FLINT3.7.0-dev
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gr_poly_shiftless_decomposition, gr_poly_shiftless_decomposition_factor

Synopsis#include <flint/gr_poly.h>
int gr_poly_shiftless_decomposition(gr_ptr c, gr_poly_vec_t slfac, gr_vec_t slshifts, gr_vec_t slmult, const gr_poly_t f, gr_ctx_t ctx)source
int gr_poly_shiftless_decomposition_factor(gr_ptr c, gr_poly_vec_t slfac, gr_vec_t slshifts, gr_vec_t slmult, const gr_poly_t f, gr_ctx_t ctx)source

Compute a decomposition

f=c∏i=1r∏jgi(x+hi,j)ei,jf = c \prod_{i=1}^{r} \prod_{j} g_i(x + h_{i,j})^{e_{i,j}}

where cc is a constant, the gig_i are squarefree of degree at least 1, gi(x)g_i(x) and gj(x+h)g_j(x + h) are coprime for i≠ji \ne j and all h∈Zh \in \mathbb{Z}, gi(x)g_i(x) and gi(x+h)g_i(x + h) are coprime for all nonzero h∈Zh \in \mathbb{Z}, and the ei,j≥1e_{i,j} \ge 1 and 0=hi,1<hi,2<⋯0 = h_{i,1} < h_{i,2} < \cdots are integers.

slfac must be a vector of polynomials over ctx, and slshifts and slmult vectors of vectors of fmpz. The factor version (the only algorithm implemented) computes the irreducible factorisation and sorts the factors into classes of shift-equivalent polynomials.

Cite this page

The FLINT team, “gr_poly_shiftless_decomposition, gr_poly_shiftless_decomposition_factor (gr_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_poly/gr_poly_shiftless_decomposition.html (generated 2026-11-02).