From 4c420b1e9b08c1b2e9ba83cd9cd9fb82de540a16 Mon Sep 17 00:00:00 2001
From: Jiri Pittner <jiri@pittnerovi.com>
Date: Tue, 5 Oct 2021 17:33:30 +0200
Subject: [PATCH] polynomial odd and even powers separation

---
 polynomial.h | 2 ++
 t.cc         | 4 +++-
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/polynomial.h b/polynomial.h
index 89ce8ca..dafb6ec 100644
--- a/polynomial.h
+++ b/polynomial.h
@@ -144,6 +144,8 @@ public:
 			}
 		return r;
 		}
+	Polynomial even_powers() const {int d=degree()/2; Polynomial r(d); for(int i=0; i<=degree(); i+=2) r[i/2] = (*this)[i]; return r;};
+	Polynomial odd_powers() const {int d=(degree()-1)/2; Polynomial r(d); if(degree()==0) {r[0]=0; return r;} for(int i=1; i<=degree(); i+=2) r[(i-1)/2] = (*this)[i]; return r;};
 	void polydiv(const Polynomial &rhs, Polynomial &q, Polynomial &r) const;
 	Polynomial operator/(const Polynomial &rhs) const {Polynomial q,r; polydiv(rhs,q,r); return q;};
 	Polynomial operator%(const Polynomial &rhs) const {Polynomial q,r; polydiv(rhs,q,r); return r;};
diff --git a/t.cc b/t.cc
index c3f391b..cead833 100644
--- a/t.cc
+++ b/t.cc
@@ -2288,7 +2288,9 @@ if(1)
 {
 int n;
 cin >>n ;
-cout <<"Hermite = "<<hermite_polynomial<int>(n);
+Polynomial<int> p=hermite_polynomial<int>(n);
+cout <<"Hermite = "<<p<<std::endl;
+cout <<"non-zero = "<< ((n&1)?p.odd_powers():p.even_powers())<<std::endl;
 }