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7.5.6.0. extractS
Procedure from library dmodideal.lib (see dmodideal_lib).
- Usage:
- extractS(I,r); I ideal, r int
- Return:
- ring
- Assume:
- I is an ideal in the first r variables of the basering and these r variables generate a commutative subring
- Purpose:
- give the ideal generated by I in the commutative subring generated by the first r variables, ordering dp
- Note:
- The returned ring contains I.
Example:
| | LIB "dmodideal.lib";
ring R = 0,(x,y),dp;
ideal f = x^2-y^2,y;
def S = BernsteinSatoIdeal(f);
setring S;
BS;
==> BS[1]=8*s(1)^4*s(2)+8*s(1)^4+12*s(1)^3*s(2)^2+56*s(1)^3*s(2)+44*s(1)^3+6*\
s(1)^2*s(2)^3+54*s(1)^2*s(2)^2+136*s(1)^2*s(2)+88*s(1)^2+s(1)*s(2)^4+16*s\
(1)*s(2)^3+77*s(1)*s(2)^2+138*s(1)*s(2)+76*s(1)+s(2)^4+10*s(2)^3+35*s(2)^\
2+50*s(2)+24
def T = extractS(BS,2);
setring T;
I;
==> I[1]=8*s(1)^4*s(2)+12*s(1)^3*s(2)^2+6*s(1)^2*s(2)^3+s(1)*s(2)^4+8*s(1)^4+\
56*s(1)^3*s(2)+54*s(1)^2*s(2)^2+16*s(1)*s(2)^3+s(2)^4+44*s(1)^3+136*s(1)^\
2*s(2)+77*s(1)*s(2)^2+10*s(2)^3+88*s(1)^2+138*s(1)*s(2)+35*s(2)^2+76*s(1)\
+50*s(2)+24
factorize(I[1]);
==> [1]:
==> _[1]=1
==> _[2]=s(1)+1
==> _[3]=s(2)+1
==> _[4]=2*s(1)+s(2)+2
==> _[5]=2*s(1)+s(2)+3
==> _[6]=2*s(1)+s(2)+4
==> [2]:
==> 1,1,1,1,1,1
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