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,  3, 15, 20, 12,  2, 10, 21,  1,  1], order=31)

In [3]: y = GF.Random(10); y
Out[3]: GF([11,  5, 20, 22, 15, 12, 28, 27,  7, 27], order=31)

In [4]: np.multiply(x, y)
Out[4]: GF([27, 15, 21,  6, 25, 24,  1,  9,  7, 27], order=31)

In [5]: x * y
Out[5]: GF([27, 15, 21,  6, 25, 24,  1,  9,  7, 27], 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([ 8, 23, 13, 24, 22,  4, 29,  2,  2, 21], order=31)

In [8]: np.multiply(x, 3)
Out[8]: GF([24,  7,  8, 10,  4, 12, 25,  6,  6,  1], order=31)

In [9]: x * 3
Out[9]: GF([24,  7,  8, 10,  4, 12, 25,  6,  6,  1], 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)