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

Parameters:¶

array: ArrayLike¶

An array over \(\mathrm{GF}(p)\) with last dimension \(m\). An array with shape (n1, n2, m) has output shape (n1, n2). By convention, the vectors are ordered from degree \(m-1\) to degree 0.

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 \(\mathrm{GF}(p^m)\).

Notes¶

This method is the inverse of the vector() method.

Examples¶

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

In [2]: a = GF.Vector([[1, 0, 2], [0, 2, 1]]); a
Out[2]: GF([11,  7], order=3^3)

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

In [4]: GF = galois.GF(3**3, repr="poly")

In [5]: a = GF.Vector([[1, 0, 2], [0, 2, 1]]); a
Out[5]: GF([α^2 + 2,  2α + 1], order=3^3)

In [6]: a.vector()
Out[6]: 
GF([[1, 0, 2],
    [0, 2, 1]], order=3)

In [7]: GF = galois.GF(3**3, repr="power")

In [8]: a = GF.Vector([[1, 0, 2], [0, 2, 1]]); a
Out[8]: GF([α^12, α^16], order=3^3)

In [9]: a.vector()
Out[9]: 
GF([[1, 0, 2],
    [0, 2, 1]], order=3)