Add doctests, import JConvex

.github/workflows/CI.yml

@@ -68,6 +68,8 @@ jobs:
             using Pkg
             Pkg.develop(PackageSpec(path=pwd()))
             Pkg.instantiate()'
+      - name: "Add Polymake for doctests" # FIXME: this is a workaround and should be removed eventually
+        run: julia --color=yes -e 'using Pkg ; Pkg.add(["Polymake"])'
       - name: "Run doctests"
         run: |
           julia --project=docs --color=yes test/doctest.jl

docs/make.jl

@@ -2,7 +2,7 @@ push!(LOAD_PATH,"../src/")
 using Documenter, JToric, DocumenterMarkdown
 
 # ensure JToric is loaded for the doc tests
-DocMeta.setdocmeta!(JToric, :DocTestSetup, :(using JToric, Random); recursive = true)
+DocMeta.setdocmeta!(JToric, :DocTestSetup, :(using JToric, Random; using JToric.Oscar); recursive = true)
 
 makedocs(sitename="JToric -- Toric Geometry in Julia")
 

pkg/JConvex/PackageInfo.g

@@ -0,0 +1,90 @@
+#############################################################################
+##
+##  PackageInfo.g       JConvex package
+##                      Martin Bies
+##
+##  Copyright 2021      University of Pennsylvania
+##
+##  A Gap package for convex geometry via Polymake in Julia
+##
+#############################################################################
+
+SetPackageInfo( rec(
+
+PackageName := "JConvex",
+
+Subtitle := "A Gap package for convex geometry via Polymake in Julia",
+
+Version := Maximum( [
+   "2021.09.21",
+] ),
+
+Date := ~.Version{[ 1 .. 10 ]},
+Date := Concatenation( ~.Date{[ 9, 10 ]}, "/", ~.Date{[ 6, 7 ]}, "/", ~.Date{[ 1 .. 4 ]} ),
+
+License := "GPL-2.0-or-later",
+
+Persons := [
+rec(
+    LastName      := "Bies",
+    FirstNames    := "Martin",
+    IsAuthor      := true,
+    IsMaintainer  := true,
+    Email := "martin.bies@alumni.uni-heidelberg.de",
+    WWWHome := "https://martinbies.github.io/",
+    PostalAddress := Concatenation(
+                 "Department of Mathematics\n",
+                 "University of Pennsylvania\n",
+                 "David Rittenhouse Laboratory\n",
+                 "209 S 33rd St\n",
+                 "Philadelphia\n",
+                 "PA 19104\n",
+                 "United States of America" ),
+    Place         := "Pennsylvania",
+    Institution   := "University of Pennsylvania"
+  ),
+],
+
+Status := "dev",
+PackageWWWHome := "https://github.com/homalg-project/ToricVarieties_project/tree/master/JConvex/",
+ArchiveFormats := ".zip",
+ArchiveURL     := "https://github.com/homalg-project/ToricVarieties_project/releases/download/2021-09-05/JConvex",
+README_URL     := Concatenation( ~.PackageWWWHome, "README" ),
+PackageInfoURL := Concatenation( ~.PackageWWWHome, "PackageInfo.g" ),
+
+AbstractHTML := "JConvex provides functionality to perform convex geometry with Polymake in Julia.",
+
+PackageDoc := rec(
+  BookName  := "JConvex",
+  ArchiveURLSubset := ["doc"],
+  HTMLStart := "doc/chap0.html",
+  PDFFile   := "doc/manual.pdf",
+  SixFile   := "doc/manual.six",
+  LongTitle := "A Gap package for convex geometry via Polymake in Julia",
+),
+
+
+Dependencies := rec(
+  GAP := ">=4.9",
+  NeededOtherPackages := [ [ "AutoDoc", ">= 2019.05.20" ],
+                           [ "NConvex", ">= 2020.11-04" ],
+                           [ "JuliaInterface", ">= 0.5.2" ],
+                         ],
+  SuggestedOtherPackages := [ ],
+  ExternalConditions := [ ],
+),
+
+AvailabilityTest := ReturnTrue,
+
+Keywords := [ "Convex geometry", "Polymake", "Julia" ],
+
+AutoDoc := rec(
+    TitlePage := rec(
+        Copyright := """
+This package may be distributed under the terms and conditions
+of the GNU Public License Version 2 or (at your option) any later version.
+"""
+    ),
+),
+
+));

