setWeights -- Set a nonstandard grading for a NCRing.

Synopsis

Usage:

setWeights(A,degList)
Inputs:
- A, an instance of the type NCRing,
- degList, a list, a list of integer weights to be assigned to the generators of A
Outputs:
- an instance of the type NCRing,

Description

This method enables the user to work with rings which are not naturally graded (the generators are not all degree 1). The user should be aware that methods which call Bergman may not work with nonstandard gradings. Perhaps the most important example is hilbertBergman, which throws an error. Instead, use hilbertSeries.

i1 : A=QQ{x,y,z}

o1 = A

o1 : NCPolynomialRing

i2 : w=x^3-y^2

       2  3
o2 = -y +x

o2 : A

i3 : isHomogeneous w

o3 = false

i4 : setWeights(A, {2,3,1})

o4 = A

o4 : NCPolynomialRing

i5 : isHomogeneous w

o5 = true

i6 : C = QQ{a,b,c}

o6 = C

o6 : NCPolynomialRing

i7 : g = ncMap(C,A,{a^3,b^2,a+b,a-b})

o7 = NCRingMap C <--- A

o7 : NCRingMap

i8 : isHomogeneous g

o8 = false

i9 : setWeights(A,{3,2,1,1})

o9 = A

o9 : NCPolynomialRing

i10 : isHomogeneous g

o10 = true

Ways to use setWeights :

setWeights(NCRing,List)

For the programmer

The object setWeights is a method function.

setWeights -- Set a nonstandard grading for a NCRing.

Synopsis

Description

See also

Ways to use setWeights :

For the programmer