# zts man page

zts — tensor spin of modules

## Synopsis

`zts [Options] <M> <N> <Seed> [<Sub>]`

## Description

This program is similar to zsp, but it works on the tensor product of two modules, M⊗N.  Zts spins up one or more vectors, and optionally calculates a matrix representation corresponding to the invariant subspace.  The program does not use the matrix representation of the generators on M⊗N, which would be too large in many cases.  This program is used, for example, to spin up vectors that have been uncondensed with tuc.

The action of the generators on both M and N must be given as square matrices, see "Input Files" below.  You can use the -g option to specify the number of generators.  The default is two generators.

Seed vectors are read from Seed.  They must be given with respect to the lexicographically ordered basis explained below.

If the Sub argument is given, zts writes a basis of the invariant subspace to Sub, calculates the action of the generators on the invariant subspace, and writes it to Sub.1, Sub.2, ....

## Options

-Q

Quiet, no messages.

-V

Verbose, more messages.

-T <MaxTime>

Set CPU time limit

-g <#Gens>

Set number of generators.  Default: 2.

-n, --no-action

Output only Sub, do not calculate Sub.1, ....

## Implementation Details

Let B=(b_1,...,b_m) be a basis of M, C=(c_1,...,c_n) a basis of N, and denote by B⊗C the lexicographically ordered basis (b_1⊗c_1, b_1⊗c_2, ..., b_m⊗c_n).  For vϵM⊗N, the coordinate row m(v,B⊗C) has mn entries which can be arranged as a m×n matrix (top to bottom, left to right).  Let M(B,v,C) denote this matrix.  Then

M(B,va,C) = m(B,a|_M,B)^trM(B,v,C)m(C,a|_N,C) for all aϵA,vϵM⊗N

Using this relation, we can calculate the image of any vector vϵM⊗N under an algebra element a, and thus spin up a vector without using the matrix representation of a on vϵM⊗N.

## Input Files

M.{1,2,...}

Generators on the left representation.

N.{1,2,...}

Generators on the right representation.

Seed

Seed vectors.

## Output Files

Sub

Invariant subspace.

Sub.{1,2,...}

Action on the invariant subspace.