37 lines
1.2 KiB
Python
37 lines
1.2 KiB
Python
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class template:
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'''Template of a p-group cover'''
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def __init__(self, height, field, group, fcts, gp_action):
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self.height = height
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self.group = group
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self.fcts = fcts #RHSs of the Artin-Schreier equations
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self.gp_action = gp_action #action of the generators of the group on z[i]'s
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self.field = field
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n = height
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variable_names = ''
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for i in range(n):
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variable_names += 'z'+str(i)+','
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for i in range(n):
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variable_names += 'f'+str(i)
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if i!=n-1:
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variable_names += ','
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R = PolynomialRing(field, 2*n, variable_names)
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z = R.gens()[:n]
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f = R.gens()[n:]
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def elementary_template(p, n):
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group = elementary_gp(p, n)
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field = GF(p)
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variable_names = ''
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for i in range(n):
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variable_names += 'z'+str(i)+','
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for i in range(n):
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variable_names += 'f'+str(i)
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if i!=n-1:
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variable_names += ','
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R = PolynomialRing(field, 2*n, variable_names)
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z = R.gens()[:n]
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f = R.gens()[n:]
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height = n
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fcts = [f[i] for i in range(n)]
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gp_action = [[z[j] + (i == j) for j in range(n)] for i in range(n)]
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return template(height, field, group, fcts, gp_action)
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