If r is a monomial, this will return the weight of r which is simply the sum of the weights of the variables in the support of r each counted with multiplicity equal to its exponent. If r is a polynomial, then the weight of the leading monomial is returned (which may differ from the weights of the other monomials of r).
In the following example, the polynomial ring R is the symmetric algebra over $V$, where $V=\mathbb{C}^4$ and is acted upon by the group $SL_4 (\mathbb{C})$.
i1 : R=QQ[x_1..x_4]; |
i2 : D=dynkinType{{"A",3}};
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i3 : W={{1,0,0},{-1,1,0},{0,-1,1},{0,0,-1}};
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i4 : setWeights(R,D,W); |
i5 : getWeights(x_1^4*x_2*x_4^6)
o5 = {3, 1, -6}
o5 : List
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The weight of 0 is undefined, so an error is returned if r is 0.