classmethod galois.FieldArray.Vandermonde(element: ElementLike, rows: int, cols: int, dtype: DTypeLike | None = None) → FieldArray

Creates an m×n Vandermonde matrix of a∈GF(q).

Parameters
element: ElementLike

An element a of 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×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)