# isCI -- whether the ring is complete intersection

## Synopsis

• Usage:
isCI R or isCI I
• Inputs:
• R, , of a polynomial algebra by an ideal contained in the irrelevant maximal ideal
• Outputs:
• , whether the local ring obtained by localizing R at the irrelevant maximal ideal is complete intersection

## Description

Checks if the local ring obtained by localizing R at the irrelevant maximal ideal is complete intersection. It is also possible to call the function on the defining ideal of R; see isCI(Ideal).

 i1 : Q = QQ[x,y,z]; i2 : isCI (Q/ideal(x^2,x*y,y*z,z^2)) o2 = false i3 : isCI (Q/ideal(x^2,y^2)) o3 = true

## Ways to use isCI :

• "isCI(QuotientRing)"
• isCI(Ideal) -- whether the ring is complete intersection

## For the programmer

The object isCI is .