starting implementation of polynomials

polynomial.h

@@ -0,0 +1,102 @@
+/*
+    LA: linear algebra C++ interface library
+    Copyright (C) 2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+
+#ifndef _POLYNOMIAL_H
+#define _POLYNOMIAL_H
+
+#include "la_traits.h"
+#include "vec.h"
+
+namespace LA {
+
+template <typename T>
+class Polynomial : public NRVec<T> {
+public:
+	Polynomial():  NRVec<T>() {};
+	Polynomial(const int n) : NRVec<T>(n+1) {};
+	Polynomial(const T &a, const int n) : NRVec<T>(n+1) {NRVec<T>::clear(); (*this)[0]=a;};
+
+	int degree() const {return NRVec<T>::size()-1;};
+	void resize(const int n, const bool preserve=true) {NRVec<T>::resize(n+1,preserve);}
+	
+	Polynomial& operator+=(const T &a) {NOT_GPU(*this); NRVec<T>::copyonwrite(); (*this)[0]+=a; return *this;}
+	Polynomial& operator-=(const T &a) {NOT_GPU(*this); NRVec<T>::copyonwrite(); (*this)[0]-=a; return *this;}
+	Polynomial operator+(const T &a) const {return Polynomial(*this) += a;};
+	Polynomial operator-(const T &a) const {return Polynomial(*this) -= a;};
+	//operator *= and * by a scalar inherited 
+	//unary- inherited
+	
+	Polynomial& operator+=(const Polynomial &rhs) 
+		{
+		NOT_GPU(*this); NRVec<T>::copyonwrite(); 
+		if(rhs.degree()>degree()) resize(rhs.degree());
+		for(int i=0; i<=rhs.degree(); ++i) (*this)[i] += rhs[i];
+		return *this;
+		}
+
+	Polynomial& operator-=(const Polynomial &rhs) 
+                {
+                NOT_GPU(*this); NRVec<T>::copyonwrite(); 
+                if(rhs.degree()>degree()) resize(rhs.degree());
+                for(int i=0; i<=rhs.degree(); ++i) (*this)[i] -= rhs[i];
+                return *this;
+                }
+	Polynomial operator+(const Polynomial &rhs) const {return Polynomial(*this) += rhs;};
+	Polynomial operator-(const Polynomial &rhs) const {return Polynomial(*this) -= rhs;};
+	Polynomial operator*(const Polynomial &rhs) const //for very long polynomials FFT should be used
+		{
+		Polynomial r(degree()+rhs.degree());
+		r.clear();
+		for(int i=0; i<=rhs.degree(); ++i) for(int j=0; j<=degree(); ++j) r[i+j] += rhs[i]*(*this)[j];
+		return r;
+		};
+
+	//@@@@
+	//simplify(threshold)
+	//derivative,integral
+	//division remainder 
+	//gcd, lcm
+	//roots, interpolation ... special only for real->complex - declare only and implent only template specialization  in .cc
+
+};
+
+//this is very general, can be used also for nesting polynomials
+template <typename T, typename C>
+C value(const Polynomial<T> &p, const C &x)
+{
+C sum(x); 
+sum=0; //get matrix dimension if C is a matrix
+for(int i=p.degree(); i>0; --i)
+  		 {
+       		 sum+= p[i];
+       		 sum= sum*x; //not *= for matrices
+       		 }
+sum += p[0];
+return sum;
+}
+
+//scalar+-polynomial
+template <typename T>
+inline Polynomial<T> operator+(const T &a, const Polynomial<T> &rhs) {return Polynomial<T>(rhs)+=a;}
+template <typename T>
+inline Polynomial<T> operator-(const T &a, const Polynomial<T> &rhs) {return Polynomial<T>(rhs)-=a;}
+
+
+}//namespace
+#endif