`fq_zech_embed_matrices`

Synopsis#include <flint/fq_zech_embed.h>

void fq_zech_embed_matrices(nmod_mat_t embed, nmod_mat_t project, const fq_zech_t gen_sub, const fq_zech_ctx_t sub_ctx, const fq_zech_t gen_sup, const fq_zech_ctx_t sup_ctx, const nmod_poly_t gen_minpoly)

Given the output of fq_zech_embed_gens for fields $k$ = sub_ctx and $K$ = sup_ctx of degrees $m \mid n$ , computes the $n \times m$ matrix embed of the embedding $\varphi: k \to K$ that maps gen_sub to gen_sup, and an $m \times n$ matrix project of a $k$ -linear projection $\pi: K \to k$ with $\pi \circ \varphi = \mathrm{id}$ , so that $\mathit{project} \cdot \mathit{embed}$ is the $m \times m$ identity. The matrices act on column vectors of coordinates in the monomial bases.

Generated from the same template as fq_embed_matrices, whose documentation has the details.

Cite this page

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

@misc{flint-doc-fq-zech-embed-fq-zech-embed-matrices,
  author       = {{The FLINT team}},
  title        = {{fq\_zech\_embed\_matrices (fq\_zech\_embed.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fq_zech_embed/fq_zech_embed_matrices.html},
  note         = {Generated 2026-11-02}
}

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