GAP (Convex) - Chapter 4: Fan

Goto Chapter: Top 1 2 3 4 5 6 Ind
[Top of Book] [Contents] [Previous Chapter] [Next Chapter]

[MathJax on]

4 Fan
4.1 Fan: Category and Representations
4.1-1 IsFan
4.2 Fan: Properties
4.2-1 IsComplete
4.2-2 IsPointed
4.2-3 IsSmooth
4.2-4 IsRegularFan
4.2-5 IsSimplicial
4.2-6 HasConvexSupport
4.3 Fan: Attributes
4.3-1 Rays
4.3-2 RayGenerators
4.3-3 RaysInMaximalCones
4.3-4 MaximalCones
4.4 Fan: Methods
4.4-1 *
4.5 Fan: Constructors
4.5-1 Fan
4.5-2 Fan
4.6 Fan: Examples
4.6-1 Fan example

### 4 Fan

#### 4.1 Fan: Category and Representations

##### 4.1-1 IsFan

`‣ IsFan`( M ) | ( category )

Returns: `true` or `false`

The GAP category of a fan. Every fan is a convex object.

Remember: Every fan is a convex object.

#### 4.2 Fan: Properties

##### 4.2-1 IsComplete

`‣ IsComplete`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is complete, i. e. if it's support is the whole space.

##### 4.2-2 IsPointed

`‣ IsPointed`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is pointed, which means that every cone it contains is strictly convex.

##### 4.2-3 IsSmooth

`‣ IsSmooth`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is smooth, i. e. if every cone in the fan is smooth.

##### 4.2-4 IsRegularFan

`‣ IsRegularFan`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is regular, i. e. if it is the normal fan of a polytope.

##### 4.2-5 IsSimplicial

`‣ IsSimplicial`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is simplicial, i. e. if every cone in the fan is simplicial.

##### 4.2-6 HasConvexSupport

`‣ HasConvexSupport`( fan ) | ( property )

Returns: `true` or `false`

Checks if the fan fan is simplicial, i. e. if every cone in the fan is simplicial.

#### 4.3 Fan: Attributes

##### 4.3-1 Rays

`‣ Rays`( fan ) | ( attribute )

Returns: a list

Returns the rays of the fan fan as a list of cones.

##### 4.3-2 RayGenerators

`‣ RayGenerators`( fan ) | ( attribute )

Returns: a list

Returns the generators rays of the fan fan as a list of of list of integers.

##### 4.3-3 RaysInMaximalCones

`‣ RaysInMaximalCones`( fan ) | ( attribute )

Returns: a list

Returns a list of lists, which represent an incidence matrix for the correspondence of the rays and the maximal cones of the fan fan. The ith list in the result represents the ith maximal cone of fan. In such a list, the jth entry is 1 if the jth ray is in the cone, 0 otherwise.

##### 4.3-4 MaximalCones

`‣ MaximalCones`( fan ) | ( attribute )

Returns: a list

Returns the maximal cones of the fan fan as a list of cones.

#### 4.4 Fan: Methods

##### 4.4-1 *

`‣ *`( fan1, fan2 ) | ( operation )

Returns: a fan

Returns the product of the fans fan1 and fan2.

#### 4.5 Fan: Constructors

##### 4.5-1 Fan

`‣ Fan`( fan ) | ( operation )

Returns: a fan

Copy constructor for fans. For completeness reasons.

##### 4.5-2 Fan

`‣ Fan`( rays, cones ) | ( operation )

Returns: a fan

Constructs the fan out of the given rays and a list of cones given by a lists of numbers of rays.

#### 4.6 Fan: Examples

##### 4.6-1 Fan example

    gap> F := Fan( [[-1,5],[0,1],[1,0],[0,-1]],[[1,2],[2,3],[3,4],[4,1]] );
    <A fan in |R^2>
    gap> RayGenerators( F );
    [ [ -1, 5 ], [ 0, 1 ], [ 1, 0 ], [ 0, -1 ] ]
    gap> RaysInMaximalCones( F );
    [ [ 1, 1, 0, 0 ], [ 0, 1, 1, 0 ], [ 0, 0, 1, 1 ], [ 1, 0, 0, 1 ] ]
    gap> IsRegularFan( F );
    true
    gap> IsComplete( F );
    true
    gap> IsSmooth( F );
    true
    gap> F1 := MaximalCones( F )[ 1 ];
    <A cone in |R^2>
    gap> DualCone( F1 );
    <A cone in |R^2>
    gap> RayGenerators( F1 );
    [ [ -1, 5 ], [ 0, 1 ] ]
    gap> F2 := StarSubdivisionOfIthMaximalCone( F, 1 );
    <A fan in |R^2>
    gap> IsSmooth( F2 );
    true
    gap> RayGenerators( F2 );
    [ [ -1, 5 ], [ -1, 6 ], [ 0, -1 ], [ 0, 1 ], [ 1, 0 ] ]

[Top of Book] [Contents] [Previous Chapter] [Next Chapter]
Goto Chapter: Top 1 2 3 4 5 6 Ind

generated by GAPDoc2HTML