plumial.core.D._D.G

_D.G()[source]

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

This method generates a column vector containing powers of g in descending order, used for matrix operations with polynomial coefficients. The vector has o elements corresponding to the number of odd bits.

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

>>> d = D(2, 5)  # o=2, e=5
>>> g_vector = d.G()
>>> # Returns Matrix([[g], [1]]) for powers g^1, g^0
Matrix Operations:
>>> d = D(3, 4)  # o=3, e=4
>>> G_vec = d.G()
>>> # Returns Matrix([[g**2], [g], [1]]) for use in polynomial operations