Allow large exponents in polynomial rings

[d0f01299-9413-4adc-b781-c6769fd02874]

OverflowError                             Traceback (most recent call last)
<ipython-input-37-db1c8bc53ef7> in <module>
----> 1 ff = x**Integer(Integer(2818407171672390179701902257344061561))
      2 ff

/var/tmp/sage-9.4-current/local/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_modn_dense_ntl.pyx in sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ.__pow__ (build/cythonized/sage/rings/polynomial/polynomial_modn_dense_ntl.cpp:19729)()
   1408         """
   1409         cdef bint recip = 0, do_sig
-> 1410         cdef long e = ee
   1411         if e != ee:
   1412             raise TypeError("Only integral powers defined.")

OverflowError: Python int too large to convert to C long

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/33300

[slel]

Description changed:

--- 
+++ 
@@ -1,7 +1,8 @@
+
+```
 OverflowError                             Traceback (most recent call last)
 <ipython-input-37-db1c8bc53ef7> in <module>
-
----
+----> 1 ff = x**Integer(Integer(2818407171672390179701902257344061561))
       2 ff

 /var/tmp/sage-9.4-current/local/lib/python3.9/site-packages/sage/rings/polynomial/polynomial_modn_dense_ntl.pyx in sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ.__pow__ (build/cythonized/sage/rings/polynomial/polynomial_modn_dense_ntl.cpp:19729)()
@@ -12,3 +13,4 @@
    1412             raise TypeError("Only integral powers defined.")

 OverflowError: Python int too large to convert to C long
+```

[slel]

comment:1

How did you define x before running ff = x^...?

What computation is intended?

Sparse polynomials might be made to accept such large exponents; dense polynomials likely not.

[d0f01299-9413-4adc-b781-c6769fd02874]

comment:2

N = 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
c1 = 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
c2 = 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
e = 0xd4088c345ced64cbbf8444321ef2af8b

R = Zmod(N)
PR.<x> = PolynomialRing(R)
pol = c2-(c1-x)^5
#
ff = x^e
print(ff % pol)

I want get ff moduled by pol polynomial, I know that I can use quotient_ring to achieve it. But could you please let it worked directly.

[d0f01299-9413-4adc-b781-c6769fd02874]

comment:3

When e is a small number sagemath will work.