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classmethod galois.Poly.Int(integer: int, field: Type[Array] | None =
None
) Poly Constructs a polynomial over \(\mathrm{GF}(p^m)\) from its integer representation.
Int()
and__int__()
are inverse operations.Examples¶
Construct a polynomial over \(\mathrm{GF}(2)\) from its integer representation.
In [1]: f = galois.Poly.Int(5); f Out[1]: Poly(x^2 + 1, GF(2)) In [2]: int(f) Out[2]: 5
Construct a polynomial over \(\mathrm{GF}(3^5)\) from its integer representation.
In [3]: GF = galois.GF(3**5) In [4]: f = galois.Poly.Int(186535908, field=GF); f Out[4]: Poly(13x^3 + 117, GF(3^5)) In [5]: int(f) Out[5]: 186535908 # The polynomial/integer equivalence In [6]: int(f) == 13*GF.order**3 + 117 Out[6]: True
Construct a polynomial over \(\mathrm{GF}(2)\) from its binary string.
In [7]: f = galois.Poly.Int(int("0b1011", 2)); f Out[7]: Poly(x^3 + x + 1, GF(2)) In [8]: bin(f) Out[8]: '0b1011'
Construct a polynomial over \(\mathrm{GF}(2^3)\) from its octal string.
In [9]: GF = galois.GF(2**3) In [10]: f = galois.Poly.Int(int("0o5034", 8), field=GF); f Out[10]: Poly(5x^3 + 3x + 4, GF(2^3)) In [11]: oct(f) Out[11]: '0o5034'
Construct a polynomial over \(\mathrm{GF}(2^8)\) from its hexadecimal string.
In [12]: GF = galois.GF(2**8) In [13]: f = galois.Poly.Int(int("0xf700a275", 16), field=GF); f Out[13]: Poly(247x^3 + 162x + 117, GF(2^8)) In [14]: hex(f) Out[14]: '0xf700a275'