pkg/JConvex/README.md

@@ -0,0 +1,22 @@
+# JConvex
+A `Gap4` package to do convex geometry by `Polymake` in `Julia`. This package is key to make the functionality of the `ToricVarieties_project` available in `Julia`.
+
+
+## Installation this package
+
+To get the latest version of this GAP 4 package pull the corresponding branch from github. This completes the installation of this package.
+
+
+## Documentation and test
+
+You can create the documentation for this package by issuing `make doc` inside the JConvex folder. Provided a running LaTeX installation, the documentation will subsequently be available inside the /doc subfolder as manual.pdf. After this step, you can also issue a test on this software by issuing `make test`.
+
+
+## Contact
+
+E-mail me if there are any questions, remarks, suggestions. Also, I would like to hear about applications of this package: `Martin Bies, martin.bies@alumni.uni-heidelberg.de`.
+
+
+## Funding
+
+Martin Bies acknowledges support by NSF grant DMS 2001673, the Simons Foundation Collaboration grant #390287 on “Homological Mirror Symmetry" and the SimonsFoundation Collaboration grant #724069 on “Special Holonomy in Geometry, Analysisand Physics”.

pkg/JConvex/doc/Doc.autodoc

@@ -0,0 +1,5 @@
+@Chapter Introduction
+
+@Section What is the goal of the JConvex package?
+
+**JConvex** aims to perform convex geometry by Polymake (and eventually also Cdd and Normaliz) in Julia. This is key to make the functionality of the ToricVarieties_package available in Julia.

pkg/JConvex/doc/clean

@@ -0,0 +1,4 @@
+#!/bin/bash
+rm -f  *.{six,aux,lab,log,dvi,ps,pdf,bbl,ilg,ind,idx,out,html,tex,pnr,txt,blg,toc,six,brf,xml,xml.bib,css,js}
+rm -f  ../maketest.g ../VERSION ../public_html.version
+

pkg/JConvex/examples/Cones.g

@@ -0,0 +1,88 @@
+#! @Chapter Cones
+
+#! @Section Examples
+
+LoadPackage( "JConvex" );
+
+#! The following demonstrates cone operations performed with Polymake:
+
+#! @Example
+P:= Cone( [ [ 2, 7 ], [ 0, 12 ], [ -2, 5 ] ] );
+#! <A cone in |R^2>
+d:= DefiningInequalities( P );
+#! [ [ -7, 2 ], [ 5, 2 ] ]
+Q:= ConeByInequalities( d );
+#! <A cone in |R^2>
+DefiningInequalities( Q );
+#! [ [ -7, 2 ], [ 5, 2 ] ]
+RayGenerators( P );
+#! [ [ -2, 5 ], [ 2, 7 ] ]
+RayGenerators( Q );
+#! [ [ -2, 5 ], [ 2, 7 ] ]
+IsPointed( P );
+#! true
+IsPointed( Q );
+#! true
+P=Q;
+#! true
+HilbertBasis( P );
+#! [ [ -2, 5 ], [ -1, 3 ], [ 0, 1 ], [ 1, 4 ], [ 2, 7 ] ]
+HilbertBasis( Q );
+#! [ [ -2, 5 ], [ -1, 3 ], [ 0, 1 ], [ 1, 4 ], [ 2, 7 ] ]
+P_dual:= DualCone( P );
+#! <A cone in |R^2>
+RayGenerators( P_dual );
+#! [ [ -7, 2 ], [ 5, 2 ] ]
+Dimension( P );
+#! 2
+List( Facets( P ), RayGenerators );
+#! [ [ [ 2, 7 ] ], [ [ -2, 5 ] ] ]
+IsRegularCone( P );
+#! false
+IsRay( P );
+#! false
+R:= Cone( [ [ 4, 5 ], [ -2, 1 ] ] );
+#! <A cone in |R^2>
+T:= IntersectionOfCones( P, R );
+#! <A cone in |R^2>
+RayGenerators( T );
+#! [ [ -2, 5 ], [ 2, 7 ] ]
+W:= Cone( [ [-3,-4 ] ] );
+#! <A ray in |R^2>
+I:= IntersectionOfCones( P, W );
+#! <A cone in |R^2>
+RayGenerators( I );
+#! [  ]
+Contains( P, I );
+#! true
+Contains( W, I );
+#! true
+Contains( P, R );
+#! false
+Contains( R, P );
+#! true
+LinealitySpaceGenerators( P );
+#! [  ]
+P:= Cone( [ [ 1, 1, -3 ], [ -1, -1, 3 ], [ 1, 2, 1 ], [ 2, 1, 2 ] ] );
+#! < A cone in |R^3>
+IsPointed( P );
+#! false
+Dimension( P );
+#! 3
+IsRegularCone( P );
+#! false
+P;
+#! < A cone in |R^3 of dimension 3 with 4 ray generators>
+RayGenerators( P );
+#! [ [ -1, -1, 3 ], [ 1, 1, -3 ], [ 1, 2, 1 ], [ 2, 1, 2 ] ]
+d:= DefiningInequalities( P );
+#! [ [ -5, 8, 1 ], [ 7, -4, 1 ] ]
+facets:= Facets( P );
+#! [ <A cone in |R^3>, <A cone in |R^3> ]
+DualCone( P );
+#! < A cone in |R^3>
+RayGenerators( DualCone( P ) );
+#! [ [ -5, 8, 1 ], [ 7, -4, 1 ] ]
+LinealitySpaceGenerators( DualCone( P ) );
+#! [ ]
+#! @EndExample

