First attempt

lib/accum.gd

@@ -0,0 +1,22 @@
+DeclareCategory("IsAccumulator", IsCopyable);
+
+DeclareOperation("ValueAccumulator", [IsAccumulator]);
+
+DeclareConstructor("AccumulatorCons", [IsAccumulator, IsObject]);
+
+DeclareOperation("RightAdd", [IsAccumulator and IsMutable, IsExtAElement] );
+DeclareOperation("LeftAdd", [IsAccumulator and IsMutable, IsExtAElement] );
+DeclareOperation("Subtract", [IsAccumulator and IsMutable, IsNearAdditiveElementWithInverse] );
+DeclareOperation("Negate", [IsAccumulator and IsMutable] );
+DeclareOperation("RightMultiply", [IsAccumulator and IsMutable, IsExtLElement] );
+DeclareOperation("LeftMultiply", [IsAccumulator and IsMutable, IsExtRElement] );
+DeclareOperation("RightDivide", [IsAccumulator and IsMutable, IsMultiplicativeElementWithInverse] );
+DeclareOperation("LeftDivide", [IsAccumulator and IsMutable, IsMultiplicativeElementWithInverse] );
+DeclareOperation("Invert", [IsAccumulator and IsMutable] );
+DeclareOperation("Exponentiate", [IsAccumulator and IsMutable, IsInt] );
+DeclareOperation("Conjugate", [IsAccumulator and IsMutable, IsMultiplicativeElementWithInverse] );
+
+DeclareCategory("IsPermutationAccumulator", IsAccumulator);
+DeclareOperation("OnPointsAccumulator", [IsPosInt, IsPermutationAccumulator]);
+DeclareOperation("OnTuplesAccumulator", [IsRowVector and IsCyclotomicCollection, 
+        IsPermutationAccumulator]);

lib/genacc.gi

@@ -0,0 +1,30 @@
+InstallMethod(Conjugate, [IsAccumulator and IsMutable, IsMultiplicativeElementWithInverse],
+        function(acc, x)
+    acc := LeftDivide(acc, x);
+    if acc = fail then
+        return fail;
+    fi;
+    return RightMultiply(acc,x);
+end);
+
+InstallMethod(Exponentiate, [IsAccumulator and IsMutable, IsInt],
+        function(acc, pow)
+    local  v, i;
+    if pow < 0 then
+        Invert(acc);
+        pow := -pow;
+    fi;
+    v := ValueAccumulator(acc);
+    if pow = 0 then
+        RightDivide(acc,v);
+    else
+        for i in [2..pow] do
+            RightMultiply(acc,v);
+        od;
+    fi;
+    return acc;
+end);
+
+
+
+

