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([20, 22, 11, 13, 14, 20, 18, 23, 29, 19], order=31)

In [3]: y = GF.Random(10); y
Out[3]: GF([29, 29,  7, 21, 25, 13, 20, 17, 23,  6], order=31)

In [4]: np.multiply(x, y)
Out[4]: GF([22, 18, 15, 25,  9, 12, 19, 19, 16, 21], order=31)

In [5]: x * y
Out[5]: GF([22, 18, 15, 25,  9, 12, 19, 19, 16, 21], 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([ 2, 12, 11, 20, 20, 13,  7, 17,  1, 27], order=31)

In [8]: np.multiply(x, 3)
Out[8]: GF([ 6,  5,  2, 29, 29,  8, 21, 20,  3, 19], order=31)

In [9]: x * 3
Out[9]: GF([ 6,  5,  2, 29, 29,  8, 21, 20,  3, 19], 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)