`fq_embed_trace_matrix`

Synopsis#include <flint/fq_embed.h>

void fq_embed_trace_matrix(fmpz_mod_mat_t res, const fmpz_mod_mat_t basis, const fq_ctx_t sub_ctx, const fq_ctx_t sup_ctx)

source

Given contexts for $k$ = sub_ctx and $K$ = sup_ctx of degrees $m \mid n$ and the $n \times m$ matrix basis of an embedding $\varphi: k \to K$ , sets res to the $m \times n$ matrix of the map $y \mapsto \varphi^{-1}(\operatorname{Tr}_{K/\varphi(k)}(y))$ . It is computed as $D_k \cdot \mathit{basis}^T \cdot M_K$ , with $D_k$ = fq_embed_dual_to_mono_matrix for $k$ and $M_K$ = fq_embed_mono_to_dual_matrix for $K$ . For $m = n$ the result is the inverse of basis.

Cite this page

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

@misc{flint-doc-fq-embed-fq-embed-trace-matrix,
  author       = {{The FLINT team}},
  title        = {{fq\_embed\_trace\_matrix (fq\_embed.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fq_embed/fq_embed_trace_matrix.html},
  note         = {Generated 2026-11-02}
}

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