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Trac 10569: This cleans up the documentation of hyperelliptic_finite_…
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…field.py
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oarsmanJT committed Jan 7, 2011
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"""
r"""
Hyperelliptic curves over a finite field
EXAMPLES::
Expand Down Expand Up @@ -31,6 +31,7 @@ def _frobenius_coefficient_bound(self):
a_1, ..., a_g modulo p^B determine frobenius polynomial uniquely.
TESTS::
sage: R.<t> = PolynomialRing(GF(37))
sage: HyperellipticCurve(t^3 + t + 1)._frobenius_coefficient_bound()
1
Expand Down Expand Up @@ -78,6 +79,7 @@ def _frobenius_matrix(self, N=None):
over GF(p^1), and must have p > (2g+1)(2N-1).
TESTS::
sage: R.<t> = PolynomialRing(GF(37))
sage: H = HyperellipticCurve(t^5 + t + 2)
sage: H._frobenius_matrix()
Expand Down Expand Up @@ -120,12 +122,16 @@ def frobenius_polynomial(self):
Charpoly of frobenius, as an element of ZZ[x].
TESTS::
sage: R.<t> = PolynomialRing(GF(37))
sage: H = HyperellipticCurve(t^5 + t + 2)
sage: H.frobenius_polynomial()
x^4 + x^3 - 52*x^2 + 37*x + 1369
A quadratic twist:
::
sage: H = HyperellipticCurve(2*t^5 + 2*t + 4)
sage: H.frobenius_polynomial()
x^4 - x^3 - 52*x^2 - 37*x + 1369
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