44 lines
1.1 KiB
Python
44 lines
1.1 KiB
Python
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p = 3
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m = 1
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F = GF(p)
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Rx.<x> = PolynomialRing(F)
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f = x
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C_super = superelliptic(f, m)
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Rxy.<x, y> = PolynomialRing(F, 2)
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f1 = superelliptic_function(C_super, x^7)
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f2 = superelliptic_function(C_super, x^4)
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AS = as_cover(C_super, [f1, f2], prec=1000)
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print(AS.uniformizer())
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def rep_jumps(AS, threshold = 30):
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ile = 1
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i = 1
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result = []
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flag = 0
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while(flag == 0):
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if len(AS.at_most_poles(i, threshold = threshold)) > ile:
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ile = len(AS.at_most_poles(i, threshold = threshold))
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result += [i]
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if i%p != 0:
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flag = 1
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i+=1
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return result
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#print(rep_jumps(AS, threshold = 30))
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def uniformizer(AS, threshold = 30):
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p = AS.characteristic
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n = AS.height
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variable_names = 'x, y'
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for i in range(n):
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variable_names += ', z' + str(i)
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Rxyz = PolynomialRing(F, n+2, variable_names)
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x, y = Rxyz.gens()[:2]
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z = Rxyz.gens()[2:]
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zmag = AS.magical_element()[0]
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v_x = as_function(AS, x).expansion_at_infty().valuation()
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dprim = AS.exponent_of_different_prim()
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d, a, b = xgcd(v_x, -dprim)
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return as_function(AS, x^a*zmag.function^b)
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