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([ 0,  3, 14,  5, 11, 14,  1, 16, 30,  4], order=31)

In [3]: y = GF.Random(10); y
Out[3]: GF([14, 10, 14, 14, 10, 21, 27,  5,  2, 28], order=31)

In [4]: np.multiply(x, y)
Out[4]: GF([ 0, 30, 10,  8, 17, 15, 27, 18, 29, 19], order=31)

In [5]: x * y
Out[5]: GF([ 0, 30, 10,  8, 17, 15, 27, 18, 29, 19], 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([21,  2, 26, 11,  2, 16,  6, 10,  0, 28], order=31)

In [8]: np.multiply(x, 3)
Out[8]: GF([ 1,  6, 16,  2,  6, 17, 18, 30,  0, 22], order=31)

In [9]: x * 3
Out[9]: GF([ 1,  6, 16,  2,  6, 17, 18, 30,  0, 22], 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)