2023-02-24 13:51:49 +01:00
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p = 3
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m = 2
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2022-11-18 15:00:34 +01:00
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F = GF(p)
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Rx.<x> = PolynomialRing(F)
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2023-03-08 14:54:07 +01:00
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f = x^3 - x
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2023-02-23 12:26:25 +01:00
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C = superelliptic(f, m)
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2023-03-08 14:54:07 +01:00
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#C1 = patch(C)
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2023-03-07 13:41:20 +01:00
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#print(C1.crystalline_cohomology_basis())
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2023-03-08 14:54:07 +01:00
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#g1 = C1.polynomial
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#g_AS = g1(x^p - x)
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#C2 = superelliptic(g_AS, 2)
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#print(convert_super_into_AS(C2))
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#converted = (C2.x)^4 - (C2.x)^2
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#print(convert_super_fct_into_AS(converted))
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2023-03-09 09:44:42 +01:00
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#b = C.crystalline_cohomology_basis()
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#print(autom(b[0]).coordinates(basis = b))
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#eta1 = (dy + dV(2xy) + V(x^5 \, dy), V(y/x))
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eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
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#eta2 = ( x \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) y) + V( (x^4 + x^2 + 1) dy), -[y/x])
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eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teichmuller())
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aux = de_rham_witt_lift(C.de_rham_basis()[1])
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print(aux)
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