GAP (polymaking) - Chapter 2: Polymake interaction

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2 Polymake interaction
2.1 Creating Polymake Objects
2.1-1 CreateEmptyFile
2.1-2 CreatePolymakeObject
2.1-3 CheckAppVerTypList
2.1-4 CreatePolymakeObjectFromFile
2.2 Accessing Properties of Polymake Objects
2.2-1 DirectoryOfPolymakeObject
2.2-2 FilenameOfPolymakeObject
2.2-3 FullFilenameOfPolymakeObject
2.2-4 NamesKnownPropertiesOfPolymakeObject
2.2-5 KnownPropertiesOfPolymakeObject
2.2-6 PropertyOfPolymakeObject
2.3 Example: Creating and Accessing Polymake Objects
2.4 Writing to Polymake Objects
2.4-1 AppendToPolymakeObject
2.4-2 AppendPointlistToPolymakeObject
2.4-3 AppendVertexlistToPolymakeObject
2.4-4 AppendInequalitiesToPolymakeObject
2.4-5 ConvertMatrixToPolymakeString
2.4-6 ClearPolymakeObject
2.4-7 WriteKnownPropertyToPolymakeObject
2.4-8 UnbindKnownPropertyOfPolymakeObject
2.5 Calling Polymake and converting its output
2.5-1 Polymake
2.6 An Example

### 2 Polymake interaction

#### 2.1 Creating Polymake Objects

The interaction with the polymake program is done via files. A `PolymakeObject` is mainly a pointer to a file and a list of known properties of the object. These properties need not be stored in the file. Whenever polymake is called, the returned value is read from standard output and stored in the `PolymakeObject` corresponding to the file for which polymake is called. The files for polymake are written in the old (non-xml) format. The first run of polymake converts them into the new (xml) format. This means that changes to the file by means of the methods outlined below after the first run of polymake will probably lead to corrupted files.

##### 2.1-1 CreateEmptyFile

`‣ CreateEmptyFile`( filename ) | ( method )

Returns: nothing

Creates an empty file with name filename. Note that filename has to include the full path and the directory for the file must exist.

##### 2.1-2 CreatePolymakeObject

`‣ CreatePolymakeObject`( ) | ( method )

`‣ CreatePolymakeObject`( appvertyp ) | ( method )

`‣ CreatePolymakeObject`( dir ) | ( method )

`‣ CreatePolymakeObject`( dir, appvertyp ) | ( method )

`‣ CreatePolymakeObject`( prefix, dir ) | ( method )

`‣ CreatePolymakeObject`( prefix, dir, appvertyp ) | ( method )

Returns: `PolymakeObject`

If called without arguments, this method generates an empty file in the directory defined by `POLYMAKE_DATA_DIR` (3.2-2). If a directory dir is given (this directory must exist), an empty file is generated in this directory. If prefix is not given, the file is called `polyN` where `N` is the current runtime. If a file of this name already exists, a number is appended separated by a dot (example: "poly1340" and "poly1340.1"). If prefix is given, the filename starts with this prefix. Optionally, the file can be generated with a header specifying application, version and type of the object. This is done by passing the triple of strings appvertyp to `CreatePolymakeObject`. A valid triple is `["polytope","2.3","RationalPolytope"]`. Validity is checked by `CheckAppVerTypList` (2.1-3).

##### 2.1-3 CheckAppVerTypList

`‣ CheckAppVerTypList`( appvertyp ) | ( method )

Returns: `bool`

Checks if the triple arppvertyp of strings specifies an application and type of polymake version 2.3. More specifically, the first entry has to be an application from `["polytope","surface","topaz"]` and the third entry has to be a type corresponding to the application given in the first entry. The second entry is not checked.

##### 2.1-4 CreatePolymakeObjectFromFile

`‣ CreatePolymakeObjectFromFile`( filename ) | ( method )

`‣ CreatePolymakeObjectFromFile`( dir, filename ) | ( method )

Returns: `PolymakeObject`

This method generates a `PolymakeObject` corresponding to the file filename in the directory dir. If dir is not given, the `POLYMAKE_DATA_DIR` is used.If no file with name filename exists in dir (or `POLYMAKE_DATA_DIR`, respectively), an empty file is created. Note that the contents of the file do not matter for the generation of the object. In particular, the object does not know any of the properties that might be encoded in the file. The only way to transfer information from files to `PolymakeObject`s is via `Polymake` (2.5-1).

#### 2.2 Accessing Properties of Polymake Objects

A `PolymakeObject` contains information about the directory of its file, the name of its file and about properties calculated by calling `Polymake` (2.5-1). The properties returned by the `polymake` program are stored under the name `polymake` assigns to them (that is, the name of the data block in the corresponding file). The following methods can be used to access the information stored in a `PolymakeObject`. But be careful! All functions return the actual object. No copies are made. So if you change one of the returned objects, you change the `PolymakeObject` itself.

