# 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.