"
- 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? In any case the usage in the
first definition of page 7 1803.. does seem implementable in the general
context; I will examine your code.
On 06/05/2018 12:15 PM, Bill Page wrote:
In an algebra where the coefficients form a Field, only the scalar
polynomials are invertible. NCPOLY implements
inverse (f:%) : % ==
not(scalar?(f)) =>
error "NCPOLY: inverse(f) - polynomial not invertible."
zero?(qeltv(f.lmmp, 1, POS_1)) =>
error "NCPOLY: inverse(f) - zero element is not invertible."
return(copy(1, 1/qeltv(f.lmmp, 1, POS_1)))
--
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.
Is there a large gap between nc_ini03.input and 1803.10627.pdf; did I
misunderstand the relationship?
Keep in mind that "1803.10627.pdf" is describing something more
general. From offline discussions with Konrad I gather that the FriCAS
coding for the latter is still somewhat of a work-in-progress but he
is willing to discuss it if there is some interest in such a
generalization.
Sticking to the supported items what is the best documentation?
---------------
Here is a clip, for comment, of an email that Bill sent me that he
thought might be of interest to everybody interested in this code from
nc_poly.spad
Ray
Doesn't this look wrong?
In nc_poly.spad
---------------
f:% ^ n:Integer ==
if zero?(n) then
return(0)
if n < 0 then
g := inverse(f)
return(g^(-n)::PositiveInteger)
f^n
------------------
Shouldn't
if zero?(n) then
return(0)
be return(1) ?
Bill
Yes, I think you are right. That looks like a typo.
RayR
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