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- # See https://math.stackexchange.com/questions/294644/basis-for-the-riemann-roch-space-lkp-on-a-curve?rq=1
- # Basis for the Riemann-Roch space L(kP) on a curve
- # find a basis for L(k[P])
- # Compute basis elements for L(n[P]) on y^2 = x^3 - x at P = (0, 0)
- R.<x> = FunctionField(QQbar)
- S.<Y> = R[]
- L.<y> = R.extension(Y^2 - (x^3 - x))
- # Verify that P is ordinary with the ideal <x - 0, y - 0>
- I = L.maximal_order().ideal(x,y)
- assert I.is_prime()
- D = I.divisor()
- print("L([P]) =", D.basis_function_space())
- print("L(2[P]) =", (2*D).basis_function_space())
- print("L(3[P]) =", (3*D).basis_function_space())
- print("L(4[P]) =", (4*D).basis_function_space())
- print("L(5[P]) =", (5*D).basis_function_space())
- print("L(6[P]) =", (6*D).basis_function_space())
- print("L(7[P]) =", (7*D).basis_function_space())
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