Project

General

Profile

Feature #1468

Adjoin indets to a poly ring

Added by John Abbott almost 4 years ago. Updated 2 months ago.

Status:
In Progress
Priority:
Normal
Assignee:
-
Category:
New Function
Target version:
CoCoALib-0.99900
Start date:
25 Jun 2020
Due date:
% Done:

10%

Estimated time:
Spent time:
0.80 h

Description

Make it easy to "adjoin" indets to a poly ring.

JAA thinks this means: given polyring QQ[x,y] and new indets a,b
  • create polyring QQ[x,y,a,b]
  • create embedding QQ[x,y] into QQ[x,y,a,b] -- just a PolyAlgHom
  • create "inverse" hom from QQ[x,y,a,b] into QQ[x,y]
  • put everything together into a convenient structure
  • make it accessible from CoCoA-5

Requested by Julian Danner

Related issues

Related to CoCoALib - Feature #992: Poly ring homomorphism to change orderingNew2016-12-13

Related to CoCoALib - Feature #562: SubringsNew2014-05-20

History

#1 Updated by John Abbott almost 4 years ago

Description above is incomplete:
  • what term ord on QQ[x,y,a,b]? For impl, it would be nice if the orderings were compatible (i.e. respected by the embedding)
  • can the new indets be indexed? e.g. QQ[x,y,a[1..2]]
  • what should the "inverse" hom do when applied to something outside the image of QQ[x,y]?
  • the convenient structure could be just a pair of RingHoms; or should the big ring be available as a field of the record?

KISS suggests making the "inverse" send all new indets to 0; it is then the caller's responsibility to ensure that it is applied only to values in the image (assume that this check is wanted).

SUGGESTION should the embedding be available to CanonicalHom? That would be nice! How to achieve this? (probably a new issue)

#2 Updated by John Abbott almost 4 years ago

  • Related to Feature #992: Poly ring homomorphism to change ordering added

#3 Updated by John Abbott over 3 years ago

  • Status changed from New to In Progress
  • % Done changed from 0 to 10

What should new indets be called? Should they be "new symbols"? Advantage is that there could be no problems with name clashes.

Where should the new indets appear relative to those already in the poly ring?
At least for a first impl, they could appear after the indets of the orig ring (at least by default).

The embedding hom is one which respects PPs (i.e. the image of a PP is a PP). The inverse almost respects PPs too (unless they map to 0); if the inverse hom maps the new indets to 1 then the inv hom does respect PPs (but is obviously not injective if applied to elems outside the image of the embedding).

REMINDER this does remind me that I was considering introducing certain types of subring (see #562) so that homs could be restricted to them. They could be useful in this context.

#4 Updated by John Abbott over 3 years ago

#5 Updated by John Abbott 2 months ago

  • Target version changed from CoCoALib-0.99850 to CoCoALib-0.99900

Also available in: Atom PDF