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+/**
+ * \file
+ * \brief Polynomial in canonical (monomial) basis
+ *//*
+ * Authors:
+ * MenTaLguY <mental@rydia.net>
+ * Krzysztof Kosiński <tweenk.pl@gmail.com>
+ *
+ * Copyright 2007-2015 Authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+#ifndef LIB2GEOM_SEEN_POLY_H
+#define LIB2GEOM_SEEN_POLY_H
+#include <assert.h>
+#include <vector>
+#include <iostream>
+#include <algorithm>
+#include <complex>
+#include <2geom/coord.h>
+#include <2geom/utils.h>
+
+namespace Geom {
+
+/** @brief Polynomial in canonical (monomial) basis.
+ * @ingroup Fragments */
+class Poly : public std::vector<double>{
+public:
+ // coeff; // sum x^i*coeff[i]
+
+ //unsigned size() const { return coeff.size();}
+ unsigned degree() const { return size()-1;}
+
+ //double operator[](const int i) const { return (*this)[i];}
+ //double& operator[](const int i) { return (*this)[i];}
+
+ Poly operator+(const Poly& p) const {
+ Poly result;
+ const unsigned out_size = std::max(size(), p.size());
+ const unsigned min_size = std::min(size(), p.size());
+ result.reserve(out_size);
+
+ for(unsigned i = 0; i < min_size; i++) {
+ result.push_back((*this)[i] + p[i]);
+ }
+ for(unsigned i = min_size; i < size(); i++)
+ result.push_back((*this)[i]);
+ for(unsigned i = min_size; i < p.size(); i++)
+ result.push_back(p[i]);
+ assert(result.size() == out_size);
+ return result;
+ }
+ Poly operator-(const Poly& p) const {
+ Poly result;
+ const unsigned out_size = std::max(size(), p.size());
+ const unsigned min_size = std::min(size(), p.size());
+ result.reserve(out_size);
+
+ for(unsigned i = 0; i < min_size; i++) {
+ result.push_back((*this)[i] - p[i]);
+ }
+ for(unsigned i = min_size; i < size(); i++)
+ result.push_back((*this)[i]);
+ for(unsigned i = min_size; i < p.size(); i++)
+ result.push_back(-p[i]);
+ assert(result.size() == out_size);
+ return result;
+ }
+ Poly operator-=(const Poly& p) {
+ const unsigned out_size = std::max(size(), p.size());
+ const unsigned min_size = std::min(size(), p.size());
+ resize(out_size);
+
+ for(unsigned i = 0; i < min_size; i++) {
+ (*this)[i] -= p[i];
+ }
+ for(unsigned i = min_size; i < out_size; i++)
+ (*this)[i] = -p[i];
+ return *this;
+ }
+ Poly operator-(const double k) const {
+ Poly result;
+ const unsigned out_size = size();
+ result.reserve(out_size);
+
+ for(unsigned i = 0; i < out_size; i++) {
+ result.push_back((*this)[i]);
+ }
+ result[0] -= k;
+ return result;
+ }
+ Poly operator-() const {
+ Poly result;
+ result.resize(size());
+
+ for(unsigned i = 0; i < size(); i++) {
+ result[i] = -(*this)[i];
+ }
+ return result;
+ }
+ Poly operator*(const double p) const {
+ Poly result;
+ const unsigned out_size = size();
+ result.reserve(out_size);
+
+ for(unsigned i = 0; i < out_size; i++) {
+ result.push_back((*this)[i]*p);
+ }
+ assert(result.size() == out_size);
+ return result;
+ }
+ // equivalent to multiply by x^terms, negative terms are disallowed
+ Poly shifted(unsigned const terms) const {
+ Poly result;
+ size_type const out_size = size() + terms;
+ result.reserve(out_size);
+
+ result.resize(terms, 0.0);
+ result.insert(result.end(), this->begin(), this->end());
