On Tue, Jun 5, 2018 at 1:01 PM, Raymond Rogers <[email protected]> wrote: > " - something that is required in order to be an Algebra. This > is orthogonal to the issue of symbolic coefficients." > > I have to think about this and your code. Are you saying that the > NCP field is created without the scalar field K being defined and we > are dealing with only the properties that are true for all NCP fields?
No. NCP as defined in the test input file: ... ALPHABET := ['x, 'y, 'z, '_\mu]; OVL ==> OrderedVariableList(ALPHABET) F ==> Complex(Fraction(Integer)) NCP ==> NCPOLY(OVL, F) ... is not a field. According the definition in "ncpoly.spad" Exports == Algebra(F) with ... the domain NCPOLY is only an Algebra, not a field. In FriCAS/Axiom you need to take the specific category definitions and the abstract algebra seriously. Be careful when comparing the notation used in the paper you cite with the SPAD code. In "ncpoly.spad" F is equivalent to the 𝕂 (\mathbb K) > In any case the usage in the first definition of page 7 1803.. > does seem implementable in the general context; Yes, I think that is Konrad's intention. The main issue as I understand it is minimization, i.e. putting the ALS representation into standard (canonical) form. This is like gcd for commutative fraction fields Fraction ... But in "ncpoly.spad" Konrad is not trying to define a Field, only an Algebra. > I will examine your code. > In the example I gave a different (symbolic) definition of the scalars F: MP ==> MPOLY(PARAMETERS,Integer) F ==> Fraction(MP) but as far as NCPOLY is concerned this is just another Field. > > On 06/05/2018 12:15 PM, Bill Page wrote: > > ... > > Something more general is required (as discussed in the paper) > > if we want a Free Field rather than just an algebra. > > Again in 1803.. page 7 there is > > Can't I add this as an operation? There doesn't seem to be anything outside > of the bounds of matrix manipulation; although it might run into trouble > subsequently. > Yes you can (and I am pretty sure this has already been done) but the result would be something more general than an Algebra. > > Sticking to the supported items what is the best documentation? I found Brigit Janko's documentation quite good. I think it corresponds more exactly to what is implemented in "ncpoly.spad". Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
