extension:

application: common

Property Types

application: group

Objects

User Functions

  •  
    group_from_cyclic_notation0 (group) → Group

    Constructs a group from a string with generators in cyclic notation. All numbers in the string are 0-based. Example: "(0,2)(1,3)"

    Parameters
    Stringgroup
    generators in cyclic notation
    Returns
    Group
    \@see group_from_cyclic_notation1
  •  
    group_from_cyclic_notation1 (group) → Group

    Constructs a group from a string with generators in cyclic notation. All numbers in the string are 1-based. Example: "(1,3)(2,4)"

    Parameters
    Stringgroup
    generators in cyclic notation
    Returns
    Group
    \@see group_from_cyclic_notation0

application: polytope

Objects

User Functions

  •  
    alternating_group (degree, domain) → GroupOfPolytope

    Constructs an alternating group of given degree.

    Parameters
    intdegree
    of the alternating group"
    intdomain
    of the polytope's symmetry group
    Returns
    GroupOfPolytope
    \@see group::alternating_group
  •  
    cocircuit_equations (P) → ListMatrix

    Find the cocircuit equations of a polytope P. There is one of these for each interior cocircuit of P, and they come as the rows of a matrix whose columns correspond to the maximal-dimensional simplices of P.

    Parameters
    PolytopeP
    the input polytope
    Options
    filenamethe
    name of a file to store the equations
    Returns
    ListMatrix
  •  
    cyclic_group (degree, domain) → GroupOfPolytope

    Constructs a cyclic group of given degree.

    Parameters
    intdegree
    of the cyclic group"
    intdomain
    of the polytope's symmetry group
    Returns
    GroupOfPolytope
    \@see group::cyclic_group
  •  
    group_from_cyclic_notation0 (group, domain) → GroupOfPolytope

    Constructs a group from a string with generators in cyclic notation. All numbers in the string are 0-based. Example: "(0,2)(1,3)"

    Parameters
    Stringgroup
    generators in cyclic notation
    intdomain
    of the polytope symmetry group
    Returns
    GroupOfPolytope
    \@see group_from_cyclic_notation1
  •  
    group_from_cyclic_notation1 (group, domain) → GroupOfPolytope

    Constructs a group from a string with generators in cyclic notation. All numbers in the string are 1-based. Example: "(1,3)(2,4)"

    Parameters
    Stringgroup
    generators in cyclic notation
    intdomain
    of the polytope symmetry group
    Returns
    GroupOfPolytope
    \@see group_from_cyclic_notation0
  •  
    max_interior_simplices (P) → Array<Set>

    Find the maximal interior simplices of a polytope P. Symmetries of P are NOT taken into account.

    Parameters
    PolytopeP
    the input polytope
    Returns
    Array<Set>
  •  
    max_interior_simplices (P)

    find the maximal interior simplices of a point configuration that DO NOT contain any point in their closure, except for the vertices. Symmetries of the configuration are NOT taken into account.

    Parameters
    PointConfigurationP
    the input point configuration
  •  
    symmetric_group (degree, domain) → GroupOfPolytope

    Constructs a symmetric group of given degree.

    Parameters
    intdegree
    of the symmetric group"
    intdomain
    of the polytope's symmetry group
    Returns
    GroupOfPolytope
    \@see group::symmetric_group
  •  
    write_simplexity_ilp ()

    UNDOCUMENTED

  •  
    UNDOCUMENTED
    •  
      cs_quotient ()

      For a centrally symmetric polytope, return the quotient space obtained by dividing out the central symmetry, i.e, identifying diametrically opposite faces

    •  
      cylinder_2 ()

      Return a 2-dimensional cylinder obtained by identifying two opposite sides of a square

    •  
      quarter_turn_manifold ()

      Return the 3-dimensional Euclidean manifold obtained by identifying opposite faces of a 3-dimensional cube by a quarter turn. After identification, two classes of vertices remain.