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Feature #1381

Type ideal for ZZ[x[1..n]]

Added by Elisa Palezzato over 4 years ago. Updated 2 months ago.

Status:
In Progress
Priority:
Normal
Assignee:
-
Category:
Data Structures
Target version:
CoCoALib-0.99880
Start date:
06 Jan 2020
Due date:
% Done:

10%

Estimated time:
Spent time:
2.45 h

Description

Is it possible to add the type ideal for the ring ZZ[x[1..n]]?

History

#1 Updated by John Abbott over 4 years ago

  • Project changed from CoCoA to CoCoALib
  • Category set to Data Structures
  • Target version set to CoCoALib-1.0

JAA moved this to CoCoALib.

I think this will not be possible before the CoCoA School in early March (or, at least, we cannot guarantee anything before then).

Probably the type name should be something like IdealOverPID; maybe even just IdealOverZZ for a first version (but hoping that most of the impl is general enough to work for PIDs).

#2 Updated by Anna Maria Bigatti over 4 years ago

I think the question was intended as: "can we let the user define an ideal over ZZ[x[1..n]]?"
Now it gives an error:

/**/ use ZZ[x,y];
/**/ I := ideal(2*x);
--> ERROR: ERR:NYI ideal of polynomials with coeffs not in a field
--> [CoCoALib] ideal(SparsePolyRing, gens)
--> I := ideal(2*x);
-->      ^^^^^^^^^^

In fact, even though we cannot (yet!) do much with them, there are possibile functions: sum, product, gens, ... so we should just move the blocking check into the "gbasis" function.

#3 Updated by John Abbott about 4 years ago

  • Target version changed from CoCoALib-1.0 to CoCoALib-0.99850

#4 Updated by John Abbott about 3 years ago

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

The relevant source code seems to be around line 364 of SparsePolyOps-ideal.C.

I'll try disabling the check inside the pseudo-ctor and see what happens... :-)

#5 Updated by John Abbott about 3 years ago

The CoCoA-5 tests all passed, and I succeeded in creating an ideal in ZZ[x,y,z].

Next thing is to check that some trivial operations work:
  • I+J, I*J
  • r*I
  • gens(I), NumGens(I)
  • IsZero(I)
  • other ops?

#6 Updated by John Abbott about 3 years ago

A quick test of ideal product suggests that it does not work properly in ZZ[...]

/**/ use ZZ[x,y,z];
/**/ I := ideal(2*x, x^2, y^3);
/**/ I;
ideal(2*x,  x^2,  y^3)
/**/ J := ideal(4*x, x^3, 2*y,3*z);
/**/ I*J;
ideal(x*z,  x*y,  x^2,  y^3*z,  y^4)  // where have all the coeffs gone?

#7 Updated by John Abbott about 3 years ago

I suspect the example in the previous note is wrong because an ideal is a recognized as "monomial over field" without actually checking that the coeff ring is a field.

#8 Updated by John Abbott about 3 years ago

I think I have fixed ideal product now: it calls the "clever monomial short-cut" only if the coeff ring is a field (and the other criteria are met).
Source code: SparsePolyOps-ideal.C around line 575.

Output is now:

ideal(8*x^2,  2*x^4,  4*x*y,  6*x*z,  4*x^3,  x^5,  2*x^2*y,  3*x^2*z,  4*x*y^3,  x^3*y^3,  2*y^4,  3*y^3*z)

Could it be worth having special monomial ideals with coeffs in ZZ (or a PID)? Not sure.

#9 Updated by John Abbott almost 3 years ago

Here is my first ad hoc test:

use ZZ[x,y,z];
I := ideal(2*x, x^2, y^3);
I;
J := ideal(4*x, x^3, 2*y,3*z);
I*J;
I+J;
IsZero(I);
x*I;
I*y;
(2*x/x)*I;
LT(I);     --> EXPECT ERROR
GBasis(J); --> EXPECT ERROR
radical(I);--> EXPECT ERROR
intersection(I,J); --> EXPECT ERROR

Currently (2021-04-28) all tests behave as hoped.

#10 Updated by John Abbott almost 3 years ago

I have just checked in my current changes... they are not well designed (but the test above works as hoped).

#11 Updated by John Abbott 2 months ago

  • Target version changed from CoCoALib-0.99850 to CoCoALib-0.99880

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