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Fix QuaternionAlgebra bug that caused QuaternionAlgebra( [1], 2, 5 ).1 to error the second time it was invoked #4427

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Apr 23, 2021
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Fix QuaternionAlgebra bug that caused QuaternionAlgebra( [1], 2, 5 ).1 to error the second time it was invoked #4427

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44 changes: 8 additions & 36 deletions lib/algsc.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -689,26 +689,9 @@ InstallAccessToGenerators( IsSCAlgebraObjCollection and IsFullSCAlgebra,
##
#V QuaternionAlgebraData
##
InstallFlushableValue( QuaternionAlgebraData, [] );
InstallFlushableValue( QuaternionAlgebraData, [ [], [] ] );
if IsHPCGAP then
ShareSpecialObj( QuaternionAlgebraData );

BindGlobal("StoreQuaternionAlgebraData", function( a, b, F, A )
local stored;
atomic readwrite QuaternionAlgebraData do
stored:= First( QuaternionAlgebraData,
t -> t[1] = a and t[2] = b and
IsIdenticalObj( t[3], FamilyObj( F ) ) );
if stored = fail then
# Store the data for the next call.
Add( QuaternionAlgebraData, MakeImmutable([ a, b, FamilyObj( F ), A ]) );
else
A:= AlgebraWithOne( F, GeneratorsOfAlgebra( stored[4] ), "basis" );
SetGeneratorsOfAlgebra( A, GeneratorsOfAlgebraWithOne( A ) );
fi;
od;
return A;
end);
fi;


Expand Down Expand Up @@ -744,16 +727,8 @@ InstallGlobalFunction( QuaternionAlgebra, function( arg )
fi;

# Generators in the right family may be already available.
atomic readonly QuaternionAlgebraData do
stored:= First( QuaternionAlgebraData,
t -> t[1] = a and t[2] = b
and IsIdenticalObj( t[3], FamilyObj( F ) ) );
od;
if stored <> fail then
A:= AlgebraWithOne( F, GeneratorsOfAlgebra( stored[4] ), "basis" );
SetGeneratorsOfAlgebra( A, GeneratorsOfAlgebraWithOne( A ) );
else

stored := GET_FROM_SORTED_CACHE( QuaternionAlgebraData, [ a, b, FamilyObj( F ) ],
function()
# Construct a filter describing element properties,
# which will be stored in the family.
filter:= IsSCAlgebraObj and IsQuaternion;
Expand All @@ -780,15 +755,12 @@ InstallGlobalFunction( QuaternionAlgebra, function( arg )
filter );
SetFilterObj( A, IsAlgebraWithOne );
#T better introduce AlgebraWithOneByStructureConstants?
return A;
end );

# Store the data for the next call.
if IsHPCGAP then
A := StoreQuaternionAlgebraData( a, b, F, A );
else
Add( QuaternionAlgebraData, [ a, b, FamilyObj( F ), A ] );
fi;

fi;
A:= AlgebraWithOne( F, GeneratorsOfAlgebra( stored ), "basis" );
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Here a new algebra gets created; setting the filter IsFullSCAlgebra would be useful.

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Great catch, fixed now, and commit message adjusted. I agree this is a bugfix.

SetGeneratorsOfAlgebra( A, GeneratorsOfAlgebraWithOne( A ) );
SetIsFullSCAlgebra( A, true );

# A quaternion algebra with negative parameters over a real field
# is a division ring.
Expand Down