+
+ assert(result.size() == out_size);
+ return result;
+ }
+ Poly operator*(const Poly& p) const;
+
+ template <typename T>
+ T eval(T x) const {
+ T r = 0;
+ for(int k = size()-1; k >= 0; k--) {
+ r = r*x + T((*this)[k]);
+ }
+ return r;
+ }
+
+ template <typename T>
+ T operator()(T t) const { return (T)eval(t);}
+
+ void normalize();
+
+ void monicify();
+ Poly() {}
+ Poly(const Poly& p) : std::vector<double>(p) {}
+ Poly(const double a) {push_back(a);}
+
+public:
+ template <class T, class U>
+ void val_and_deriv(T x, U &pd) const {
+ pd[0] = back();
+ int nc = size() - 1;
+ int nd = pd.size() - 1;
+ for(unsigned j = 1; j < pd.size(); j++)
+ pd[j] = 0.0;
+ for(int i = nc -1; i >= 0; i--) {
+ int nnd = std::min(nd, nc-i);
+ for(int j = nnd; j >= 1; j--)
+ pd[j] = pd[j]*x + operator[](i);
+ pd[0] = pd[0]*x + operator[](i);
+ }
+ double cnst = 1;
+ for(int i = 2; i <= nd; i++) {
+ cnst *= i;
+ pd[i] *= cnst;
+ }
+ }
+
+ static Poly linear(double ax, double b) {
+ Poly p;
+ p.push_back(b);
+ p.push_back(ax);
+ return p;
+ }
+};
+
+inline Poly operator*(double a, Poly const & b) { return b * a;}
+
+Poly integral(Poly const & p);
+Poly derivative(Poly const & p);
+Poly divide_out_root(Poly const & p, double x);
+Poly compose(Poly const & a, Poly const & b);
+Poly divide(Poly const &a, Poly const &b, Poly &r);
+Poly gcd(Poly const &a, Poly const &b, const double tol=1e-10);
+
+/*** solve(Poly p)
+ * find all p.degree() roots of p.
+ * This function can take a long time with suitably crafted polynomials, but in practice it should be fast. Should we provide special forms for degree() <= 4?
+ */
+std::vector<std::complex<double> > solve(const Poly & p);
+
+#ifdef HAVE_GSL
+/*** solve_reals(Poly p)
+ * find all real solutions to Poly p.
+ * currently we just use solve and pick out the suitably real looking values, there may be a better algorithm.
+ */
+std::vector<double> solve_reals(const Poly & p);
+#endif
+double polish_root(Poly const & p, double guess, double tol);
+
+
+/** @brief Analytically solve quadratic equation.
+ * The equation is given in the standard form: ax^2 + bx + c = 0.
+ * Only real roots are returned. */
+std::vector<Coord> solve_quadratic(Coord a, Coord b, Coord c);
+
+/** @brief Analytically solve cubic equation.
+ * The equation is given in the standard form: ax^3 + bx^2 + cx + d = 0.
+ * Only real roots are returned. */
+std::vector<Coord> solve_cubic(Coord a, Coord b, Coord c, Coord d);
+
+
+inline std::ostream &operator<< (std::ostream &out_file, const Poly &in_poly) {
+ if(in_poly.size() == 0)
+ out_file << "0";
+ else {
+ for(int i = (int)in_poly.size()-1; i >= 0; --i) {
+ if(i == 1) {
+ out_file << "" << in_poly[i] << "*x";
+ out_file << " + ";
+ } else if(i) {
+ out_file << "" << in_poly[i] << "*x^" << i;
+ out_file << " + ";
+ } else
+ out_file << in_poly[i];
+
+ }
+ }
+ return out_file;
+}
+
+} // namespace Geom
+
+#endif //LIB2GEOM_SEEN_POLY_H
+
+/*
+ Local Variables:
+ mode:c++
+ c-file-style:"stroustrup"
+ c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+ indent-tabs-mode:nil
+ fill-column:99
+ End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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