`ca_mat_dft`

Synopsis#include <flint/ca_mat.h>

void ca_mat_dft(ca_mat_t res, int type, ca_ctx_t ctx)source

Sets res to a matrix of the discrete Fourier transform of length $n$ , the smaller of the two dimensions (along the larger dimension the entries repeat periodically). With $\omega = e^{2 \pi i / n}$ , the entries $A_{j,k}$ are $\omega^{-jk}$ for type = 0, $\omega^{jk}/n$ for type 1, $\omega^{-jk}/\sqrt{n}$ for type 2 and $\omega^{jk}/\sqrt{n}$ for type 3. Types 0 and 1 are inverse to each other, and so are types 2 and 3. The entries are elements of the cyclotomic field $\mathbb{Q}(\omega)$ (and $\sqrt{n}$ ).

Cite this page

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

@misc{flint-doc-ca-mat-ca-mat-dft,
  author       = {{The FLINT team}},
  title        = {{ca\_mat\_dft (ca\_mat.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/ca_mat/ca_mat_dft.html},
  note         = {Generated 2026-11-02}
}

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