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97 lines
3.4 KiB
Python
97 lines
3.4 KiB
Python
import math
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#defines the field itself
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#responsible for creating elements and performing operations
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#all elements contain a pointer to the field that created them
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#elements from different fields can't interact, even if they're equivalent
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class GF:
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def __init__(self, *args):
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def getcharacteristic(a):
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for i in (2, 3, 5, 7, 11, 13, 17, 19, 23):
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if a%i == 0:
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b = math.log(a, i)
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if not math.isclose(b, int(b+1e-6), abs_tol=1e-6) :
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raise ValueError('%i is not a prime power' % a)
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return i, int(b+1e-6)
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if len(args) == 1:
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p, n = getcharacteristic(args[0])
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elif len(args) > 2:
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raise TypeError('too many arguments')
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else:
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p, n = args
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self.characteristic = p
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self.order = p**n
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self.degree = n
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file = open('gf' + str(p) + '.txt', 'r')
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pol = file.readlines()[n-2]
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file.close()
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#removes newline then splits into individual terms
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pol = pol[:-1].split(',')
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#(exponent, coefficient) for each term of the polynomial
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self.poly = []
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for i in pol:
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if '(' in i:
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a, b = i.split('(')
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#constant term isn't given an exponent in the txt file
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a = a if a else 0
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self.poly.append((int(a), int(b[:-1])))
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else:
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self.poly.append((int(i),1))
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if p == 2:
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self.poly.append((0,1))
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#performs a modulus operation using self.poly
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def mod(self, other):
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#copy the provided list
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other = list(other)
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#creates a new element with the given value
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def new(val):
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#splits integers into their binary components
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def bisplit(bal):
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pass
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if isisntance(val, int):
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if self.characteristic != 2:
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raise TypeError('integer definition of field elements is only allowed in fields of characteristic 2')
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#TODO cover binary conversion
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#covers the case that the value is an iterable of individual terms
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#first term is for exponent zero, etc.
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#accepts integers or strings
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else:
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#makes val into a list in order to check the number of terms
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if isinstance(val, str):
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#strings are interpreted as the first character being most significant
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val = [i for i in val[::-1]]
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else:
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val = list(val)
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pol = [0] * len(val)
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for i in range(len(val)):
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if isinstance(val[i], int):
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pol[i] = val[i]
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else:
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#TODO for christs sake refactor this
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try:
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pol[i] = val[i]
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except ValueError:
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try:
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pol[i] = int(val[i])
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except ValueError:
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a = ord(val[i].tolower())
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if 97 <= a <= 122:
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pol[i] = a - 87
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else:
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raise ValueError('polynomial coefficient is uninterprettable')
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pol = self.mod(pol)
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class GFElement:
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def __init_(self, value, field):
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self.field = field |