plumial.core.P._P.H

_P.H()

Create matrix of k polynomial coefficients for odd cycle elements.

This method generates a matrix where each row contains the coefficients of the k polynomial (with respect to g) for each odd p-value in the cycle. This is used for matrix operations analyzing the polynomial structure of Collatz cycles.

Return type:

MutableDenseMatrix

Returns:

SymPy Matrix with each row containing k polynomial coefficients for odd cycle elements

Mathematical Structure:

For each odd p in cycle, extract coefficients of p.k() polynomial w.r.t. g Matrix shape: (number_of_odd_elements, max_polynomial_degree + 1)

Examples

>>> p = P(133)  # Cycle with odd elements
>>> h_matrix = p.H()
>>> # Returns matrix with k polynomial coefficients for each odd cycle element

Matrix Operations:

>>> p = P(281)  # 8-element cycle
>>> H_mat = p.H()
>>> # Matrix with rows for each odd element's k polynomial coefficients

Note

Only processes odd cycle elements as these are most relevant for analysis