The module Matrices in SymPy doesn't support type mpq from gmpy2.

[adukova]

Example

In[1]:   from sympy import Matrix,S,symbols,QQ,I,init_printing,Poly
            from sympy.polys.domains import QQ
            import gmpy2  as gm
            init_printing()
In[2]:    k2=QQ(1,4)
            k1=QQ(-3,1)
            k0=QQ(1345789308645,512855373753735374)
            type(k2),type(k1),type(k0)
Out[2]: (mpq, mpq, mpq)
In[3]:    A=Matrix([[k0,k1],[k2,k0]])
In[4]:    type(A[0,0]);type(A[0,1]),type(A[1,0]),type(A[1,1])
Out[4]: (sympy.core.numbers.Integer,
             sympy.core.numbers.Rational,
             sympy.core.numbers.Rational)

It does not allow to work with long arithmetic in linear algebra.

[jksuom]

Matrix elements are converted to SymPy types by default. There is a variant class PolyMatrix whose instances do not convert the input data. That can be used, for instance, by from sympy.polys.polymatrix import PolyMatrix as Matrix.

[adukova]

@jksuom Thank you very much. I'll try to do it.

[adukova]

@jksuom
Thank you for your advice. Now matrix elements have type mpq. Unfortunately this does not solve my problems. From the module Matrices I use only rank and nullspace. The function rank works as long as for type Rational. May be it is needed to change the function rref in order to it can work with gmpy2. Do you have any thoughts on this? Thank you in advance.

[sylee957]

@adukova
Is the rank or nullspace giving the wrong answer?
I have got the result from the matrix above

>>> A.nullspace()
[]
>>> A.rank()
2

And I think Mathematica gives the same answer.

[jksuom]

Can you describe the problems you meet?

[adukova]

I have matrices of sizes about 50 x 50. The entries are rational numbers with long numerators and denominators (about 50 digits and more). I need ranks for a finite sequence from such matrices (about 50 terms). Maple solves this problem in reasonable time (from 1 sec to 1 hour). The analogous routine in SymPy for some example can not solve the problem in five hours. I think the problem is that the module Matrices can not work with the library gmpy2. Moreover if entries were complex numbers the function rank in SymPy returned a wrong result. But this problem is solved now (see issue #16823).

[adukova]

Thank you all. It seems in the case of real matrices the problem is solved:

1. with the help of PolyMatrix we create a matrix with mpq entries (thank you jksuom),
2. the function rank() must be used with parameters r = M.rank(iszerofunc=lambda v: v==QQ.zero).
   Now the problem is solved with very high speed. It remains to check the case of matrices with complex elements. It is not clear what is considered as zero.

[sylee957]

I have found the behavior that the matrix gets gradually filled with SymPy number types in each step of computation. So the booster may not last long.
I think that sympify automatically sanitizes the custom number types in the poly module to sympy number types. Is it an intended behavior?

[jksuom]

sympify automatically sanitizes the custom number types in the poly module to sympy number types. Is it an intended behavior?

That should not happen. The existing variant matrix subclasses (RawMatrix, PolyMatrix) replace _sympify with identity mapping to avoid that. It seems to me that the best choice would be conversion to the ring data type. (I am working on that.)

[adukova]

@jksuom

Dear jksuom,

Unfortunately, I know you only as jksuom in the forum GitHub .

Thank you very much for your advice to my daughter Adukova Nataliya (GitHub issue # 16883).
Your advice help me to improve the work of my SymPy module for the Wiener-Hopf factorization
of matrix polynomials.

Can I thank you in my article for Journal of Symbolic Computation?
What your name can I note in my "Acknowledgments"?

Best wishes,

V. Adukov

[jksuom]

Can I thank you in my article for Journal of Symbolic Computation?

Yes, of course, you can do that.

What your name can I note in my "Acknowledgments"?

My name is Kalevi Suominen.

[adukova]

@jksuom
Thank you