Creates an \(m \times n\) Vandermonde matrix of \(a \in \mathrm{GF}(q)\).

Parameters¶

element: ElementLike¶

An element \(a\) of \(\mathrm{GF}(q)\).

rows: int¶

The number of rows \(m\) in the Vandermonde matrix.

cols: int¶

The number of columns \(n\) in the Vandermonde matrix.

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¶

A \(m \times n\) Vandermonde matrix.

Examples¶

In [1]: GF = galois.GF(2**3, display="power")

In [2]: a = GF.primitive_element; a
Out[2]: GF(α, order=2^3)

In [3]: V = GF.Vandermonde(a, 7, 7); V
Out[3]: 
GF([[  1,   1,   1,   1,   1,   1,   1],
    [  1,   α, α^2, α^3, α^4, α^5, α^6],
    [  1, α^2, α^4, α^6,   α, α^3, α^5],
    [  1, α^3, α^6, α^2, α^5,   α, α^4],
    [  1, α^4,   α, α^5, α^2, α^6, α^3],
    [  1, α^5, α^3,   α, α^6, α^4, α^2],
    [  1, α^6, α^5, α^4, α^3, α^2,   α]], order=2^3)