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Feature #1532

Convenient RingHom pseudo-ctors

Added by John Abbott over 3 years ago. Updated about 2 months ago.

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

10%

Estimated time:
Spent time:
0.95 h

Description

CoCoALib should offer some convenient pseudo-ctors for RingHom.

One example would be from QQ[x,y,z] into QQ(x)[y,z]; where indets names are to be preserved.

Prompted by a question from Florian Walsh.

Related issues

Related to CoCoA-5 - Design #1533: RingElem and IndetSymbols not compatibleIn Progress2020-11-06

Related to CoCoALib - Feature #1329: New syntax for creating homomorphisms (PolyAlgebraHom)Closed2019-10-08

History

#1 Updated by John Abbott over 3 years ago

Here is the example Florian wanted:

P1 ::= QQ[x,y,z];
P2 ::= QQ(x)[y,z]; --> cannot do this directly
phi := PolyAlgebraHom(P1,P2, [RingElem(P2, name) | name in ["x","y","z"]]);

It would be nice to have an easy way to make such ringhoms.

Probably we should try examples before aiming to write down exact semantics.

#2 Updated by John Abbott over 3 years ago

  • Related to Design #1533: RingElem and IndetSymbols not compatible added

#3 Updated by John Abbott over 3 years ago

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

Here is a prototype in CoCoA-5... we would also need a version for cocoalib!!

define AllSymbols(R)
  if IsZZ(R) or IsQQ(R) then return []; endif;
  if IsPolyRing(R) then return concat(AllSymbols(CoeffRing(R)), IndetSymbols(R)); endif;
  if IsQuotientRing(R) then return AllSymbols(BaseRing(R)); endif;
  if IsFractionField(R) then return AllSymbols(BaseRing(R)); endif;
  println "How did we get here? R = ", R;
  error("surprise!");
enddefine; -- AllSymbols

define NaturalHom(P1,P2)
  if not(IsPolyRing(P1)) then error("NaturalHom: not a polyring -- giving up!"); endif;
  Symbols1 := AllSymbols(P1);
  Symbols2 := AllSymbols(P2);
  CommonSymbols := intersection(Symbols1, Symbols2);
  if CommonSymbols = [] then error("NaturalHom: no common symbols"); endif;
  ExtraSymbols1 := diff(Symbols1, CommonSymbols);
  images := [];
  foreach symb in Symbols1 do
    if symb isin ExtraSymbols1 then
      append(ref images, zero(P2));
    else
      append(ref images, RingElem(P2, concat([symb.head], symb.indices)));
    endif;
  endforeach;
  return PolyAlgebraHom(P1, P2, images);
enddefine; -- NaturalHom

#4 Updated by John Abbott over 3 years ago

Florian mentions that Singular has something called imap...

#5 Updated by Anna Maria Bigatti over 3 years ago

  • Related to Feature #1329: New syntax for creating homomorphisms (PolyAlgebraHom) added

#6 Updated by John Abbott over 3 years ago

It might be possible to extend the impl give above to handle quotients of poly rings, and perhaps also "towers" of poly rings (or are they already handled?)

What about the case QQ[x,y] to ZZ/(p)[x,y]? It would be convenient (but is also unclean).

#7 Updated by John Abbott about 2 months ago

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

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