better fricas and giac conversion for symbolic matrices

[fchapoton]

and a similar problem with giac.

Here it is

sage: fricas(sin(x)).sage()                                                     
sin(x)
sage: M = matrix(SR, 1, [sin(x)])                                               
sage: fricas(M)                                                                 
+sin +
+   x+
sage: fricas(M).sage()                                                          
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
~/sage/local/lib/python3.8/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6664)()
    571             try:
--> 572                 args = [SR.coerce(a) for a in args]
    573             except TypeError as err:

~/sage/local/lib/python3.8/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (build/cythonized/sage/structure/parent.c:10692)()
   1113 
-> 1114     cpdef coerce(self, x):
   1115         """

~/sage/local/lib/python3.8/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.coerce (build/cythonized/sage/structure/parent.c:10618)()
   1143                     _record_exception()
-> 1144             raise TypeError(_LazyString(_lazy_format, ("no canonical coercion from %s to %s", parent(x), self), {}))
   1145         else:

TypeError: no canonical coercion from <class 'sage.functions.trig.Function_sin'> to Symbolic Ring

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-63-0b5b80f0dcc8> in <module>
----> 1 fricas(M).sage()

~/sage/local/lib/python3.8/site-packages/sage/interfaces/interface.py in sage(self, *args, **kwds)
   1090             [0 0]
   1091         """
-> 1092         return self._sage_(*args, **kwds)
   1093 
   1094     def __repr__(self):

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _sage_(self)
   1864         if head == "Matrix":
   1865             base_ring = self._get_sage_type(domain[1])
-> 1866             rows = self.listOfLists().sage()
   1867             return matrix(base_ring, rows)
   1868 

~/sage/local/lib/python3.8/site-packages/sage/interfaces/interface.py in sage(self, *args, **kwds)
   1090             [0 0]
   1091         """
-> 1092         return self._sage_(*args, **kwds)
   1093 
   1094     def __repr__(self):

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _sage_(self)
   1856         if head == "List":
   1857             n = P.get_integer('#(%s)' % self._name)
-> 1858             return [self.elt(k).sage() for k in range(1, n + 1)]
   1859 
   1860         if head == "Vector" or head == "DirectProduct":

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in <listcomp>(.0)
   1856         if head == "List":
   1857             n = P.get_integer('#(%s)' % self._name)
-> 1858             return [self.elt(k).sage() for k in range(1, n + 1)]
   1859 
   1860         if head == "Vector" or head == "DirectProduct":

~/sage/local/lib/python3.8/site-packages/sage/interfaces/interface.py in sage(self, *args, **kwds)
   1090             [0 0]
   1091         """
-> 1092         return self._sage_(*args, **kwds)
   1093 
   1094     def __repr__(self):

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _sage_(self)
   1856         if head == "List":
   1857             n = P.get_integer('#(%s)' % self._name)
-> 1858             return [self.elt(k).sage() for k in range(1, n + 1)]
   1859 
   1860         if head == "Vector" or head == "DirectProduct":

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in <listcomp>(.0)
   1856         if head == "List":
   1857             n = P.get_integer('#(%s)' % self._name)
-> 1858             return [self.elt(k).sage() for k in range(1, n + 1)]
   1859 
   1860         if head == "Vector" or head == "DirectProduct":

~/sage/local/lib/python3.8/site-packages/sage/interfaces/interface.py in sage(self, *args, **kwds)
   1090             [0 0]
   1091         """
-> 1092         return self._sage_(*args, **kwds)
   1093 
   1094     def __repr__(self):

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _sage_(self)
   1943             # we treat Expression Integer and Expression Complex
   1944             # Integer just the same
-> 1945             return FriCASElement._sage_expression(P.get_InputForm(self._name))
   1946 
   1947         if head == 'DistributedMultivariatePolynomial':

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _sage_expression(fricas_InputForm)
   1630         register_symbol(convert_rootOf, {'fricas': 'rootOf'})
   1631 
-> 1632         ex, _ = FriCASElement._parse_and_eval(fricas_InputForm)
   1633         # postprocessing of rootOf
   1634         from sage.rings.all import QQbar, PolynomialRing

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1234 
   1235         if s[a] == FriCASElement._LEFTBRACKET:
-> 1236             return FriCASElement._parse_list(s, start=a)
   1237         elif s[a] == FriCASElement._STRINGMARKER:
   1238             return FriCASElement._parse_string(s, start=a)

~/sage/local/lib/python3.8/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1279             args.append(e)
   1280             a += 1
-> 1281         return fun(*args), a
   1282 
   1283     @staticmethod

~/sage/local/lib/python3.8/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6826)()
    583                     if callable(method):
    584                         return method()
--> 585                 raise TypeError("cannot coerce arguments: %s" % (err))
    586 
    587         else: # coerce == False

TypeError: cannot coerce arguments: no canonical coercion from <class 'sage.functions.trig.Function_sin'> to Symbolic Ring

CC: @mantepse

Component: interfaces: optional

Keywords: FriCAS, giac

Author: Frédéric Chapoton

Branch/Commit: c1c5ef5

Reviewer: Martin Rubey

Issue created by migration from https://trac.sagemath.org/ticket/30815

[fchapoton]

Changed keywords from none to FriCAS

[fchapoton]

Commit: c1c5ef5

[fchapoton]

Changed keywords from FriCAS to FriCAS, giac

[fchapoton]

Branch: u/chapoton/30815

[fchapoton]

Author: Frédéric Chapoton

[fchapoton]

New commits:

c1c5ef5

trrac 30815 better conversion of symbolic matrices to giac and fricas

[mantepse]

comment:3

Thank you!

[mantepse]

Reviewer: Martin Rubey

[fchapoton]

comment:4

NOTE : conversion to maple also needs the same kind of fix. TODO once this ticket is merged.

[vbraun]

Changed branch from u/chapoton/30815 to c1c5ef5