Opened 11 years ago

Closed 11 years ago

#381 closed proposed feature (wontfix)

weighted TOP ordering

Reported by: steenpass Owned by: steenpass
Priority: minor Milestone: 3-1-4 and higher
Component: dontKnow Version: 3-1-3
Keywords: weighted TOP ordering Cc: Diego, Ruano, <diego@…>


From Diego Ruano:

Dear Singular team,


For some list decoding algorithms (in coding theory), one uses the weighted TOP ordering for computing Gröbner bases over modules. Magma has implemented this term ordering (TOPW in Magma), but we would like to use Singular as usual.

We are wondering if you could implement this term ordering in Singular, please?

The formal definition of weighted TOP is:

Given weights w_1, ... w_q,
x^a e_i < x^b e_j
if and only if a + w_i < b + w_j
or if (a + w_i = b + w_j and i < j).

One can find the definition of this term ordering and an application in:

Best regards,


Change History (2)

comment:1 Changed 11 years ago by Oleksandr

Owner: changed from somebody to steenpass

comment:2 Changed 11 years ago by steenpass

Resolution: wontfix
Status: newclosed

There is no predefined weighted TOP ordering in Singular. However, this can be emulated as follows:

Use extra variables y_1, ..., y_q and define the ordering by the matrix

1, w_1, ...,w_q
0,   1
0,     1
0,       ...
0,           1

If you want to make sure that the y_i only occur up to power 1, you can define a quotient ring by maxideal(2). Be careful not to allow any terms without y_i.

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