Singular

7.7.7.0. ivDHilbertSickle

Usage:
ivDHilbertSickle(L,n[,degbound]); L a list of intmats, n an integer,
degbound an optional integer

Return:
list

Purpose:
Computing K-dimension, Hilbert series and mistletoes

Assume:
- basering is a Letterplace ring.
- All rows of each intmat correspond to a Letterplace monomial.
- If you specify a different degree bound degbound,
degbound <= attrib(basering,uptodeg) holds.

Note:
- If L is the list returned, then L[1] is an integer, L[2] is an intvec
which contains the coefficients of the Hilbert series and L[3]
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[2] 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 R; ==> // coefficients: QQ ==> // number of vars : 10 ==> // block 1 : ordering a ==> // : names x(1) y(1) x(2) y(2) x(3) y(3) x(4) y(4) x(\ 5) y(5) ==> // : weights 1 1 1 1 1 1 1 1 \ 1 1 ==> // block 2 : ordering dp ==> // : names x(1) y(1) ==> // block 3 : ordering dp ==> // : names x(2) y(2) ==> // block 4 : ordering dp ==> // : names x(3) y(3) ==> // block 5 : ordering dp ==> // : names x(4) y(4) ==> // block 6 : ordering dp ==> // : names x(5) y(5) ==> // block 7 : ordering C 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 ivDHilbertSickle(G,2); // invokes the procedure without a degree bound ==> [1]: ==> 6 ==> [2]: ==> 1,2,2,1 ==> [3]: ==> [1]: ==> 1,2 ==> [2]: ==> 2,1,2 ivDHilbertSickle(I,2,3); // invokes the procedure with degree bound 3 ==> [1]: ==> 9 ==> [2]: ==> 1,2,3,3 ==> [3]: ==> [1]: ==> 1,2,2 ==> [2]: ==> 2,1 ==> [3]: ==> 2,2,1 ==> [4]: ==> 2,2,2