isWellDefined(LocalRing) -- whether a local ring is well defined

Description

This method checks whether the local ring was produced by localization at a prime ideal.

i1 : R = QQ[x,y,z,w]

o1 = R

o1 : PolynomialRing

i2 : P = ideal"xz-y2,yw-z2,xw-yz"; -- The twisted cubic curve

o2 : Ideal of R

i3 : isWellDefined R_P

o3 = true

i4 : Q = ideal"xz-y2,z(yw-z2)-w(xw-yz)";

o4 : Ideal of R

i5 : isWellDefined R_Q

o5 = false

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LocalRings/doc.m2:234:0.