# printHilbertSequence -- prints the Hilbert sequence as a table

## Synopsis

• Usage:
printHilbertSequence H
• Inputs:
• H, , the Hilbert sequence of a module
• Outputs:
• a net, a table representing H

## Description

This function gives a convenient expression of the Hilbert sequence, particularly in terms of the multiplicity sequence. For instance, if I is an ideal, then the multiplicity sequence of I appears as the top row of the table for the Hilbert sequence of gr_mGr_I.

 i1 : R = QQ[x_1..x_9] o1 = R o1 : PolynomialRing i2 : I = minors(2, genericMatrix(R, 3, 3)) o2 = ideal (- x x + x x , - x x + x x , - x x + x x , - x x + x x , - 2 4 1 5 3 4 1 6 3 5 2 6 2 7 1 8 ------------------------------------------------------------------------ x x + x x , - x x + x x , - x x + x x , - x x + x x , - x x + x x ) 3 7 1 9 3 8 2 9 5 7 4 8 6 7 4 9 6 8 5 9 o2 : Ideal of R i3 : multiplicitySequence I o3 = HashTable{4 => 6 } 5 => 12 6 => 12 7 => 6 8 => 3 9 => 2 o3 : HashTable i4 : printHilbertSequence hilbertSequence grGr I o4 = 0 1 2 3 4 5 6 7 8 9 +----------------------------- 9 | . . . . 6 12 12 6 3 2 8 | . . . . -18 -30 -21 -9 -4 . 7 | . . . . 19 23 10 3 . . 6 | . . . . -8 -5 -1 . . . 5 | . . . . 1 . . . . . 4 | . . . . . . . . . . 3 | . . . . . . . . . . 2 | . . . . . . . . . . 1 | . . . . . . . . . . 0 | . . . . . . . . . .