Installation

In this chapter we cover the basics of starting a SymDPoly project.

There are two options:

1. Run simple command line scripts using Ammonite (best for one-off computations)
2. Work with a full SBT project (best for multi file projects, and for use with an IDE)

Simple command line scripts (Ammonite)

First, install the Ammonite REPL.

• On Linux/Mac OS X, follow the instructions here.
• On Windows, download the latest release – the filename should look like 2.12-1.6.5, where the 1.6.5 can change depending on the Ammonite version. Rename the file to amm.bat, and place it either in your path, or in the directory where you want to use it.

You’ll also need a recent version of the Java Virtual Machine (minimum Java 1.8). To verify this, you can run java -version from the command line, and you should obtain an output similar to

openjdk version "1.8.0_191"
OpenJDK Runtime Environment (build 1.8.0_191-8u191-b12-2ubuntu0.18.04.1-b12)
OpenJDK 64-Bit Server VM (build 25.191-b12, mixed mode)

Then, download one of the example scripts, for example examples/CHSH.sc, and run it from the command line using amm CHSH.sc.

You should obtain the following output:

Compiling /home/denis/w/symdpoly/examples/CHSH.sc
Compiling /home/denis/w/symdpoly/examples/CHSH.sc #2
We maximize the CHSH expression [A(0) B(0)] + [A(0) B(1)] + [A(1) B(0)] - [A(1) B(1)]
We discovered a symmetry group of order 16 with generators Vector({A(0) -> - B(1), A(1) -> B(0), B(0) -> A(1), B(1) -> - A(0)}, {A(0) -> - A(1), A(1) -> - A(0), B(0) -> - B(0)})
Resulting relaxation: Moment relaxation with 1 monomials, a moment matrix of size 5 x 5, and 0 localizing matrix/ces
We wrote SDP data description files for SDPA (chsh.dat-s), Mosek (chsh.cbf) and SeDuMi (chsh.sedumi.mat)

NB: older versions of Ammonite (until version 1.6.4) used to send usage statistics to Google Analytics by default, with a possibility to opt-out (--no-remote-logging).

Using SymDPoly as part of a Scala project (SBT)

First, install the SBT build tool. While the download page is here, specific instructions are available:

• For Linux.

• For macOS.

• For Windows.

Creating a project

Start with an empty folder, and add the following build.sbt file in it.

resolvers += Resolver.bintrayRepo("denisrosset", "maven")

libraryDependencies += "net.alasc" %% "symdpoly-core"    % "0.7.6"

Add now a single file Test.scala to your project:

import net.alasc.symdpoly._
import net.alasc.symdpoly.defaults._

object Test extends App {
  print(examples.quantum.CHSH.relaxation.program.sdpa.data)
}

And enter sbt run in the command line. After a few lines concerning package retrieval and compilation, you should see:

[info] Running Test 
* SDPA solves a minimization dual problem, while we express a maximization problem 
* also, the original objective has constant term cte = 0.0 (constant terms are not supported by SDPA)
* the real objective is thus cte - obj_SDPA value
1
1
5
4.0
0 1 1 1 -1.0
0 1 2 2 -1.0
0 1 3 3 -1.0
0 1 4 4 -1.0
0 1 5 5 -1.0
1 1 2 4 -1.0
1 1 3 4 -1.0
1 1 2 5 -1.0
1 1 3 5 1.0

This output corresponds to the problem data in SDPA sparse format, as requested.