# Pade approximant function from mpmath

I'd like to use the pade function from the mpmath library in Sage since in the last documentation released in 2023, Sage allows for speed up of some of mpmath's function. Nevertheless, the same code that is working in Python is not working in Sage, because it signs an error related to the types inserted in the mpmath.pade function. This pade function should receive as inputs a list of mpf or mpc type values representing truncated power series coefficients and give back two polynomials p and q representing the numerator and denominator of the Padé approximant for that series, respectively. I don't know what to do, I have typed all my variables in Sage as mpmath's mpf or mpc types and provided a list containing this types to the mpmath.pade function but is not working. There's no problem with respect to the pade polynomials orders and the truncated series order. The error in my code accuses the following:

TypeError                                 Traceback (most recent call last)
/tmp/ipykernel_1480/1416428611.py in <module>
48
49 seq_inf = generate_recurrence_sequence_inf(n)
---> 50 p_inf, q_inf = mpr.mp.pade(seq_inf, n//Integer(2),n//Integer(2))

/usr/lib/python3/dist-packages/mpmath/calculus/differentiation.py in pade(ctx, a, L, M)
631     # ...
632     # a[L+M-1]*q[1] + ... + a[L]*q[M] = -a[L+M]
--> 633     A = ctx.matrix(M)
634     for j in range(M):
635         for i in range(min(M, L+j+1)):

/usr/lib/python3/dist-packages/mpmath/matrices/matrices.py in __init__(self, *args, **kwargs)
330             self.__cols = A._matrix__cols
331         else:
--> 332             raise TypeError('could not interpret given arguments')
333
334     def apply(self, f):

TypeError: could not interpret given arguments


What am I doing wrong?

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