`fq_embed_gens`

Synopsis#include <flint/fq_embed.h>

void fq_embed_gens(fq_t gen_sub, fq_t gen_sup, fmpz_mod_poly_t minpoly, const fq_ctx_t sub_ctx, const fq_ctx_t sup_ctx)source

Given contexts for fields $k$ = sub_ctx of degree $m$ and $K$ = sup_ctx of degree $n$ with $m \mid n$ , computes a generator gen_sub of $k$ over $\mathbb{F}_p$ , its minimal polynomial minpoly, and a root gen_sup of minpoly in $K$ . These data define the embedding $k \to K$ that maps gen_sub to gen_sup.

For $m = 1$ both generators are set to the generator of the prime field context ( $-c_0/c_1$ for the defining polynomial $c_1 x + c_0$ ) and minpoly is not modified (it should be $x - \mathit{gen\_sub}$ , which the caller must set before calling fq_embed_matrices); otherwise _fq_embed_gens_naive is called. Different roots give different embeddings, which differ by a power of the Frobenius map; the one returned is not in general compatible with the Conway polynomials of the two fields.

Cite this page

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

@misc{flint-doc-fq-embed-fq-embed-gens,
  author       = {{The FLINT team}},
  title        = {{fq\_embed\_gens (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_gens.html},
  note         = {Generated 2026-11-02}
}

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