Exponent Overflow error in PolynomialRing()
Let R=F71[x,y] be a polynomial ring over the finite field of p=71 elements and let f=x7+y5∈R be a polynomial. I need to compute powers of f of the form fpe−1 where e≥1 is an integer, that is, the polynomials f70,f5040,f357910,f25411680,….
from sage.all import *
from sage.arith.power import generic_power
p = 71
R = PolynomialRing(GF(p), 'X, Y')
X, Y = R.gens()
f = X**7 + Y**5
for e in range(1, 10):
exponent = p**e - 1
print(generic_power(f, exponent))
However, I quickly into an exponent overflow error when computing f357910. Here is the log:
Traceback (most recent call last):
File "/home/root/test.py", line 12, in <module>
print(f**exponent)
File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 2467, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:23225)
File "sage/libs/singular/polynomial.pyx", line 385, in sage.libs.singular.polynomial.singular_polynomial_pow (build/cythonized/sage/libs/singular/polynomial.cpp:5214)
File "sage/libs/singular/singular.pyx", line 1496, in sage.libs.singular.singular.overflow_check (build/cythonized/sage/libs/singular/singular.cpp:12737)
OverflowError: exponent overflow (2505370)
Based on the logs, it seems like sage uses Singular libraries to compute the powers of f. Is it possible to change the maximum exponent allowed by Singular?