classmethod galois.FieldArray.Vector(dtype: = None)

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: = 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)