Re: CliffordPackage

[Martin Baker]

Bertfried,

Thanks very much for this.

These changes make good sense to me. I will just note for the record that they
change the user interface and would therefore break any applications already
using CliffordAlgebra but the changes are important enough to justify that.

> a) I would not restrict Clifford algebras to 'Field' but
> rather to 'Ring' or 'IntegralDomain'.

OK, I will check if division or swapping of operands is done. Its easy enough
to check if they are done directly but also other packages are used so I need
for check for secondary effects. One issue is that LinearSystemMatrixPackage
is used which requires a Field so I need to find an alternative way to
calculate recip() if possible. Or perhaps recip() should try to coerce the
Ring into a Field and if that fails then recip() fails. Also I need to better
understand more details of the mechanism for inheriting from say 'Field' or
'Ring' and while I'm about it I will follow up on hints that I need to
understand the spad category mechanism. So this may take me some time!

> b) I would like to see there the possibility to
> have an arbitrary bilinear form,

Do you have any views about whether the bilinear form should be supplied to
the domain constructor as 'List List Ring', 'SquareMatrix Ring' or create a
custom domain called BilinearForm ? Would I be correct in thinking that Matrix
or a custom domain would not add much value so I might as well use a List of
Lists for efficiency?

> If you want test cases I could produce a pdf with several multiplication
tables

Yes please, this would be very helpful, no rush though, as it will take me
some time to absorb all this good information that you have given me.

Martin

[Martin Rubey]

Bertfried Fauser <bertfrie...@googlemail.com> writes:


> I doubt threre is any other place (and I will see if I can chack that,
> a grep over the code should do, I found CliffordAlgebra mentioned in
>
> * browse.daase
> * category.daase
> * operation.daase
> * compres.daase
> * interp.daase
> * exposed.lsp.pamphlet.svn-base
> * clifford.spad.pamphlet
> * abbrevs.input
> * extract-spad.mk
> * comdb.text
> * libdb.text
> * DEPENDENTS.DAASE
> * CLIF.spad
> * /USERS.DAASE/index.KA
> * hyper/pages/.svn/text-base/CLIF.ht.svn-base
> * hyper/pages/.svn/text-base/QUAT.ht.svn-base
> * hyper/pages/QUAT.ht
> * hyper/pages/QUAT2.ht
> * hyper/pages/xmpexp.ht
> * hyper/pages/ug02.ht
> * hyper/pages/ug13.ht
> * hyper/pages/CLIF.ht
> * input/clifford.input.pamphlet
> * paste/CLIF.input
> * paste/CLIF.phts
> * padhelp/Quaternion.help
> * spadhelp/CliffordAlgebra.help
> * topics.data
> * command.list
> )
>
> I am not a grep expert, so things may have sliped through, otherwise I
> think the above given list proves that CliffordAlgebra is not used by
> any other package.

It's not a proof, unfortunately (only a strong hint), because the
compiler tries to be smart: packages and domains do not necessarily need
to be mentioned, if the name of the operation or the types of the
arguments determine the operation uniquely.

Martin