From 1ee984eda2b75c2edd79629fda54270937269f6c Mon Sep 17 00:00:00 2001
From: Jiri Pittner <jiri@pittnerovi.com>
Date: Wed, 24 Jan 2024 13:41:39 +0100
Subject: [PATCH] small additions to permutations

---
 permutation.cc | 43 +++++++++++++++++++++++++++++++++++++++----
 permutation.h  |  4 +++-
 2 files changed, 42 insertions(+), 5 deletions(-)

diff --git a/permutation.cc b/permutation.cc
index 8df6e95..f8f5322 100644
--- a/permutation.cc
+++ b/permutation.cc
@@ -135,11 +135,27 @@ if(n!=q.size()) laerror("product of incompatible permutations");
 NRPerm<T> r(n);
 for(T i=1; i<=n; ++i) r[i] = (*this)[q[i]];
 return r;
-
 }
 
 template <typename T>
-NRPerm<T> NRPerm<T>::conjugate_by(const NRPerm<T> &q) const
+NRPerm<T> NRPerm<T>::multiply(const NRPerm<T> &q, bool inverse) const
+{
+#ifdef DEBUG
+        if(!this->is_valid() || !q.is_valid()) laerror("multiplication of invalid permutation");
+#endif
+
+T n=this->size();
+if(n!=q.size()) laerror("product of incompatible permutations");
+NRPerm<T> r(n);
+if(inverse) for(T i=1; i<=n; ++i) r[q[i]] = (*this)[i];
+else for(T i=1; i<=n; ++i) r[i] = (*this)[q[i]];
+return r;
+}
+
+
+
+template <typename T>
+NRPerm<T> NRPerm<T>::conjugate_by(const NRPerm<T> &q, bool inverse) const
 {
 #ifdef DEBUG
         if(!this->is_valid() || !q.is_valid()) laerror("multiplication of invalid permutation");
@@ -149,11 +165,30 @@ T n=this->size();
 if(n!=q.size()) laerror("product of incompatible permutations");
 NRPerm<T> qi=q.inverse();
 NRPerm<T> r(n);
-for(T i=1; i<=n; ++i) r[i] = qi[(*this)[q[i]]];
+if(inverse)  for(T i=1; i<=n; ++i) r[i] = q[(*this)[qi[i]]];
+else for(T i=1; i<=n; ++i) r[i] = qi[(*this)[q[i]]];
 return r;
-
 }
 
+template <typename T>
+NRPerm<T> NRPerm<T>::commutator(const NRPerm<T> &q, bool inverse) const
+{
+#ifdef DEBUG
+        if(!this->is_valid() || !q.is_valid()) laerror("multiplication of invalid permutation");
+#endif
+
+T n=this->size();
+if(n!=q.size()) laerror("product of incompatible permutations");
+NRPerm<T> qi=q.inverse();
+NRPerm<T> pi=this->inverse();
+NRPerm<T> r(n);
+if(inverse)  for(T i=1; i<=n; ++i) r[i] = qi[pi[q[(*this)[i]]]];
+else for(T i=1; i<=n; ++i) r[i] = pi[qi[(*this)[q[i]]]];
+return r;
+}
+
+
+
 template <typename T>
 CyclePerm<T> CyclePerm<T>::conjugate_by(const CyclePerm<T> &q) const
 {
diff --git a/permutation.h b/permutation.h
index a90fb6b..6f67540 100644
--- a/permutation.h
+++ b/permutation.h
@@ -67,7 +67,9 @@ public:
 	NRPerm operator|(const NRPerm &rhs) const; //concatenate the permutations rhs,this, renumbering rhs (not commutative)
 	NRPerm operator*(const NRPerm &q) const; //q is rhs and applied first, this applied second
 	NRPerm operator*(const CyclePerm<T> &r) const;
-	NRPerm conjugate_by(const NRPerm &q) const; //q^-1 p q
+	NRPerm multiply(const NRPerm<T> &q, bool inverse) const; //multiplication but optionally q inversed
+	NRPerm conjugate_by(const NRPerm &q, bool reverse=false) const; //q^-1 p q or q p q^-1
+	NRPerm commutator(const NRPerm &q, bool inverse=false) const;  //p^-1 q^-1 p q or q^-1 p^-1 q p
 	int parity() const; //returns +/- 1
 	void randomize(void); //uniformly random by Fisher-Yates shuffle
 	bool next(); //generate next permutation in lex order