pkg/JConvex/examples/Polytopes.g

@@ -0,0 +1,120 @@
+#! @Chapter Polytopes
+
+#! @Section Examples
+
+LoadPackage( "JConvex" );
+
+#! The following demonstrates polytope operations performed with Polymake:
+
+#! @Example
+P := Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 2 ] ] );
+#! <A polytope in |R^3>
+ine := FacetInequalities( P );
+#! [ [ 0, 0, 0, 1 ], [ 0, 0, 2, -1 ], [ 0, 2, 0, -1 ], [ 2, -2, -2, 1 ] ]
+P2 :=  PolytopeByInequalities( ine );
+#! <A polytope in |R^3>
+Vertices( P2 );
+#! [ [ 0, 0, 0 ], [ 0, 1, 0 ], [ 1, 0, 0 ], [ 1, 1, 2 ] ]
+IsNormalPolytope( P );
+#! false
+IsVeryAmple( P );
+#! false
+Q := Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 1 ] ] );
+#! <A polytope in |R^3>
+IsNormalPolytope( Q );
+#! true
+IsVeryAmple( Q );
+#! true
+Q;
+#! <A normal very ample polytope in |R^3 with 4 vertices>
+T := Polytope( [ [ 0, 0, 0 ], [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 4 ] ] ); 
+#! <A polytope in |R^3>
+I := Polytope( [ [ 0, 0, 0 ], [ 0, 0, 1 ] ] );
+#! <A polytope in |R^3>
+J := T + I;
+#! <A polytope in |R^3>
+Vertices( J );
+#! [ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ], [ 1, 0, 1 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 1, 1, 4 ], [ 1, 1, 5 ] ]
+FacetInequalities( J );
+#! [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 1, -1, 0, 0 ], [ 1, 0, -1, 0 ], [ 1, 0, 4, -1 ], [ 1, 4, 0, -1 ], [ 4, -4, -4, 1 ] ]
+IsVeryAmple( J );
+#! true
+IsNormalPolytope( J );
+#! false
+J;
+#! <A very ample polytope in |R^3 with 8 vertices>
+#! @EndExample
+
+#! We now compute example 2.2.20 in the book Toric Varieties by Cox, Little, Schenk:
+
+#! @Example
+A:= [ [1,1,1,0,0,0], [1,1,0,1,0,0], [1,0,1,0,1,0], [ 1,0,0,1,0,1], 
+[ 1,0,0,0,1,1], [ 0,1,1,0,0,1], [0,1,0,1,1,0], [0,1,0,0,1,1], 
+[0,0,1,1,1,0], [0,0,1,1,0,1] ];
+#! [ [ 1, 1, 1, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 0 ], [ 1, 0, 1, 0, 1, 0 ],
+#! [ 1, 0, 0, 1, 0, 1 ], [ 1, 0, 0, 0, 1, 1 ], [ 0, 1, 1, 0, 0, 1 ], 
+#!  [ 0, 1, 0, 1, 1, 0 ], [ 0, 1, 0, 0, 1, 1 ], [ 0, 0, 1, 1, 1, 0 ], 
+#! [ 0, 0, 1, 1, 0, 1 ] ]
+H:= Polytope( A );
+#! <A polytope in |R^6>
+IsVeryAmple( H );
+#! true <- we receive false!
+IsNormalPolytope( H );
+#! false
+H;
+#! <A very ample polytope in |R^6 with 10 vertices>
+#! @EndExample
+
+#! More applications include:
+
+#! @Example
+l:= [ [ 0, 0, 1 ], [ 0, 0, 0 ], [ 1, 0, 0 ], [ 1, 0, 1 ], [ 0, 1, 0 ], 
+[ 0, 1, 1 ], [ 1, 1, 4 ], [ 1, 1, 5 ] ];;
+P:= Polytope( l );
+#! <A polytope in |R^3>
+IsNormalPolytope( P );
+#! false
+lattic_points:= LatticePoints( P );
+#! [ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 1, 0, 0 ], [ 1, 0, 1 ], 