##### 2.2-1 DirectoryOfPolymakeObject

`‣ DirectoryOfPolymakeObject`( poly ) | ( method )

Returns: Directory

Returns the directory of the file associated with poly.

##### 2.2-2 FilenameOfPolymakeObject

`‣ FilenameOfPolymakeObject`( poly ) | ( method )

Returns: String

Returns the name of the file associated with poly. This does only mean the name of the file, not the full path. For the full path and file name see `FullFilenameOfPolymakeObject` (2.2-3)

##### 2.2-3 FullFilenameOfPolymakeObject

`‣ FullFilenameOfPolymakeObject`( poly ) | ( method )

Returns: String

Returns the file associated with the `PolymakeObject` poly with its complete path.

##### 2.2-4 NamesKnownPropertiesOfPolymakeObject

`‣ NamesKnownPropertiesOfPolymakeObject`( poly ) | ( method )

Returns: List of Strings

Returns a list of the names of all known properties. This does only include the properties returned by `Polymake` (2.5-1), `"dir"` and `"filename"` are not included. If no properties are known, `fail` is returned.

##### 2.2-5 KnownPropertiesOfPolymakeObject

`‣ KnownPropertiesOfPolymakeObject`( poly ) | ( method )

Returns: Record

Returns the record of all known properties. If no properties are known, `fail` is returned.

##### 2.2-6 PropertyOfPolymakeObject

`‣ PropertyOfPolymakeObject`( poly, name ) | ( method )

Returns the value of the property name if it is known. If the value is not known, `fail` is returned. name must be a `String`.

#### 2.3 Example: Creating and Accessing Polymake Objects

Suppose the file `/tmp/threecube.poly` contains the three dimensional cube in polymake form. Now generate a `PolymakeObject` from this file and call `Polymake` (2.5-1) to make the vertices of the cube known to the object.

    ### suppose we have a polymake file /tmp/threecube.poly
    ### containing a cube in three dimensions
    gap> cube:=CreatePolymakeObjectFromFile(Directory("/tmp"),"threecube.poly");
    <polymake object. No properties known>
    gap> FilenameOfPolymakeObject(cube);
    "threecube.poly"
    gap> FullFilenameOfPolymakeObject(cube);
    "/tmp/threecube.poly"
       #nothing is known about the cube:
    gap> NamesKnownPropertiesOfPolymakeObject(cube);
    fail
    gap> Polymake(cube,"VERTICES");
    [ [ -1, -1, -1 ], [ 1, -1, -1 ], [ -1, 1, -1 ], [ 1, 1, -1 ], [ -1, -1, 1 ],
      [ 1, -1, 1 ], [ -1, 1, 1 ], [ 1, 1, 1 ] ]
       # Now <cube> knows its vertices:
    gap> Print(cube);
    <polymake object threecube.poly. Properties known: [ "VERTICES" ]>
    gap> PropertyOfPolymakeObject(cube,"VERTICES");
    [ [ -1, -1, -1 ], [ 1, -1, -1 ], [ -1, 1, -1 ], [ 1, 1, -1 ], [ -1, -1, 1 ],
      [ 1, -1, 1 ], [ -1, 1, 1 ], [ 1, 1, 1 ] ]
    gap> KnownPropertiesOfPolymakeObject(cube);
    rec(
      VERTICES := [ [ -1, -1, -1 ], [ 1, -1, -1 ], [ -1, 1, -1 ], [ 1, 1, -1 ],
          [ -1, -1, 1 ], [ 1, -1, 1 ], [ -1, 1, 1 ], [ 1, 1, 1 ] ] )

#### 2.4 Writing to Polymake Objects

To transfer data from GAP to polymake, the following methods can be used. But bear in mind that none of these functions test if the resulting polymake file is still consistent.

##### 2.4-1 AppendToPolymakeObject

`‣ AppendToPolymakeObject`( poly, string ) | ( method )

Returns: nothing

This appends the string string to the file associated to the `PolymakeObject` poly. It is not tested if the string is syntactically correct as a part of a polymake file. It is also not tested if the string is compatible with the data already contained in the file.

INEQUALITIES, POINTS and VERTICES can be appended to a polymake object using the following functions:

##### 2.4-2 AppendPointlistToPolymakeObject

`‣ AppendPointlistToPolymakeObject`( poly, pointlist ) | ( method )

Returns: nothing

Takes a list pointlist of vectors and converts it into a string which represents a polymake block labeled "POINTS". This string is then added to the file associated with poly. The "POINTS" block of the file associated with poly then contains points with leading ones, as polymake uses affine notation.

##### 2.4-3 AppendVertexlistToPolymakeObject

`‣ AppendVertexlistToPolymakeObject`( poly, pointlist ) | ( method )

Returns: nothing

Does the same as `AppendPointlistToPolymakeObject`, but with "VERTICES" instead of "POINTS".