lib/lazypermacc.gi

@@ -0,0 +1,144 @@
+DeclareRepresentation("IsLazyPermutationAccumulatorRep", 
+        IsPositionalObjectRep and IsPermutationAccumulator, 2);
+BindGlobal("AccumulatorsFamily", NewFamily(IsAccumulator));
+
+BindGlobal("LazyPermutationAccumulatorDefaultType", 
+        NewType(AccumulatorsFamily, IsMutable and IsLazyPermutationAccumulatorRep));
+
+
+InstallMethod(AccumulatorCons,[IsLazyPermutationAccumulatorRep, IsPerm],
+        function(type, p)
+    return Objectify(LazyPermutationAccumulatorDefaultType, [[],[p],[],[true]]);    
+end);
+
+InstallMethod(RightMultiply, [IsLazyPermutationAccumulatorRep and IsMutable, IsPerm],
+        function(acc,p)
+    Add(acc![2],p);
+    Add(acc![4],true);
+    return acc;
+end);
+
+InstallMethod(LeftMultiply, [IsLazyPermutationAccumulatorRep and IsMutable, IsPerm],
+        function(acc,p)
+    Add(acc![1],p);
+    Add(acc![3],true);
+    return acc;
+end);
+
+InstallMethod(RightDivide, [IsLazyPermutationAccumulatorRep and IsMutable, IsPerm],
+        function(acc,p)
+    Add(acc![2],p);
+    Add(acc![4],false);    
+    return acc;
+
+end);
+
+InstallMethod(LeftDivide, [IsLazyPermutationAccumulatorRep and IsMutable, IsPerm],
+        function(acc,p)
+    Add(acc![1],p);
+    Add(acc![3],false);
+    return acc;
+end);
+
+InstallMethod(Invert, [IsLazyPermutationAccumulatorRep and IsMutable],
+        function(acc)
+    local x;
+    x := acc![1];
+    acc![1] := acc![2];
+    acc![2] := x;
+    x := acc![3];
+    acc![3] := List(acc![4], y-> not y);
+    acc![4] := List(x, y-> not y);
+    return acc;
+end);
+
+InstallMethod(Exponentiate, [IsLazyPermutationAccumulatorRep and IsMutable, IsInt],
+        function (acc, pow)
+    local  i, new, x, l, j;
+    if pow < 0 then 
+        Invert(acc);
+        pow := -pow;
+    fi;
+    if pow = 0 then
+        for i in [1..4] do
+            acc![i] := [];
+        od;
+        return acc;
+    fi;
+    if pow = 1 then
+        return acc;
+    fi;
+    new := [[],[],[],[]];
+    for i in [1..4] do
+        x  := acc![i];
+        l := ShallowCopy(x);
+        for j in [2..pow] do
+            Append(l,x);
+        od;
+        acc![i] := l;
+    od;
+    return acc;
+end);
+
+
+InstallMethod(ShallowCopy,[IsLazyPermutationAccumulatorRep],
+        function(acc)
+    return Objectify(LazyPermutationAccumulatorDefaultType, List([1..4],
+                   i -> ShallowCopy(acc![i])));
+end);
+
+#
+# Could be implemented better usign an EagerPermutationAccumulator
+#
+
+InstallMethod(ValueAccumulator, [IsLazyPermutationAccumulatorRep],
+        function(acc)
+    local  v, l, i;
+    v := ();
+    l := Length(acc![1]);
+    for i in [l,l-1..1] do
+        if acc![3][i] then
+            v := v*acc![1][i];
+        else
+            v := v/acc![1][i];
+        fi;
+    od;
+    for i in [1..Length(acc![2])] do
+        if acc![4][i] then
+            v := v*acc![2][i];
+        else
+            v := v/acc![2][i];
+        fi;
+    od;
+    acc![2] := [v];
+    acc![1] := [];
+    acc![3] := [];
+    acc![4] := [true];    
+    return v;
+end);
+
+
+InstallMethod(OnPointsAccumulator,[IsPosInt, IsLazyPermutationAccumulatorRep], 
+        function(pt, acc)
+    local  l, i;
+    l := Length(acc![1]);
+    for i in [l,l-1..1] do
+        if acc![3][i] then
+            pt := pt^acc![1][i];
+        else
+            pt := pt/acc![1][i];
+        fi;
+    od;
+    for i in [1..Length(acc![2])] do
+        if acc![4][i] then
+            pt := pt^acc![2][i];
+        else
+            pt := pt/acc![2][i];
+        fi;
+    od;
+    return pt;
+end);
+
+
+
+

lib/permacc.gi

@@ -0,0 +1,12 @@
+InstallMethod(RightAdd,[IsPermutationAccumulator and IsMutable, IsExtAElement], ReturnFail);
+InstallMethod(LeftAdd,[IsPermutationAccumulator and IsMutable, IsExtAElement], ReturnFail);
+InstallMethod(Subtract,[IsPermutationAccumulator and IsMutable, 
+        IsNearAdditiveElementWithInverse], ReturnFail);
+InstallMethod(Negate,[IsPermutationAccumulator and IsMutable], ReturnFail);
+
+InstallMethod(OnTuplesAccumulator, 
+        [IsSmallList and IsCyclotomicCollection and IsRowVector, IsPermutationAccumulator],
+        function(tup,acc)
+    return List(tup, x -> OnPointsAccumulator(acc,x));
+end);
+

lib/read3.g

@@ -251,3 +251,8 @@ ReadLib("function.gd");
 
 # random sources
 ReadLib("random.gi");
+
+# accumulators
+
+ReadLib("accum.gd");
+

lib/read5.g

@@ -258,3 +258,9 @@ ReadLib( "function.gi");
 # floateans, now really install all handlers
 ReadLib( "float.gi" );
 ReadLib( "ieee754.g" );
+
+# accumulators
+
+ReadLib("genacc.gi");
+ReadLib("permacc.gi");
+ReadLib("lazypermacc.gi");