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Weights Modifier

In forming a ring, one of the possible modifiers that may be added has one of the forms: (i) Weights(W_1,...,W_n) where W_i is a positive integer specifying the weight of the i-th indeterminate (the number of weights listed must be equal to the number of indeterminates) or (ii) Weights(M) where M is a matrix with as many columns as there are indeterminates. In the latter case, the i-th indeterminate has the multi-degree given by the i-th column of M. The first row of the matrix M must have all positive entries.

If the weights are not specified the default value is 1 for all indeterminates.

example

    
Use S ::= Q[a,b,c], Weights(1,2,3);
Deg(b);
2
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L := [1,2,3];
Use S ::= Q[a,b,c], Weights(L);
Deg(b);
2
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W := Mat([[1,2,3],[4,5,6]]);
Use S ::= Q[a,b,c], Weights(W);
Deg(b);
2
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MDeg(b);  -- the multi-degree of b
[2, 5]
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Deg(b^3+a^2c);
6
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MDeg(b^3+a^2c);
[6, 15]
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WeightsMatrix();
Mat[
  [1, 2, 3],
  [4, 5, 6]
]
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WeightsList(); -- returns the first row of the Weights Matrix
[1, 2, 3]
-------------------------------