plumial.core.P._P.G

_P.G()

Create column vector of g powers from g^(o-1) down to g^0.

This method delegates to the D object’s G() method to generate a column vector containing powers of g in descending order, used for matrix operations with polynomial coefficients.

Return type:

MutableDenseMatrix

Returns:

SymPy Matrix column vector with g powers [g^(o-1), g^(o-2), …, g^1, g^0]

Mathematical Structure:

For o odd bits, creates: [g^(o-1), g^(o-2), …, g^1, g^0]^T

Examples

>>> p = P(133)  # o=2, e=5
>>> g_vector = p.G()
>>> # Returns Matrix([[g], [1]]) for powers g^1, g^0

Matrix Operations:

>>> p = P(281)  # o=3, e=5
>>> G_vec = p.G()
>>> # Returns Matrix([[g**2], [g], [1]]) for use in polynomial operations

Note

This method delegates to the associated D object: self._d.G()