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