13 lines
781 B
Python
13 lines
781 B
Python
p = 3
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m = 2
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F = GF(p)
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Rx.<x> = PolynomialRing(F)
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f = x^3 - x
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C = superelliptic(f, m)
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Rxy.<x, y> = PolynomialRing(F, 2)
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omega = (((2*C.x^18 + 2*C.x^16 + 2*C.x^14 + 2*C.x^10 + 2*C.x^8 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/(C.x^13 + C.x^11 + C.x^9))*C.y) * C.dx
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print(decomposition_omega0_omega8(omega)[0] - decomposition_omega0_omega8(omega)[1] == omega and decomposition_omega0_omega8(omega)[0].is_regular_on_U0() and decomposition_omega0_omega8(omega)[1].is_regular_on_Uinfty())
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h = ((C.x^10 + C.x^8 + C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/C.x^6)*C.y
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print(decomposition_g0_g8(h))
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print(decomposition_g0_g8(h)[0] - decomposition_g0_g8(h)[1] + decomposition_g0_g8(h)[2] == h and decomposition_g0_g8(h)[0].function in Rxy and decomposition_g0_g8(h)[1].expansion_at_infty().valuation() >= 0) |