np.multiply¶

np.multiply(x, y)[source]¶

Multiplies two Galois field arrays element-wise.

References

https://numpy.org/doc/stable/reference/generated/numpy.multiply.html

Examples

Multiplying two Galois field arrays results in field multiplication.

In [1]: GF = galois.GF(31)

In [2]: x = GF.Random(10); x
Out[2]: GF([20, 13,  3, 25, 11, 19, 10, 17, 25,  9], order=31)

In [3]: y = GF.Random(10); y
Out[3]: GF([11,  8, 29, 14,  0, 18, 25, 14, 19, 13], order=31)

In [4]: np.multiply(x, y)
Out[4]: GF([ 3, 11, 25,  9,  0,  1,  2, 21, 10, 24], order=31)

In [5]: x * y
Out[5]: GF([ 3, 11, 25,  9,  0,  1,  2, 21, 10, 24], order=31)

Multiplying a Galois field array with an integer results in scalar multiplication.

In [6]: GF = galois.GF(31)

In [7]: x = GF.Random(10); x
Out[7]: GF([ 4, 20, 12,  5, 24, 28, 27, 18, 30, 27], order=31)

In [8]: np.multiply(x, 3)
Out[8]: GF([12, 29,  5, 15, 10, 22, 19, 23, 28, 19], order=31)

In [9]: x * 3
Out[9]: GF([12, 29,  5, 15, 10, 22, 19, 23, 28, 19], order=31)

In [10]: print(GF.properties)
GF(31):
  characteristic: 31
  degree: 1
  order: 31
  irreducible_poly: Poly(x + 28, GF(31))
  is_primitive_poly: True
  primitive_element: GF(3, order=31)

# Adding `characteristic` copies of any element always results in zero
In [11]: x * GF.characteristic
Out[11]: GF([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], order=31)