From 59f3bb9eea396d9469b905f589a969b4c7d618ab Mon Sep 17 00:00:00 2001
From: Jiri Pittner <jiri@pittnerovi.com>
Date: Tue, 5 Oct 2021 17:15:47 +0200
Subject: [PATCH] implemented Hermite polynomials

---
 polynomial.cc |  6 ++++++
 polynomial.h  | 16 ++++++++++++++++
 t.cc          |  9 ++++++++-
 3 files changed, 30 insertions(+), 1 deletion(-)

diff --git a/polynomial.cc b/polynomial.cc
index 7d531d5..2175fd5 100644
--- a/polynomial.cc
+++ b/polynomial.cc
@@ -285,6 +285,12 @@ INSTANTIZE(unsigned int)
 INSTANTIZE(double)
 INSTANTIZE(std::complex<double>)
 
+#define INSTANTIZE2(T) \
+template Polynomial<T> hermite_polynomial(int); \
+
+INSTANTIZE2(int)
+INSTANTIZE2(double)
+
 
 
 }//namespace
diff --git a/polynomial.h b/polynomial.h
index a41598b..89ce8ca 100644
--- a/polynomial.h
+++ b/polynomial.h
@@ -23,6 +23,7 @@
 #include "la_traits.h"
 #include "vec.h"
 #include "nonclass.h"
+#include "matexp.h"
 
 namespace LA {
 
@@ -223,5 +224,20 @@ return p*q/poly_gcd(p,q,thr);
 }
 
 
+template <typename T>
+Polynomial<T> hermite_polynomial(int n) //physicists definition
+{
+Polynomial<T> h(n);
+h.clear();
+h[n]=ipow((T)2,n);
+for(int m=1; n-2*m>=0; m+=1)
+	{
+	int i=n-2*m;
+	h[i] = (-h[i+2] *(i+2)*(i+1)) /(4*m);
+	}
+return h;
+}
+
+
 }//namespace
 #endif
diff --git a/t.cc b/t.cc
index 95d5560..c3f391b 100644
--- a/t.cc
+++ b/t.cc
@@ -2156,7 +2156,7 @@ if(tot!=partitions(n)) laerror("internal error in partition generation or enumer
 if(space_dim!=longpow(unitary_n,n)) {cout<<space_dim<<" "<<ipow(unitary_n,n)<<endl;laerror("integer overflow or internal error in space dimensions");}
 }
 
-if(1)
+if(0)
 {
 int n;
 cin >>n ;
@@ -2284,5 +2284,12 @@ Polynomial<double> qq=q.pow(n);
 cout <<"test binom "<<(p-qq).norm()<<endl;
 }
 
+if(1)
+{
+int n;
+cin >>n ;
+cout <<"Hermite = "<<hermite_polynomial<int>(n);
+}
+
 
 }