galois.FieldArray.vector

galois.FieldArray.vector(dtype: DTypeLike | None = None) → FieldArray

Converts an array over \(\mathrm{GF}(p^m)\) to length-\(m\) vectors over the prime subfield \(\mathrm{GF}(p)\).

Parameters:¶

dtype: DTypeLike | None = None¶: The numpy.dtype of the array elements. The default is None which represents the smallest unsigned data type for this FieldArray subclass (the first element in dtypes).

Returns:¶

An array over \(\mathrm{GF}(p)\) with last dimension \(m\).

Notes¶

This method is the inverse of the Vector() constructor. For an array with shape (n1, n2), the output shape is (n1, n2, m). By convention, the vectors are ordered from degree \(m-1\) to degree 0.

Examples¶

Integer Polynomial Power

In [1]: GF = galois.GF(3**3)

In [2]: a = GF([11, 7]); a
Out[2]: GF([11,  7], order=3^3)

In [3]: vec = a.vector(); vec
Out[3]: 
GF([[1, 0, 2],
    [0, 2, 1]], order=3)

In [4]: GF.Vector(vec)
Out[4]: GF([11,  7], order=3^3)

In [5]: GF = galois.GF(3**3, repr="poly")

In [6]: a = GF([11, 7]); a
Out[6]: GF([α^2 + 2,  2α + 1], order=3^3)

In [7]: vec = a.vector(); vec
Out[7]: 
GF([[1, 0, 2],
    [0, 2, 1]], order=3)

In [8]: GF.Vector(vec)
Out[8]: GF([α^2 + 2,  2α + 1], order=3^3)

In [9]: GF = galois.GF(3**3, repr="power")

In [10]: a = GF([11, 7]); a
Out[10]: GF([α^12, α^16], order=3^3)

In [11]: vec = a.vector(); vec
Out[11]: 
GF([[1, 0, 2],
    [0, 2, 1]], order=3)

In [12]: GF.Vector(vec)
Out[12]: GF([α^12, α^16], order=3^3)