weil.cpp

/* SPDX-FileCopyrightText: © 2022 Maik Herbers */
/* SPDX-License-Identifier: GPL-3.0-or-later */

#include <algorithm>
#include <cstdlib>
#include <cstring>
#include <exception>
#include <fstream>
#include <iostream>
#include <optional>
#include <sstream>

#ifndef _GNU_SOURCE
#define _GNU_SOURCE
#endif
#include <getopt.h>
#include <unistd.h>

#include "common.hpp"
#include "discriminant_form.hpp"
#include "sl2z.hpp"

int
print_help(bool error)
{
	const char* s = "Usage:\n"
			"\tweil [options] <command> [arguments]\n"
			"\n"
			"Commands:\n"
			"  DS-info <file>                            output some information about the discriminant form associated\n"
			"                                            to the gram matrix in `file'\n"
			"  DS-c-kernel <file> <c>                    compute `D_c' where `D' is the discriminant form associated\n"
			"                                            to the gram matrix in `file'\n"
			"  DS-c-image <file> <c>                     compute `D^c' where `D' is the discriminant form associated\n"
			"                                            to the gram matrix in `file'\n"
			"  DS-c-star <file> <c>                      compute `D^c*' where `D' is the discriminant form associated\n"
			"                                            to the gram matrix in `file'\n"
			"  Lattice-smith-gram-matrix <file>          compute the gram matrix of the quadratic form in `file'  with\n"
			"                                            respect to the smith basis\n"
			"  DS-get-orbits <gram> <aut>                compute the orbits in the discriminant form associated to the gram\n"
			"                                            matrix `gram' under the action induced by the automorphisms in `aut'\n"
			"  SL2Z-split <m>                            split the matrix `m' in SL2Z into generators\n"
			"  VV-Theta-Series [options] <file> <prec>   compute the vector valued theta series associated to the\n"
			"                                            lattice with gram matrix in `file' up to precision `prec'\n"
			"  Transformation-Matrix <file> <aut> <M>    compute the transformation matrix (up to a root of unity and a square root)\n"
			"                                            of the action induced by `M' on the vector space spanned by the component\n"
			"                                            functions of the vector-valued theta function of the lattice associated to\n"
			"                                            the gram matrix in `file' modulo the modulo the automorphisms in `aut'\n"
			"\n"
			"Options:\n"
			"  --help, -h                                show this help message\n"
			"  --print-style=STYLE                       use this style to print things: pretty (default), sage, pari, latex\n"
			"\n"
			"Options specific to VV-Theta-series:\n"
			"  --with-automorphisms=AUT                  compute the component functions only for one representative of the orbits\n"
			"                                            induced by the automorphisms AUT each. this may significantly reduce the\n"
			"                                            required memory at a cost of run time.";

	(error ? std::cerr : std::cout) << s << std::endl;

	return error ? EXIT_FAILURE : EXIT_SUCCESS;
}

static std::optional<weil::mpz_matrix>
read_square_mpz_matrix(const char* file)
{

	std::vector<mpz_class> v;

	std::ifstream in{ file };