26 lines
836 B
Python
26 lines
836 B
Python
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p = 5
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m = 2
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F = GF(p^2, 'a')
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a = F.gens()[0]
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Rx.<x> = PolynomialRing(F)
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f = x^3 + x^2 + 1
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C_super = superelliptic(f, m)
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Rxy.<x, y> = PolynomialRing(GF(p), 2)
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fArS1 = superelliptic_function(C_super, y*x)
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fArS2 = superelliptic_function(C_super, y*x^2)
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fArS3 = superelliptic_function(C_super, y + x)
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AS1 = as_cover(C_super, [fArS1, fArS2, fArS3], prec=150)
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AS2 = as_cover(C_super, [fArS2, fArS3, fArS1], prec=150)
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print(AS1.genus() == AS2.genus())
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##################
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p = 5
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m = 2
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Rx.<x> = PolynomialRing(GF(p))
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f = x^3 + x^2 + 1
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C_super = superelliptic(f, m)
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Rxy.<x, y> = PolynomialRing(GF(p), 2)
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fArS1 = superelliptic_function(C_super, y*x)
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fArS2 = superelliptic_function(C_super, y*x^2)
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AS1 = as_cover(C_super, [fArS1, fArS2], prec=1000)
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omega = as_form(AS1, 1/y)
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print(omega.expansion_at_infty().valuation()==AS1.exponent_of_different())
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