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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


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