-
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 isNone
which represents the smallest unsigned data type for thisFieldArray
subclass (the first element indtypes
).
- dtype: DTypeLike | None =
- 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¶
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)