np.multiply

np.multiply(x, y)

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([25,  5,  9, 23, 11, 24,  3,  3,  0, 17], order=31)

In [3]: y = GF.Random(10); y
Out[3]: GF([22, 16, 10, 29,  7, 30,  2, 15,  5, 22], order=31)

In [4]: np.multiply(x, y)
Out[4]: GF([23, 18, 28, 16, 15,  7,  6, 14,  0,  2], order=31)

In [5]: x * y
Out[5]: GF([23, 18, 28, 16, 15,  7,  6, 14,  0,  2], 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([16, 18,  6, 20,  9,  1, 27, 16,  8, 12], order=31)

In [8]: np.multiply(x, 3)
Out[8]: GF([17, 23, 18, 29, 27,  3, 19, 17, 24,  5], order=31)

In [9]: x * 3
Out[9]: GF([17, 23, 18, 29, 27,  3, 19, 17, 24,  5], order=31)

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

# 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)