Situation:
- R local ring in variables x and parameters t,
- It family of zero-dimensional ideals in R
Partial Standard Basis:
system of generators of It,
union of Sx and St where
- h(t=0) non-zero for all h in Sx
- h(t=0)=0 for all h in St
- restriction of Sx to t=0 is standard basis of I
- further condintions on St