A ring S satisfies Serre’s S2 condition if every codimension 1 ideal contains a nonzerodivisor and every principal ideal generated by a nonzerodivisor is equidimensional of codimension one. If R is an affine reduced ring, then there is a unique smallest extension R⊂S⊂frac(R) satisfying S2, and S is finite as an R-module.
There are several methods to compute S. Currently, only two of these methods is implemented in this package. Stay tuned, or help write the other methods!
i1 : A = ZZ/101[a..d]; |
i2 : I = monomialCurveIdeal(A,{1,3,4})
3 2 2 2 3 2
o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o2 : Ideal of A
|
i3 : R = A/I; |
i4 : (F,G) = makeS2 R
ZZ
---[w , a, b, c, d]
101 0,0
o4 = (map(-------------------------------------------------------------------
2 2 2
(b*c - a*d, w d - c , w c - b*d, w b - a*c, w a - b , w
0,0 0,0 0,0 0,0 0,0
------------------------------------------------------------------------
------,R,{a, b, c, d}),
- a*d)
------------------------------------------------------------------------
/ ZZ
| ---[w , a, b, c, d]
| 101 0,0
map(frac(R),frac|-------------------------------------------------------
| 2
|(b*c - a*d, w d - c , w c - b*d, w b - a*c, w a
\ 0,0 0,0 0,0 0,0
------------------------------------------------------------------------
\
|
| b*d
------------------|,{---, a, b, c, d}))
2 2 | c
- b , w - a*d)|
0,0 /
o4 : Sequence
|