# Singular

##### 7.7.7.0. ivDHilbert
Procedure from library `fpadim.lib` (see fpadim_lib).

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

Return:
list

Purpose:
Computing the K-dimension and the Hilbert series

Assume:
- basering is a Letterplace ring
- all rows of each intmat correspond to a Letterplace monomial
for the encoding of the variables see 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 integer corresponding to the
dimension, L[2] is an intvec which contains the coefficients of the
Hilbert series
- If degbound is set, there will be a degree bound 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; ==> // characteristic : 0 ==> // 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 //the procedure without a degree bound ivDHilbert(G,2); ==> [1]: ==> 6 ==> [2]: ==> 1,2,2,1 // the procedure with degree bound 5 ivDHilbert(I,2,5); ==> [1]: ==> 17 ==> [2]: ==> 1,2,3,3,4,4 ```