flower/include/polynomial.hh

   1 /*
   2   This file is part of LilyPond, the GNU music typesetter.
   3
   4   Copyright (C) 1993--2010 Han-Wen Nienhuys <hanwen@xs4all.nl>
   5
   6   LilyPond is free software: you can redistribute it and/or modify
   7   it under the terms of the GNU General Public License as published by
   8   the Free Software Foundation, either version 3 of the License, or
   9   (at your option) any later version.
  10
  11   LilyPond is distributed in the hope that it will be useful,
  12   but WITHOUT ANY WARRANTY; without even the implied warranty of
  13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14   GNU General Public License for more details.
  15
  16   You should have received a copy of the GNU General Public License
  17   along with LilyPond.  If not, see <http://www.gnu.org/licenses/>.
  18 */
  19
  20 /*
  21  * polynomial.hh -- routines for manipulation of polynomials in one var
  22  */
  23
  24 #ifndef POLY_H
  25 #define POLY_H
  26
  27 #include "std-vector.hh"
  28 #include "arithmetic-operator.hh"
  29 #include "real.hh"
  30
  31 /// structure for a polynomial in one var.
  32 struct Polynomial
  33 {
  34   /// degree of polynomial
  35   int degree ()const;
  36
  37   /// coefficients
  38   vector<Real> coefs_;
  39
  40   // leading coef
  41   Real &lc ();
  42
  43   // leading coef
  44   Real lc () const;
  45   void print () const;
  46   Real eval (Real) const;
  47   void print_sols (vector<Real>) const;
  48   void check_sols (vector<Real>) const;
  49   void check_sol (Real x) const;
  50   static Polynomial multiply (const Polynomial &p1, const Polynomial &p2);
  51   static Polynomial power (int exponent, const Polynomial &src);
  52
  53   /// chop low coefficients
  54   void clean ();
  55
  56   /// eliminate #x#  close to  zero
  57   void real_clean ();
  58   void scalarmultiply (Real fact);
  59   void operator *= (Real f) { scalarmultiply (f); }
  60   void operator /= (Real f) { scalarmultiply (1 / f); }
  61   void operator += (Polynomial const &p2);
  62   void operator *= (Polynomial const &p2);
  63   void operator -= (Polynomial const &p2);
  64   Polynomial (Real a, Real b = 0.0);
  65   Polynomial (){}
  66   void set_negate (const Polynomial &src);
  67
  68   /// take the derivative
  69   void differentiate ();
  70   int set_mod (const Polynomial &u, const Polynomial &v);
  71
  72   void debug_clean ();
  73
  74   vector<Real> solve_quadric ()const;
  75   vector<Real> solve_cubic ()const;
  76   vector<Real> solve_linear ()const;
  77
  78   vector<Real> solve () const;
  79 };
  80
  81 IMPLEMENT_ARITHMETIC_OPERATOR (Polynomial, -);
  82 IMPLEMENT_ARITHMETIC_OPERATOR (Polynomial, +);
  83 IMPLEMENT_ARITHMETIC_OPERATOR (Polynomial, *);
  84
  85 inline Polynomial
  86 operator * (Polynomial p, Real a)
  87 {
  88   p *= a;
  89   return p;
  90 }
  91 inline Polynomial
  92 operator * (Real a, Polynomial p)
  93 {
  94   p *= a;
  95   return p;
  96 }
  97 #endif
  98