galois.Poly

class galois.Poly(coeffs, field=<class 'galois.gf2.GF2'>)

Bases: object

asdf

Examples

Create polynomials over GF(2)

# Construct a polynominal over GF(2)
In [20]: a = galois.Poly([1,0,1,1]); a
Out[20]: Poly(x^3 + x + 1 , GF2)

# Construct the same polynomial by only specifying its non-zero coefficients
In [21]: b = galois.Poly.NonZero([1,1,1], [3,1,0]); b
Out[21]: Poly(x^3 + x + 1 , GF2)

Create polynomials over GF(7)

# Construct the GF(7) field
In [22]: GF = galois.GF_factory(7, 1)

# Construct a polynominal over GF(7)
In [23]: a = galois.Poly([4,0,3,0,0,2], field=GF); a
Out[23]: Poly(4x^5 + 3x^3 + 2 , GF7)

# Construct the same polynomial by only specifying its non-zero coefficients
In [24]: b = galois.Poly.NonZero([4,3,2], [5,3,0], field=GF); b
Out[24]: Poly(4x^5 + 3x^3 + 2 , GF7)

Polynomial arithmetic

In [25]: a = galois.Poly([1,0,6,3], field=GF); a
Out[25]: Poly(x^3 + 6x + 3 , GF7)

In [26]: b = galois.Poly([2,0,2], field=GF); b
Out[26]: Poly(2x^2 + 2 , GF7)

In [27]: a + b
Out[27]: Poly(x^3 + 2x^2 + 6x + 5 , GF7)

In [28]: a - b
Out[28]: Poly(x^3 + 5x^2 + 6x + 1 , GF7)

# Compute the quotient of the polynomial division
In [29]: a / b
Out[29]: Poly(4x , GF7)

# True division and floor division are equivalent
In [30]: a / b == a // b
Out[30]: True

# Compute the remainder of the polynomial division
In [31]: a % b
Out[31]: Poly(5x + 3 , GF7)

__init__(coeffs, field=<class 'galois.gf2.GF2'>)

Initialize self. See help(type(self)) for accurate signature.

Methods

NonZero(coeffs, degrees[, field])	Examples
__init__(coeffs[, field])	Initialize self.
divmod(dividend, divisor)

Attributes

coeffs
degree	The degree of the polynomial, i.e. the highest degree with non-zero coefficient.
field	The finite field to which the coefficients belong.
str

classmethod NonZero(coeffs, degrees, field=<class 'galois.gf2.GF2'>)

Examples

# Construct a polynomial over GF2 only specifying the non-zero terms
In [32]: a = galois.Poly.NonZero([1,1,1], [3,1,0]); a
Out[32]: Poly(x^3 + x + 1 , GF2)

static divmod(dividend, divisor)

property coeffs

property degree

The degree of the polynomial, i.e. the highest degree with non-zero coefficient.

Type

int

property field

The finite field to which the coefficients belong.

Type

galois.GF2 or galois.GFp

property str