On Tue, Mar 18, 2025 at 01:59:47PM +0100, 'Ralf Hemmecke' via FriCAS - computer
algebra system wrote:
>
> In fact, I find it a bit strange that in the design of AN it was decided to
> internally build on Kernel(Expression(INT)). Well, maybe it was not decided,
> but just happened (for most of the cases), because many functions from
> ExpressionSpace are just inherited from Rep:=Expression(INT).
It was natural to inherit representation and operations from
Expression(Integer). But operations in Expression(Integer)
produce kernels from Kernel(Expression(Integer)). Also,
AlgebraicNumber has operations like norm and subst which
take kernels as arguments. Those operations are defined
in ExpressionSpace, so we make AlgebraicNumber into
ExpressionSpace. Oops, now the kernels live in two caches :(
There seem to be two possible ways to solve this. We have
now ExpressionSpace2 which can express fact that kernels
are not from Kernel(AlgebraicNumber), so we could declare
that AlgebraicNumber is ExpressionSpace2(SomeNewKernel)
and implement SomeNewKernel as Kernel(Expression(Integer)).
Alternatively, we can give some new signatures to 'norm'
and 'subst'. Actually, 'norm' could be declared in
some Category and implemented in Expression. But trouble
is that currently there in Kernel in signature of 'norm'.
--
Waldek Hebisch
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