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Groebner

  

InitialForm

  

compute the initial form of a polynomial

  

WeightedDegree

  

compute the weighted degree of a polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

InitialForm(f, T)

InitialForm(f, W, V)

WeightedDegree(f, W, V)

Parameters

f

-

polynomial or list or set of polynomials

T

-

ShortMonomialOrder

W

-

list or vector of rational weights

V

-

list of variable names

Description

• 

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.

Examples

withGroebner:

fx3+x2y+y2

f:=x3+x2y+y2

(1)

WeightedDegreef,1,2,x,y

4

(2)

InitialFormf,1,2,x,y

x2y+y2

(3)

MMatrixOrdertdegx,y,x,y

M:=1,1,0,1

(4)

InitialFormf,tdegx,y

x3+x2y

(5)

See Also

degree

LeadingTerm

MatrixOrder

 


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