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Feature #1198

Non-standard DegRevLex (NonStdDegRevLex, WDegRevLex)

Added by John Abbott almost 6 years ago. Updated over 4 years ago.

Status:
New
Priority:
Normal
Assignee:
-
Category:
New Function
Target version:
CoCoALib-1.0
Start date:
27 Jun 2018
Due date:
% Done:

0%

Estimated time:
Spent time:
0.80 h

Description

There is a family of cases where a "DegRevLex" ordering with "non-standard" weights is useful.
This can be implemented by a matrix ordering, but that is inefficient (esp. if there are many indets, then creating the ring can cost more than the computation in the ring).

Maybe the PPOrdering family should be called WDegRevLex?

History

#1 Updated by Anna Maria Bigatti almost 6 years ago

In particular we should have a dedicated OrdvArith implementation for it.

This should make exponents faster, and even the creation of the ring faster (useful for SC2 computations, with many big rings, and trivial GBases)

#2 Updated by John Abbott almost 6 years ago

Here are some thoughts about the design/impl.

If the GradingDim is 1 then we have a vector of positive "weights": W_1, W_2, ... , W_n
The rest of the matrix is an antidiagonal of -1 with the rest being zeros.
This is term-ord equivalent to a matrix whose lower rows are just prefixes of the first row (filled with zeroes to the correct number of columns): for example

[[3, 4, 5],
 [3, 4, 0],
 [3, 0, 0]]

Note that "encoding" and "decoding" are simple and fast operations.

The GradingDim is greater than 1 then it is a little more complicated but not too bad.
Roughly speaking we split the matrix into "column blocks" where each block is determined by the row index where the first non-zero element appears. Each column block is then handled as for the case with GradingDim equal to 1.

#3 Updated by John Abbott over 4 years ago

  • Target version changed from CoCoALib-0.99650 November 2019 to CoCoALib-1.0

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