44 lines
1.8 KiB
Python
44 lines
1.8 KiB
Python
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def decomposition_g0_g8(fct):
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'''Writes fct as a difference g0 - g8, with g0 regular on the affine patch and g8 at the points in infinity.'''
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C = fct.curve
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g = C.genus()
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if fct.coordinates() != g*[0]:
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raise ValueError("The given function cannot be written as g0 - g8.")
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Fxy, Rxy, x, y = C.fct_field
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fct = Fxy(fct.function)
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num = fct.numerator()
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den = fct.denominator()
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aux_den = superelliptic_function(C, Rxy(den))
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g0 = superelliptic_function(C, 0)
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g8 = superelliptic_function(C, 0)
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for monomial in num.monomials():
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aux = superelliptic_function(C, monomial)
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if aux.expansion_at_infty().valuation() >= aux_den.expansion_at_infty().valuation():
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g8 += num.monomial_coefficient(monomial)*aux/aux_den
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else:
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g0 += num.monomial_coefficient(monomial)*aux/aux_den
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return (g0, g8)
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def decomposition_omega0_omega8(omega, prec=50):
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'''Writes omega as a difference omega0 - omega8, with omega0 regular on the affine patch and omega8 at the points in infinity.'''
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C = omega.curve
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Fxy, Rxy, x, y = C.fct_field
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fct = Fxy(omega.form)
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num = fct.numerator()
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den = fct.denominator()
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aux_den = superelliptic_function(C, Rxy(den))
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g0 = superelliptic_function(C, 0)
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g8 = superelliptic_function(C, 0)
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dx_valuation = C.dx.expansion_at_infty(prec=prec).valuation()
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for monomial in num.monomials():
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aux = superelliptic_function(C, monomial)
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if aux.expansion_at_infty(prec=prec).valuation() + dx_valuation >= aux_den.expansion_at_infty(prec=prec).valuation():
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g8 += num.monomial_coefficient(monomial)*aux/aux_den
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else:
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g0 += num.monomial_coefficient(monomial)*aux/aux_den
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g0, g8 = g0*C.dx, g8*C.dx
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if g0.is_regular_on_U0():
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return (g0, g8)
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else:
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raise Error("Something went wrong.")
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