhaps that should be a separate ticket after #22422 is merged.

The conversions I've entered are not dependent on #22422 and can be merged at any time. If either of you can identify additional functions that can be added easily with this ticket, let me know.