corrected as_transform at non-totally ramified pts
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@ -202,14 +202,21 @@ def artin_schreier_transform(power_series, prec = 10):
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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jump = max(-(power_series.valuation()), 0)
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jump = max(-(power_series.valuation()), 0)
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try:
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try:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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if jump != 0:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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except:
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except:
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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return (jump, power_series.list()[0])
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return (jump, power_series.list()[0])
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T_rev = new_reverse(T, prec = prec)
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if jump != 0:
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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T_rev = new_reverse(T, prec = prec)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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return(jump, correction, t_old, z)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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return(jump, correction, t_old, z)
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if jump == 0:
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aux = t^p - t
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z = new_reverse(aux, prec = prec)
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z = z(t = power_series)
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return(0, correction, t, z)
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def are_forms_linearly_dependent(set_of_forms):
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def are_forms_linearly_dependent(set_of_forms):
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@ -1,10 +1,10 @@
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p = 3
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p = 3
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F = GF(3)
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F = GF(3^2, 'a')
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Rx.<x> = PolynomialRing(F)
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Rx.<x> = PolynomialRing(F)
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P1 = superelliptic(x^2 + 1, 1)
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P1 = superelliptic(x^2 + 1, 2)
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fct1 = (P1.x)^2
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fct1 = (P1.x)^2
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fct2 = fct1 + (P1.x)/(P1.y - P1.x)
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fct2 = fct1 + (P1.x)/(P1.y - P1.x)
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fct3 = (P1.x)^4
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fct3 = (P1.x)^4
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C = heisenberg_cover(P1, [fct1, fct2, fct3], prec=300)
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C = heisenberg_cover(P1, [1/2*fct1, fct2, fct3], prec=300)
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print(C)
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print(C)
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a, b, c = heisenberg_group_action_matrices_holo(C)
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a1, b1, c1 = heisenberg_group_action_matrices_holo(C)
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@ -225,15 +225,21 @@ def artin_schreier_transform(power_series, prec = 10):
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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jump = max(-(power_series.valuation()), 0)
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jump = max(-(power_series.valuation()), 0)
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try:
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try:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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if jump != 0:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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except:
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except:
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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return (jump, power_series.list()[0])
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return (jump, power_series.list()[0])
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T_rev = new_reverse(T, prec = prec)
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if jump != 0:
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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T_rev = new_reverse(T, prec = prec)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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return(jump, correction, t_old, z)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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return(jump, correction, t_old, z)
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if jump == 0:
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aux = t^p - t
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z = new_reverse(aux, prec = prec)
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z = z(t = power_series)
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return(0, correction, t, z)
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def are_forms_linearly_dependent(set_of_forms):
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def are_forms_linearly_dependent(set_of_forms):
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from sage.rings.polynomial.toy_variety import is_linearly_dependent
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from sage.rings.polynomial.toy_variety import is_linearly_dependent
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@ -221,14 +221,21 @@ def artin_schreier_transform(power_series, prec = 10):
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
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jump = max(-(power_series.valuation()), 0)
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jump = max(-(power_series.valuation()), 0)
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try:
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try:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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if jump != 0:
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T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
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except:
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except:
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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print("no ", str(jump), "-th root; divide by", power_series.list()[0])
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return (jump, power_series.list()[0])
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return (jump, power_series.list()[0])
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T_rev = new_reverse(T, prec = prec)
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if jump != 0:
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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T_rev = new_reverse(T, prec = prec)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
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return(jump, correction, t_old, z)
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z = 1/t^(jump) + Rt(correction)(t = t_old)
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return(jump, correction, t_old, z)
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if jump == 0:
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aux = t^p - t
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z = new_reverse(aux, prec = prec)
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z = z(t = power_series)
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return(0, correction, t, z)
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def are_forms_linearly_dependent(set_of_forms):
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def are_forms_linearly_dependent(set_of_forms):
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