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Improve bicoset code #2686

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Aug 9, 2018
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Improve bicoset code #2686

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8 changes: 5 additions & 3 deletions lib/csetgrp.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -329,9 +329,11 @@ DeclareCategory("IsRightCoset", IsDomain and IsExternalOrbit and
## <Prop Name="IsBiCoset" Arg='C'/>
##
## <Description>
## A (right) coset is considered a <E>bicoset</E> if its set of elements simultaneously forms a left
## coset for the same subgroup. This is the case, for example, if the coset representative normalizes
## the subgroup.
## <Index>bicoset</Index>
## A (right) coset <M>Ug</M> is considered a <E>bicoset</E> if its set of
## elements simultaneously forms a left coset for the same subgroup. This is
## the case if and only if the coset representative <M>g</M> normalizes the
## subgroup <M>U</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
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10 changes: 5 additions & 5 deletions lib/csetgrp.gi
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Expand Up @@ -634,7 +634,7 @@ function(c)
local s,r;
s:=ActingDomain(c);
r:=Representative(c);
return ForAll(GeneratorsOfGroup(s),x->r*x/r in s);
return ForAll(GeneratorsOfGroup(s),x->x^r in s);
end);

InstallMethodWithRandomSource(Random,
Expand Down Expand Up @@ -667,11 +667,11 @@ function(a,b)
local c;
if ActingDomain(a)<>ActingDomain(b) then TryNextMethod();fi;
if not IsBiCoset(a) then # product does not require b to be bicoset
TryNextMethod();
ErrorNoReturn("right cosets can only be multiplied if the left operand is a bicoset");
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Making this an error will hard block any future attempt to define multiplication of ordinary cosets (e.g. as multiplication of sets) in a more general way through other methods. Is this deliberate?

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This was quite deliberate, i.e., I thought quite a while about whether to change this into an error; or whether to instead change the Inverse method to use TryNextMethod() instead of Error -- in any case, I think they should match.

However, in the end I think a clear helpful error message is far better than a "method not found", just to support a hypothetical future extension which may never come. Besides, we actually don't stop anybody from adding one: they just have to rank their method higher than ours (and make sure to stay compatibly / invoke TryNextMethod() if needed). Finally, we can of course always change the error into something else if it ever becomes necessary.

fi;
c:=RightCoset(ActingDomain(a), Representative(a) * Representative(b) );
if IsBiCoset(b) then
SetIsBiCoset(c,true);
if HasIsBiCoset(b) then
SetIsBiCoset(c,IsBiCoset(b));
fi;

return c;
Expand All @@ -684,7 +684,7 @@ local s,r;
s:=ActingDomain(a);
r:=Representative(a);
if not IsBiCoset(a) then
Error("Inversion only works for cosets of normal subgroups");
ErrorNoReturn("only right cosets which are bicosets can be inverted");
fi;
r:=RightCoset(s,Inverse(r));
SetIsBiCoset(r,true);
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25 changes: 25 additions & 0 deletions tst/testbugfix/2018-08-08-bicosets.tst
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@@ -0,0 +1,25 @@
# We used to allow multiplying and inverting right cosets for which this
# was not valid. This test verifies this is not the case anymore.
# See <https://github.com/gap-system/gap/issues/2555>
gap> G := SymmetricGroup(3);;
gap> U := Group( (1,2) );;
gap> cos1 := RightCoset(U, (1,2));;
gap> cos2 := RightCoset(U, (1,3));;
gap> IsBiCoset(cos1);
true
gap> IsBiCoset(cos2);
false

#
gap> cos1*cos1 = cos1;
true
gap> cos1*cos2 = cos2;
true
gap> cos2*cos1;
Error, right cosets can only be multiplied if the left operand is a bicoset

#
gap> cos1^-1 = cos1;
true
gap> cos2^-1;
Error, only right cosets which are bicosets can be inverted