Making the module holonomic usable

[shubhamtibra]

• Fixed smaller bugs. Fixed Converting holonomic function to a symbolic expression #11288 , Fixed RuntimeError: maximum recursion depth exceeded while calling a Python object #11314 , Fixed Improve change_ics(self, b) #11315 , Fixed from_sympy(sin(x)**2/x).integrate((x, 0, 1)) fails #11316 , Fixed rename from_sympy to from_expr #11318 , Fixed UnboundLocalError in holonomic #11321 , Fixed sympy.holonomic.to_sympy(1/sin(x)) gives RecursionError #11326 , Fixed from_sympy(sqrt(x)) fails #11327
• Added support for RR domain. Fixes HolonomicFunction converts floats to rationals #11325 .

>>> expr_to_holonomic(1.1329138213*x, x0=1, domain=RR).to_expr()
1.1329138213⋅x

• Added support for multivariable fields. Fixes Can holonomic functions be extended to multiple variables #11323 .

>>> expr_to_holonomic(a*x, x=x,domain=QQ[a], lenics=2).integrate(x).to_expr()
a*x**2/2

[shubhamtibra]

Ping @certik @jksuom .

[certik]

I wonder if for speed reasons, you should rather be importing this at the top of the module? I think importing each time can be slow.

[certik]

I think that this looks great. Any objections @jksuom ?

[certik]

I think you should use S(2)/3 here, otherwise you get a floating point number. Floating point numbers can be handled differently, either now or in the future, so the test could fail, but S(2)/3 should always work and be robust.

[jksuom]

I agree that floating point numbers should be avoided in the tests unless they are the very subject of the test.. I think this is ready to be merged after that is fixed.

[shubhamtibra]

Importing GlobalPolynomialRing at the top in sympy/polys/domains/domain.py is causing this error:

>>> bin/test holonomic
Traceback (most recent call last):
  File "bin/test", line 105, in <module>
    import sympy
  File "/home/shubham/sympy/sympy/__init__.py", line 49, in <module>
    from .polys import *
  File "/home/shubham/sympy/sympy/polys/__init__.py", line 5, in <module>
    from . import polytools
  File "/home/shubham/sympy/sympy/polys/polytools.py", line 54, in <module>
    from sympy.polys.domains import FF, QQ, ZZ
  File "/home/shubham/sympy/sympy/polys/domains/__init__.py", line 5, in <module>
    from . import domain
  File "/home/shubham/sympy/sympy/polys/domains/domain.py", line 13, in <module>
    from sympy.polys.domains.old_polynomialring import GlobalPolynomialRing
  File "/home/shubham/sympy/sympy/polys/domains/old_polynomialring.py", line 5, in <module>
    from sympy.polys.domains.ring import Ring
  File "/home/shubham/sympy/sympy/polys/domains/ring.py", line 5, in <module>
    from sympy.polys.domains.domain import Domain
ImportError: cannot import name Domain

Seems like Domain needs to be imported before GlobalPolynomialRing.

[jksuom]

Seems like Domain needs to be imported before GlobalPolynomialRing.

That seems a good solution (if no other circular imports appear).

[shubhamtibra]

But importing GlobalPolynomialRing at the top in sympy/polys/domains/domain.py will still cause an error. Apparently, one cannot import GlobalPolynomialRing until the importing of Domain is done. So the statement from sympy.polys.domains.old_polynomialring import GlobalPolynomialRing should be inside the class. I can't think of an other solution.

[jksuom]

I also think that must be done so. This is not the only case where importing in the class seems to be necessary.

[jksuom]

I think this is ready. Merging.