isLeftRegular -- Determines if a given (homogeneous) element is regular in a given degree

Synopsis

Usage:

isLeftRegular(x,n) or isRightRegular(x,n)
Inputs:
- x, an instance of the type NCRingElement,
- n, an integer, the degree in which regularity is checked.
Outputs:
- a Boolean value,

Description

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

Ways to use isLeftRegular :

isLeftRegular(NCRingElement,ZZ)

For the programmer

The object isLeftRegular is a method function.

isLeftRegular -- Determines if a given (homogeneous) element is regular in a given degree

Synopsis

Description

See also

Ways to use isLeftRegular :

For the programmer