Given an element x in an NCRing, isLeftRegular returns true if a*x=0 implies a=0 for all a in the specified homogeneous degree n. Likewise isRightRegular returns true if x*a=0 implies a=0 for all elements a of degree n. The method calls leftMultiplicationMap or rightMultiplicationMap as appropriate and checks the kernel in the specified degree.
i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z})
--Calling Bergman for NCGB calculation.
Complete!
o1 = B
o1 : NCQuotientRing
|
i2 : g = -y^3-x*y*z+y*x*z+x^3
3 3
o2 = -y +yxz-xyz+x
o2 : B
|
i3 : isLeftRegular(g,6) o3 = true |
i4 : C = QQ{x,y}
o4 = C
o4 : NCPolynomialRing
|
i5 : D = C/ncIdeal{x^2+x*y,y^2}
--Calling Bergman for NCGB calculation.
Complete!
o5 = D
o5 : NCQuotientRing
|
i6 : isLeftRegular(x,1) o6 = true |
i7 : isRightRegular(x,1) o7 = false |
The object isLeftRegular is a method function.