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7.7.7.0. ivSickleHil
Procedure from library fpadim.lib (see fpadim_lib).
- Usage:
- ivSickleHil(L,n[,degbound]); L a list of intmats, n an integer,
degbound an optional integer
- Return:
- list
- Purpose:
- Computing the mistletoes and the Hilbert series
- Assume:
- - basering is a Letterplace ring.
- all rows of each intmat correspond to a Letterplace monomial
as explained in the overview
- if you specify a different degree bound degbound,
degbound <= attrib(basering,uptodeg) should hold.
- Note:
- - If L is the list returned, then L[1] is an intvec, L[2] is a list,
containing the mistletoes as intvecs.
- If degbound is set, a degree bound will be added. By default there
is no degree bound.
- n is the number of variables.
- If I = L[1] is the intvec returned, then I[k] is the (k-1)-th
coefficient of the Hilbert series.
- If the K-dimension is known to be infinite, a degree bound is needed
Example:
| | LIB "fpadim.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
//some intmats, which contain monomials in intvec representation as rows
intmat I1[2][2] = 1,1,2,2; intmat I2[1][3] = 1,2,1;
intmat J1[1][2] = 1,1; intmat J2[2][3] = 2,1,2,1,2,1;
print(I1);
==> 1 1
==> 2 2
print(I2);
==> 1 2 1
print(J1);
==> 1 1
print(J2);
==> 2 1 2
==> 1 2 1
list G = I1,I2;// ideal, which is already a Groebner basis
list I = J1,J2; // ideal, which is already a Groebner basis
ivSickleHil(G,2); // invokes the procedure without any degree bound
==> [1]:
==> 1,2,2,1
==> [2]:
==> [1]:
==> 1,2
==> [2]:
==> 2,1,2
ivSickleHil(I,2,5); // invokes the procedure with degree bound 5
==> [1]:
==> 1,2,3,3,4,4
==> [2]:
==> [1]:
==> 1,2,2,1
==> [2]:
==> 1,2,2,2,1
==> [3]:
==> 1,2,2,2,2
==> [4]:
==> 2,1
==> [5]:
==> 2,2,1
==> [6]:
==> 2,2,2,1
==> [7]:
==> 2,2,2,2,1
==> [8]:
==> 2,2,2,2,2
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