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PositiveGrading4

extend a positive grading (for CoCoA-4 multigradings limitation)
Syntax 

PositiveGrading4(M:MATRIX):MATRIX

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 QQ[x[1..5]], Weights(PG);
  MDeg(x[2]); -- ignore the first entry to get the degree wrt G
[1, 1, 0]
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  Tail(MDeg(x[2]));
[1, 0]
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See Also