CoCoA:PositiveGrading4

PositiveGrading4

extend a positive grading (for CoCoA-4

   multigradings limitation)

Description

This function returns a matrix defining a similar multigrading.

Because of an innate limitation (see Weights Modifier)

CoCoA-4 does not allow zero entries in the first row of the weights matrix. This function returns a matrix which has an extra first row which is a suitable combination of the following rows and has no zero entries. This we can work in CoCoA-4 with any positive grading being the first component the multidegree redundant.

Example

  G := Mat([[1,1,1,0,0], [0,0,0,1,1]]);
  PG := PositiveGrading4(G);
  Use Q[x[1..5]], Weights(PG);
  MDeg(x[2]); -- ignore the first entry to get the degree wrt G
[1, 1, 0]
-------------------------------
  Tail(MDeg(x[2]));
[1, 0]
-------------------------------

Syntax

PositiveGrading4(M:MATRIX):MATRIX

Weights Modifier

IsPositiveGrading

HilbertSeriesMultiDeg

   <type>matrix</type>