##### 2.4-4 AppendInequalitiesToPolymakeObject

`‣ AppendInequalitiesToPolymakeObject`( poly, ineqlist ) | ( method )

Returns: nothing

Just appends the inequalities given in ineqlist to the polymake object poly (with caption "INEQUALITIES"). Note that this does not check if an "INEQUALITIES" section does already exist in the file associated with poly.

##### 2.4-5 ConvertMatrixToPolymakeString

`‣ ConvertMatrixToPolymakeString`( name, matrix ) | ( method )

Returns: String

This function takes a matrix matrix and converts it to a string. This string can then be appended to a polymake file via `AppendToPolymakeObject` (2.4-1) to form a block of data labeled name. This may be used to write blocks like INEQUALITIES or FACETS.

##### 2.4-6 ClearPolymakeObject

`‣ ClearPolymakeObject`( poly ) | ( method )

`‣ ClearPolymakeObject`( poly, appvertyp ) | ( method )

Returns: nothing

Deletes all known properties of the `PolymakeObject` poly and replaces its file with an empty one.
If the triple of strings appvertyp specifying application, version and type (see `CheckAppVerTypList` (2.1-3)) is given, the file is replaced with a file that contains only a header specifying application, version and type of the polymake object.

There are also methods to manipulate the known values without touching the file of the `PolymakeObject`:

##### 2.4-7 WriteKnownPropertyToPolymakeObject

`‣ WriteKnownPropertyToPolymakeObject`( poly, name, data ) | ( method )

Takes the object data and writes it to the known properties section of the `PolymakeObject` poly. The string name is used as the name of the property. If a property with that name already exists, it is overwritten. Again, there is no check if data is consistent, correct or meaningful.

##### 2.4-8 UnbindKnownPropertyOfPolymakeObject

`‣ UnbindKnownPropertyOfPolymakeObject`( poly, name ) | ( method )

If the `PolymakeObject` poly has a property with name name, that property is unbound. If there is no such property, `fail` is returned.

#### 2.5 Calling Polymake and converting its output

##### 2.5-1 Polymake

`‣ Polymake`( poly, option: PolymakeNolookup ) | ( method )

This method calls the polymake program (see `POLYMAKE_COMMAND` (3.2-1)) with the option option. You may use several keywords such as `"FACETS VERTICES"` as an option. The returned value is cut into blocks starting with keywords (which are taken from output and not looked up in option). Each block is then interpreted and translated into GAP readable form. This translation is done using the functions given in `ObjectConverters` (4.1-4). The first line of each block of polymake output is taken as a keyword and the according entry in `ObjectConverters` (4.1-4) is called to convert the block into GAP readable form. If no conversion function is known, an info string is printed and `fail` is returned. If only one keyword has been given as option, `Polymake` returns the result of the conversion operation. If more than one keyword has been given or the output consists of more than one block, `Polymake` returns `fail`. In any case, the calculated values for each block are stored as known properties of the `PolymakeObject` poly as long as they are not `fail`. If `Polymake` is called with an option that corresponds to a name of a known property of poly, the known property is returned. In this case, there is no call of the external program. (see below for suppression of this feature).

Note that the command `Polymake` returns `fail` if nothing is returned by the program polymake or more than one block of data is returned. For example, the returned value of `Polymake(poly,"VISUAL")` is always `fail`. Likewise, `Polymake(poly,"POINTS VERTICES")` will return `fail` (but may add new known properties to poly). For a description of the conversion functions, see chapter 4.

If the option PolymakeNolookup is set to anything else than false, the polymake program is called even if poly already has a known property with name option.

Note that whenever `Polymake` returns `fail`, a description of the problem is stored in `POLYMAKE_LAST_FAIL_REASON` (3.1-2). If you call `Polymake` with more than one keyword, `POLYMAKE_LAST_FAIL_REASON` (3.1-2) is changed before polymake is called. So any further reason to return `fail` will overwrite it.

#### 2.6 An Example

Let's generate a three dimensional permutahedron.

        gap> S:=SymmetricGroup(3);
        Sym( [ 1 .. 3 ] )
        gap> v:=[1,2,3];
        [ 1, 2, 3 ]
        gap> points3:=Orbit(S,v,Permuted);;
             # project to reduce ambient dimension
        gap> points:=points3{[1..6]}{[1,2]};;
        gap> permutahedron:=CreatePolymakeObject();
        <polymake object. No properties known>
        gap> AppendPointlistToPolymakeObject(permutahedron,points);
        gap> Polymake(permutahedron,"VOLUME");
        3
        gap> Polymake(permutahedron,"N_VERTICES");
        6
              #Now <permutahedron> knows its number of vertices, but not the vertices:
        gap> PropertyOfPolymakeObject(permutahedron,"VERTICES");
        fail
        gap> NamesKnownPropertiesOfPolymakeObject(permutahedron);
        [ "VOLUME", "N_VERTICES" ]
            #Let's look at the object!
        gap> Polymake(permutahedron,"VISUAL");
        #I  There was no or wrong polymake output
        fail
        gap> Polymake(permutahedron,"DIM");
        2

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