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