Currently only localizations at prime ideals of a polynomial ring are supported.
i1 : S = QQ[x,y,z,w]; |
i2 : I = ideal"xz-y2,yw-z2,xw-yz"; -- The twisted cubic curve o2 : Ideal of S |
i3 : R = S_I o3 = R 2 2 o3 : LocalRing, maximal ideal (- y + x*z, - z + y*w, - y*z + x*w) |
i4 : K = frac(S/I) o4 = K o4 : FractionField |
The maximal ideal and a residue map to the residue field are stored in the ring.
i5 : max R 2 2 o5 = ideal (- y + x*z, - z + y*w, - y*z + x*w) o5 : Ideal of R |
i6 : R.maxIdeal 2 2 o6 = ideal (- y + x*z, - z + y*w, - y*z + x*w) o6 : Ideal of S |
i7 : R.residueMap o7 = map (K, R, {x, y, z, w}) o7 : RingMap K <--- R |
Objects over the base ring can be localized easily.
i8 : I ** R 2 2 o8 = ideal (- y + x*z, - z + y*w, - y*z + x*w) o8 : Ideal of R |
The object LocalRing is a type, with ancestor classes EngineRing < Ring < Type < MutableHashTable < HashTable < Thing.