+#! [ 1, 1, 4 ], [ 1, 1, 5 ] ]
+u:= Cartesian( lattic_points, lattic_points );;
+k:= Set( List( u, u-> u[1]+u[2] ) );
+#! [ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 0, 1, 2 ],
+#! [ 0, 2, 0 ], [ 0, 2, 1 ], [ 0, 2, 2 ], [ 1, 0, 0 ], [ 1, 0, 1 ], [ 1, 0, 2 ], 
+#! [ 1, 1, 0 ], [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 4 ], [ 1, 1, 5 ], [ 1, 1, 6 ], 
+#! [ 1, 2, 4 ], [ 1, 2, 5 ], [ 1, 2, 6 ], [ 2, 0, 0 ], [ 2, 0, 1 ], [ 2, 0, 2 ], 
+#! [ 2, 1, 4 ], [ 2, 1, 5 ], [ 2, 1, 6 ], [ 2, 2, 8 ], [ 2, 2, 9 ], [ 2, 2, 10 ] ]
+Q:= 2*P;
+#! <A polytope in |R^3 with 8 vertices>
+LatticePoints( Q );
+#! [ [ 0, 0, 0 ], [ 0, 0, 1 ], [ 0, 0, 2 ], [ 0, 1, 0 ], [ 0, 1, 1 ], [ 0, 1, 2 ],
+#! [ 0, 2, 0 ], [ 0, 2, 1 ], [ 0, 2, 2 ], [ 1, 0, 0 ], 
+#!   [ 1, 0, 1 ], [ 1, 0, 2 ], [ 1, 1, 0 ], [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 3 ], 
+#! [ 1, 1, 4 ], [ 1, 1, 5 ], [ 1, 1, 6 ], [ 1, 2, 4 ], [ 1, 2, 5 ], [ 1, 2, 6 ], 
+#! [ 2, 0, 0 ], [ 2, 0, 1 ], [ 2, 0, 2 ], [ 2, 1, 4 ], 
+#!   [ 2, 1, 5 ], [ 2, 1, 6 ], [ 2, 2, 8 ], [ 2, 2, 9 ], [ 2, 2, 10 ] ]
+P:= Polytope( [ [ 1, 1 ], [ 1, -1 ], [ -1, 1 ], [ -1, -1 ] ] );
+#! <A polytope in |R^2>
+Q:= PolarPolytope( P );
+#! <A polytope in |R^2>
+Vertices( Q );
+#! [ [ -1, 0 ], [ 0, -1 ], [ 0, 1 ], [ 1, 0 ] ]
+T := PolarPolytope( Q );
+#! <A polytope in |R^2>
+Vertices( T );
+#! [ [ -1, -1 ], [ -1, 1 ], [ 1, -1 ], [ 1, 1 ] ]
+P:= Polytope( [ [ 0, 0 ], [ 1, -1], [ -1, 1 ], [ -1, -1 ] ] );
+#! <A polytope in |R^2>
+#! @EndExample
+
+#! @BeginLatexOnly
+#! Let us now find out if the vertices of the polytope defined by the following inequalities:
+#! $$x_2\geq 0,1-x_1-x_2\geq 0,1+x_1-x_2\geq 0.$$
+#! @EndLatexOnly
+
+#! @Example
+P := PolytopeByInequalities( [ [ 0, 0, 1 ], [ 1, -1, -1 ], [ 1, 1, -1 ] ] );
+#! <A polytope in |R^2>
+Vertices( P );
+#! [ [ -1, 0 ], [ 0, 1 ], [ 1, 0 ] ]
+#! @EndExample

pkg/JConvex/gap/Cone.gd

@@ -0,0 +1,24 @@
+#############################################################################
+##
+##  Cone.gd             JConvex package
+##                      Martin Bies
+##
+##  Copyright 2021      University of Pennsylvania
+##
+##  A Gap package to do convex geometry by Polymake
+##
+#! @Chapter Cones
+##
+#############################################################################
+
+###############################
+##
+#! @Section Attributes of Cones
+##
+###############################
+
+#! @Arguments C
+#! @Returns a polymake cone
+#! @Description
+#! Converts the cone to a Polymake cone.
+DeclareAttribute( "ExternalPolymakeCone",  IsCone  );