LMCAS::anonymous_namespace{fglm.cpp} 命名空间参考

函数
int	checked_dimension (const std::vector< FGLMPoly > &source_basis, size_t num_vars)
std::vector< Rational >	coordinates (const FGLMPoly &polynomial, const std::map< Monomial, size_t > &index)
FGLMPoly	dependent_polynomial (const Monomial &monomial, const std::vector< Rational > &combination, const std::vector< Monomial > &basis, const MonomialOrder &order, size_t num_vars)
void	generate_standard_degree (Monomial &current, size_t variable, int remaining, const std::vector< Monomial > &leading, std::vector< Monomial > &standard)
std::vector< Monomial >	standard_basis (const std::vector< FGLMPoly > &source_basis, size_t num_vars, int dimension)

函数说明

checked_dimension()

int LMCAS::anonymous_namespace{fglm.cpp}::checked_dimension	(	const std::vector< FGLMPoly > &	source_basis,
		size_t	num_vars )

在文件 fglm.cpp 第 72 行定义.

                                                                                {
    if (!is_zero_dimensional(source_basis, num_vars)) {
        throw std::runtime_error(
            "FGLM: ideal is not zero-dimensional. "
            "FGLM only works for zero-dimensional ideals.");
    }
    int dimension = quotient_dimension(source_basis, num_vars);
    if (dimension <= 0 || dimension > 1000) {
        throw std::runtime_error(
            "FGLM: quotient dimension is too large or could not be determined. "
            "dim = " + std::to_string(dimension));
    }
    return dimension;
}

引用了 checked_dimension(), LMCAS::is_zero_dimensional() , 以及 LMCAS::quotient_dimension().

被这些函数引用 checked_dimension().

函数调用图:

这是这个函数的调用关系图:

coordinates()

std::vector< Rational > LMCAS::anonymous_namespace{fglm.cpp}::coordinates	(	const FGLMPoly &	polynomial,
		const std::map< Monomial, size_t > &	index )

在文件 fglm.cpp 第 40 行定义.

                                                                         {
    std::vector<Rational> vector(index.size(), Rational(0));
    for (const auto& [monomial, coefficient] : polynomial.terms) {
        auto found = index.find(monomial);
        if (found != index.end()) vector[found->second] = coefficient;
    }
    return vector;
}

引用了 coordinates().

被这些函数引用 coordinates().

函数调用图:

这是这个函数的调用关系图:

dependent_polynomial()

FGLMPoly LMCAS::anonymous_namespace{fglm.cpp}::dependent_polynomial	(	const Monomial &	monomial,
		const std::vector< Rational > &	combination,
		const std::vector< Monomial > &	basis,
		const MonomialOrder &	order,
		size_t	num_vars )

在文件 fglm.cpp 第 50 行定义.

                                                                           {
    FGLMPoly result(num_vars);
    result.add_term(monomial, Rational(1));
    for (size_t index = 0; index < combination.size() && index < basis.size(); ++index) {
        if (!combination[index].is_zero()) {
            result.add_term(basis[index], -combination[index]);
        }
    }
    result.sort_terms(order);
    result.normalize();
    if (!result.is_zero()) {
        Rational leading = result.lead_coeff();
        if (!(leading == Rational(1))) {
            for (auto& term : result.terms) term.second = term.second / leading;
        }
    }
    return result;
}

引用了 LMCAS::basis, dependent_polynomial() , 以及 LMCAS::order.

被这些函数引用 dependent_polynomial().

函数调用图:

这是这个函数的调用关系图:

generate_standard_degree()

void LMCAS::anonymous_namespace{fglm.cpp}::generate_standard_degree	(	Monomial &	current,
		size_t	variable,
		int	remaining,
		const std::vector< Monomial > &	leading,
		std::vector< Monomial > &	standard )

在文件 fglm.cpp 第 10 行定义.

                                                             {
    if (variable == current.size() - 1) {
        current[variable] = remaining;
        if (is_standard(current, leading)) standard.push_back(current);
        current[variable] = 0;
        return;
    }
    for (int exponent = 0; exponent <= remaining; ++exponent) {
        current[variable] = exponent;
        generate_standard_degree(current, variable + 1, remaining - exponent,
                                 leading, standard);
    }
    current[variable] = 0;
}

引用了 LMCAS::exponent, generate_standard_degree(), LMCAS::fglm_detail::is_standard() , 以及 LMCAS::variable.

被这些函数引用 generate_standard_degree() , 以及 standard_basis().

函数调用图:

这是这个函数的调用关系图:

standard_basis()

std::vector< Monomial > LMCAS::anonymous_namespace{fglm.cpp}::standard_basis	(	const std::vector< FGLMPoly > &	source_basis,
		size_t	num_vars,
		int	dimension )

在文件 fglm.cpp 第 27 行定义.

                                                                     {
    auto leading = leading_monomials(source_basis);
    std::vector<Monomial> standard;
    for (int degree = 0;
         degree <= dimension + 2 && static_cast<int>(standard.size()) < dimension;
         ++degree) {
        Monomial current(num_vars, 0);
        generate_standard_degree(current, 0, degree, leading, standard);
    }
    return standard;
}

引用了 generate_standard_degree(), LMCAS::fglm_detail::leading_monomials() , 以及 standard_basis().

被这些函数引用 standard_basis().

函数调用图:

这是这个函数的调用关系图: