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PhylogeneticTrees :: toricJoinDim

toricJoinDim -- Dimension of a join of toric varieties

Synopsis

Description

A randomized algorithm for computing the affine dimension of a join of toric varieties, using Terracini’s Lemma.

Each input matrix defines a parameterization of the variety. For each, a vector of parameter values is chosen at random from a large finite field. The dimension of the sum of the tangent spaces at those points is computed.

This algorithm is much much faster than computing the join variety.

i1 : A = matrix{{4,3,2,1,0},{0,1,2,3,4}}

o1 = | 4 3 2 1 0 |
     | 0 1 2 3 4 |

              2        5
o1 : Matrix ZZ  <--- ZZ
i2 : B = matrix{{1,1,1,1,1}}

o2 = | 1 1 1 1 1 |

              1        5
o2 : Matrix ZZ  <--- ZZ
i3 : toricJoinDim(A,B)

o3 = 3
i4 : toricJoinDim(B,B)

o4 = 1

Caveat

All input matrices must have the same number of columns.

See also

Ways to use toricJoinDim :