I was trying to figure out if SAGE can raise to the pth power quickly
in characteristic p. It seems that it doesn't. Am I right to think
that or am I missing something? Here is what led me to this

sage: F = FiniteField(3)
sage: P.<x> = PolynomialRing(F)
sage: PP.<y> = PolynomialRing(P)
sage: u = x^6 + y^7 + 1
sage: for e in range(237, 248):
   ...:     time r = u^e
   ...:
CPU times: user 27.97 s, sys: 0.07 s, total: 28.04 s
Wall time: 28.08 s
CPU times: user 28.03 s, sys: 0.03 s, total: 28.06 s
Wall time: 28.08 s
CPU times: user 27.50 s, sys: 0.04 s, total: 27.54 s
Wall time: 27.56 s
CPU times: user 27.15 s, sys: 0.03 s, total: 27.17 s
Wall time: 27.18 s
CPU times: user 27.46 s, sys: 0.04 s, total: 27.50 s
Wall time: 27.51 s
CPU times: user 26.66 s, sys: 0.03 s, total: 26.69 s
Wall time: 26.70 s
CPU times: user 27.14 s, sys: 0.03 s, total: 27.18 s
Wall time: 27.20 s
CPU times: user 27.29 s, sys: 0.06 s, total: 27.35 s
Wall time: 27.46 s
CPU times: user 26.35 s, sys: 0.04 s, total: 26.38 s
Wall time: 26.39 s
CPU times: user 26.21 s, sys: 0.03 s, total: 26.24 s
Wall time: 26.25 s
CPU times: user 26.42 s, sys: 0.03 s, total: 26.46 s
Wall time: 26.47 s
sage:


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