Macaulay2 » Documentation
Packages » MultiplicitySequence :: printHilbertSequence
next | previous | forward | backward | up | index | toc

printHilbertSequence -- prints the Hilbert sequence as a table

Synopsis

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 | . . . . .   .   .   .  .  .

See also

Ways to use printHilbertSequence :

For the programmer

The object printHilbertSequence is a method function.