From f7bf1598ee95149bff7f01e26a9c3fd04654cdb2 Mon Sep 17 00:00:00 2001
From: kalmarek <kalmar@amu.edu.pl>
Date: Wed, 25 Mar 2020 03:36:36 +0100
Subject: [PATCH] make multiplication abstract

---
 src/FPGroups.jl |  4 ----
 src/Groups.jl   | 35 +++++++++++++++++++++++++++--------
 2 files changed, 27 insertions(+), 12 deletions(-)

diff --git a/src/FPGroups.jl b/src/FPGroups.jl
index 0c472cb..e04726a 100644
--- a/src/FPGroups.jl
+++ b/src/FPGroups.jl
@@ -122,10 +122,6 @@ end
 #
 ###############################################################################
 
-(*)(W::FPGroupElem, Z::FPGroupElem) = r_multiply(W, Z.symbols)
-(*)(W::FPGroupElem, s::FPSymbol) = r_multiply(W, [s])
-(*)(s::FPSymbol, W::FPGroupElem) = l_multiply(W, [s])
-
 function reduce!(W::FPGroupElem)
     reduced = false
     while !reduced
diff --git a/src/Groups.jl b/src/Groups.jl
index 3fe742d..7ac68ab 100644
--- a/src/Groups.jl
+++ b/src/Groups.jl
@@ -270,14 +270,32 @@ for (mul, f) in ((:rmul!, :push!), (:lmul!, :pushfirst!))
     end
 end
 
-    end
+function rmul!(out::T, x::T, y::T) where T<: GWord
+    if out === x
+        out = deepcopy(out)
+        return freereduce!(append!(out, y))
+    elseif out === y
+        out = deepcopy(out)
+        return freereduce!(prepend!(out, x))
+    else
+        slenx = syllablelength(x)
+        sleny = syllablelength(y)
+        resize!(syllables(out), slenx+sleny)
+        syllables(out)[1:slenx] .= syllables(x)
+        syllables(out)[slenx+1:slenx+sleny] .= syllables(y)
+        return freereduce!(out)
     end
 end
 
+lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x)
 
-(*)(W::GWord, Z::GWord) = r_multiply(W, Z.symbols)
-(*)(W::GWord, s::GSymbol) = r_multiply(W, [s])
-(*)(s::GSymbol, W::GWord) = l_multiply(W, [s])
+function AbstractAlgebra.mul!(out::T, x::T, y::T) where T <: GWord
+    return rmul!(out, x, y)
+end
+
+(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
+(*)(W::GWord, s::GSymbol) = rmul!(deepcopy(W), W, s)
+(*)(s::GSymbol, W::GWord) = lmul!(deepcopy(W), W, s)
 
 function power_by_squaring(W::GWord, p::Integer)
     if p < 0
@@ -293,18 +311,19 @@ function power_by_squaring(W::GWord, p::Integer)
     t = trailing_zeros(p) + 1
     p >>= t
     while (t -= 1) > 0
-        r_multiply!(W, W.symbols)
+        append!(W, W)
     end
     Z = deepcopy(W)
     while p > 0
         t = trailing_zeros(p) + 1
         p >>= t
         while (t -= 1) >= 0
-            r_multiply!(W, W.symbols)
+            append!(W, W)
         end
-        r_multiply!(Z, W.symbols)
+        append!(Z, W)
     end
-    return Z
+
+    return freereduce!(Z)
 end
 
 (^)(x::GWord, n::Integer) = power_by_squaring(x,n)