2023-02-13 13:05:48 +01:00
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p = 3
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m = 2
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#F = GF(p)
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F = GF(p)
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2022-12-19 14:37:14 +01:00
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Rx.<x> = PolynomialRing(F)
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2023-02-13 13:05:48 +01:00
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f = x^5 + 1
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g = f(x^p - x)
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Cf = superelliptic(f, m)
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C = superelliptic(g, m)
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#class superelliptic_automorphism:
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# def __init__
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def autom(omega):
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C1 = omega.curve
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f = omega.form
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F = C1.base_ring
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Rxy.<x, y> = PolynomialRing(F, 2)
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RxyQ = FractionField(Rxy)
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f = RxyQ(f)
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return superelliptic_form(C1, f(x=x+1, y=y))
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def automdR(omega):
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C1 = omega.curve
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om0 = omega.omega0.form
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f = omega.f.function
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F = C1.base_ring
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Rxy.<x, y> = PolynomialRing(F, 2)
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RxyQ = FractionField(Rxy)
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f = RxyQ(f)
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om0 = RxyQ(om0)
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f = f(x=x+1, y=y)
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om0 = om0(x=x+1, y=y)
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f = superelliptic_function(C1, f)
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om0 = superelliptic_form(C1, om0)
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return superelliptic_cech(C1, om0, f)
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A = C.de_rham_basis()
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gC = C.genus()
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M = matrix(C.base_ring, 2*gC, 2*gC)
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for i in range(2*gC):
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M[:, i] = vector(automdR(A[i]).coordinates())
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print(M, M^p == identity_matrix(2*gC))
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N = C.verschiebung_matrix().transpose()
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print(magmathis(M, N))
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