-
classmethod galois.FieldArray.Vandermonde(element: ElementLike, rows: int, cols: int, dtype: DTypeLike | None =
None
) FieldArray 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 isNone
which represents the smallest unsigned data type for thisFieldArray
subclass (the first element indtypes
).
- 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)