/***************************************************************************************************
 * File:         $URL: https://svn.bolitho.us/Library/Trunk/Src/Math/Polynomial.hpp $
 * Author:       $Author: OBTUSE\matthew $
 * Revision:     $Rev: 1588 $
 * Last Updated: $Date: 2008-08-23 09:36:02 -0700 (Sat, 23 Aug 2008) $
 * 
 * 
 * Copyright (c) 2004-2007, Matthew G Bolitho
 * All rights reserved.
 *
 *
 * Microsoft Reference License (Ms-RL)
 *   
 * This license governs use of the accompanying software. If you use the software, you accept 
 * this license. If you do not accept the license, do not use the software.
 *
 * 1. Definitions
 *  - The terms "reproduce," "reproduction" and "distribution" have the same meaning here as under 
 *    U.S. copyright law.
 *  - "You" means the licensee of the software.
 *  - "Your company" means the company you worked for when you downloaded the software.
 *  - "Reference use" means use of the software within your company as a reference, in read only 
 *    form, for the sole purposes of debugging your products, maintaining your products, or 
 *    enhancing the interoperability of your products with the software, and specifically excludes 
 *    the right to distribute the software outside of your company.
 *  - "Licensed patents" means any Licensor patent claims which read directly on the software as 
 *    distributed by the Licensor under this license.
 * 
 * 2. Grant of Rights
 *  (A) Copyright Grant- Subject to the terms of this license, the Licensor grants you a non-transferable, 
 *      non-exclusive, worldwide, royalty-free copyright license to reproduce the software for reference use.
 *  (B) Patent Grant- Subject to the terms of this license, the Licensor grants you a non-transferable,
 *      non-exclusive, worldwide, royalty-free patent license under licensed patents for reference use.
 * 
 * 3. Limitations
 *  (A) No Trademark License - This license does not grant you any rights to use the Licensor's name
 *      logo, or trademarks.
 *  (B) If you begin patent litigation against the Licensor over patents that you think may apply 
 *      to the software (including a cross-claim or counterclaim in a lawsuit), your license to the 
 *      software ends automatically.
 *  (C) The software is licensed "as-is." You bear the risk of using it. The Licensor gives no express 
 *      warranties, guarantees or conditions. You may have additional consumer rights under your local 
 *      laws which this license cannot change. To the extent permitted under your local laws, the 
 *      Licensor excludes the implied warranties of merchantability, fitness for a particular purpose 
 *      and non-infringement.
 *
 ***************************************************************************************************/




#pragma once

#include "Utility/NumberTraits.hpp"
#include "Math/Math.hpp"

namespace Bolitho
{
  namespace Math
  {
    template<INT Degree, class T>
    class PolynomialN
    {
    public:
      PolynomialN();
      template<SIZE_T Degree2>
      PolynomialN(CONST PolynomialN<Degree2,T>& P);
      
      T operator()(T x) CONST;
      T Evaluate(T x) CONST;
      
      T Integral (T Min, T Max) CONST;
      PolynomialN<Degree-1,T> Derivative() CONST;
      PolynomialN<Degree+1,T> Integral() CONST;
      
      BOOL operator == (CONST PolynomialN& p) CONST;
      BOOL operator != (CONST PolynomialN& p) CONST;
      
      operator CONST T* () CONST
      { return m_Coefficients; }
      operator T* ()
      { return m_Coefficients; }
      
      BOOL IsZero() CONST;
      VOID SetZero();
      
      template<INT Degree2>
      PolynomialN& operator  = (CONST PolynomialN<Degree2,T> &p);
      PolynomialN& operator += (CONST PolynomialN& p);
      PolynomialN& operator -= (CONST PolynomialN& p);
      PolynomialN  operator -  () CONST;
      PolynomialN  operator +  (CONST PolynomialN& p) CONST;
      PolynomialN  operator -  (CONST PolynomialN& p) CONST;
      
      template<SIZE_T Degree2>
      PolynomialN<Degree+Degree2,T> Multiply(CONST PolynomialN<Degree2,T>& P) CONST;
      
      PolynomialN& operator += (T s);
      PolynomialN& operator -= (T s);
      PolynomialN& operator *= (T s);
      PolynomialN& operator /= (T s);
      PolynomialN  operator +  (T s) CONST;
      PolynomialN  operator -  (T s) CONST;
      PolynomialN  operator *  (T s) CONST;
      PolynomialN  operator /  (T s) CONST;
      
      PolynomialN Scale(T s) CONST;
      PolynomialN Shift(T t) CONST;
      
      PolynomialN& AddScaled(CONST PolynomialN& p, T scale);
      
      Array<T> GetSolutions(T x, T Epsilon = 0) CONST;
      
    private:
      T m_Coefficients[Degree+1];
    };
    
#include "PolynomialImpl.hpp"
    
  }
}
