compute the initial form of a polynomial
compute the weighted degree of a polynomial
InitialForm(f, W, V)
WeightedDegree(f, W, V)
polynomial or list or set of polynomials
list or vector of rational weights
list of variable names
The WeightedDegree command computes the weighted degree of a polynomial f with respect to a vector of rational weights W. The output is a rational number, the weighted degree of f, which is similar to the ordinary degree except that each power of a variable Vi contributes Wi to the degree of each term, instead of 1.
The InitialForm command extracts the terms of f with maximal weighted degree. The output is a polynomial. One can also specify a monomial order T instead of a vector of weights, and the first row in a matrix representation for T will be used automatically. See the MatrixOrder help page for more details.
f ≔ x3+x2⁢y+y2
M ≔ MatrixOrder⁡tdeg⁡x,y,x,y
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