`fq_embed_dual_to_mono_matrix`

Synopsis#include <flint/fq_embed.h>

void fq_embed_dual_to_mono_matrix(fmpz_mod_mat_t res, const fq_ctx_t ctx)source

Sets the $d \times d$ matrix res to the inverse of fq_embed_mono_to_dual_matrix. By Euler's formula the dual basis of $1, x, \ldots, x^{d-1}$ is $b_0 / f'(x), \ldots, b_{d-1} / f'(x)$ , where $f(X)/(X - x) = \sum b_j X^j$ , so the matrix is the product of the multiplication matrix of $1/f'(x)$ and the Hankel matrix of the coefficients of $f$ .

Cite this page

The FLINT team, “fq_embed_dual_to_mono_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_dual_to_mono_matrix.html (generated 2026-11-02).

@misc{flint-doc-fq-embed-fq-embed-dual-to-mono-matrix,
  author       = {{The FLINT team}},
  title        = {{fq\_embed\_dual\_to\_mono\_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_dual_to_mono_matrix.html},
  note         = {Generated 2026-11-02}
}

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