isHomogeneous(NCRingMap) -- Determines if an NCRingMap preserves the natural grading

Synopsis

Function: isHomogeneous
Usage:

isHomogeneous f
Inputs:
- f, an instance of the type NCRingMap,
Outputs:
- a Boolean value,

Description

This method returns true if the map f is degree 0; that is, if the generators of the source of f are mapped to elements of the same degree in the target.

i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{w,x,y,z})
--Calling Bergman for NCGB calculation.
Complete!

o1 = A

o1 : NCQuotientRing

i2 : B = QQ{w,x,y,z}/ncIdeal{w*x+x*w,w*y+y*w,x*y+y*x}
--Calling Bergman for NCGB calculation.
Complete!

o2 = B

o2 : NCQuotientRing

i3 : f = ncMap(B,A,gens B)

o3 = NCRingMap B <--- A

o3 : NCRingMap

i4 : isHomogeneous f

o4 = true

i5 : C = QQ{a,b,c}

o5 = C

o5 : NCPolynomialRing

i6 : g = ncMap(C,A,{a^3,b^2,a+b,a-b})

o6 = NCRingMap C <--- A

o6 : NCRingMap

i7 : isHomogeneous g

o7 = false

i8 : setWeights(A,{3,2,1,1})

o8 = A

o8 : NCQuotientRing

i9 : isHomogeneous g

o9 = true

Ways to use this method: