27 lines
1015 B
Python
27 lines
1015 B
Python
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p = 2
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F = GF(p)
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Rx.<x> = PolynomialRing(F)
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C = superelliptic(x, 1)
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AS = as_cover(C, [C.x^3, C.x^5], prec = 200)
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B = AS.holo_polydifferentials_basis(3)
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print(len(B) == (2 * 3 - 1) * (AS.genus() - 1)) #is the dimension as predicted by Riemann--Roch?
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I2 = AS.canonical_ideal_polynomials(2)
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R = I2[0].parent() #ring, to which the polynomials belong
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J2 = R.ideal(I2) #ideal defined by the set I
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print(J2.is_prime(), len(R.gens()) - J2.dimension() - 1)
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I3 = AS.canonical_ideal_polynomials(3)
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J3 = R.ideal(I2 + I3)
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print(J3.is_prime(), len(R.gens()) - J3.dimension() - 1)
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p = 5
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F = GF(p)
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Rx.<x> = PolynomialRing(F)
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C = superelliptic(x, 1)
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AS = as_cover(C, [C.x^8], prec = 200)
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I2 = AS.canonical_ideal_polynomials(2, threshold=15)
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R = I2[0].parent() #ring, to which the polynomials belong
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J2 = R.ideal(I2) #ideal defined by the set I
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print(J2.is_prime(), len(R.gens()) - J2.dimension() - 1)
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I3 = AS.canonical_ideal_polynomials(3, threshold=20)
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J3 = R.ideal(I2 + I3)
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print(J3.is_prime(), len(R.gens()) - J3.dimension() - 1)
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