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LineageTable -- a hash table of Gröbner basis polynomials and their lineages

Description

A lineage table is a hashtable whose values are a Gröbner basis for the ideal I or the ideal generated by L, and keys are the lineages of the corresponding elements.

A lineage of a polynomial is a natural number, or an ordered pair of lineages, tracing its history in the given Gröbner basis computation. Lineages that are natural numbers are assigned to the original input polynomials.

i1 : R = ZZ/101[x,y,z, MonomialOrder=>Lex];
 
i2 : I = ideal {2*x + 10*y^2*z, 8*x^2*y + 10*x*y*z^3};

o2 : Ideal of R
 
i3 : allowableThreads = 2;
 
i4 : H = tgb I

                                 5 2      3 4
o4 = LineageTable{(0, 1) => - 25y z  - 19y z }
                               2
                  0 => 2x + 10y z
                         2           3
                  1 => 8x y + 10x*y*z

o4 : LineageTable
 
i5 : instance(H, LineageTable)

o5 = true
 
i6 : matrix H

o6 = | 2x+10y2z 8x2y+10xyz3 -25y5z2-19y3z4 |

             1      3
o6 : Matrix R  <-- R

See also

Functions and methods returning an object of class LineageTable:

  • minimize(LineageTable) -- turn a Gröbner basis computed using threaded Gröbner bases into a minimal one
  • reduce -- produce a reduced Gröbner basis from one computed by threaded Gröbner bases
  • reduce(LineageTable) -- see reduce -- produce a reduced Gröbner basis from one computed by threaded Gröbner bases
  • tgb -- threaded Gröbner bases
  • tgb(List) -- see tgb -- threaded Gröbner bases

Methods that use an object of class LineageTable:

  • matrix(LineageTable) -- extract a matrix of polynomials from values of a LineageTable after deleting null values

For the programmer

The object LineageTable is a type, with ancestor classes HashTable < Thing.

The source of this document is in ThreadedGB.m2:489:0.