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7.5.6.0. BFBoundsBudur
Procedure from library dmodideal.lib (see dmodideal_lib).
- Usage:
- BFBoundsBudur(F,m); F an ideal, m an intvec
- Return:
- ring
- Assume:
- basering is a commutative polynomial ring in characteristic 0
- Purpose:
- determine upper and lower bounds of the Bernstein-Sato ideal associated to m with
the method of (Bud12)
- Note:
- The returned ring contains lists Bj, containing the Bernstein-Sato ideals
associated to e_j,
shiftedIdeals, containing the shifted ideals from (Bud12) 4.7,
and ideals upperBound, lowerBound which give upper bound and lower bound
for the Bernstein-Sato-Ideal associated to m respectively.
Example:
| | LIB "dmodideal.lib";
ring r = 0,(x,y,z),dp;
setring r;
ideal F = x*z,2*x^2*y^2*z+x^4+y^4;
def A = BFBoundsBudur(F,intvec(1,1));
setring A;
lead(upperBound);
==> _[1]=2*s(1)^8*s(2)^2
==> _[2]=s(1)^9*s(2)
lead(lowerBound);
==> _[1]=s(1)^11*s(2)
==> _[2]=2*s(1)^10*s(2)^2
==> _[3]=2*s(1)^10*s(2)^2
==> _[4]=4*s(1)^9*s(2)^3
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