Definition of the problem

The problem is defined in a TOML file. The file must contain the following fields:

• symmetry_name: Name of the symmetry group.
• NOB: Number of bodies.
• m: An array of masses of the bodies.
• dim: The dimension of the space.
• Group generators
  • action_type: The type of the action of the group. It can be
    • 0: Circular action
    • 1: Dihedral action
    • 2: Brake action
  • kern: A string containing a GAP command to generate the kernel of the $\tau$ representation. The following helper functions ara available:
    • TrivialKerTau(2) for the trivial kernel of the $\tau$ representation when $d=2$
    • TrivialKerTau(3) for the trivial kernel of the $\tau$ representation when $d=3$
  • rotV: A string containing a GAP command to generate the $O(d)$ part of the first generator of the group. It must be an orthogonal matrix of size $d \times d$
  • rotS: A string containing a GAP command to generate the $\Sigma_n$ part of the first generator of the group. It must be a permutation.
  • If the action is dihedral or brake:
    • refV: A string containing a GAP command to generate the $O(d)$ part of the second generator of the group. It must be an orthogonal matrix of size $d \times d$
    • refS: A string containing a GAP command to generate the $\Sigma_n$ part of the second generator of the group. It must be a permutation.

The file must also contain the following optional fields:

• F: The number of fourier coefficients (default: 24)
• steps: The number of steps to be used for the point representation of the path (default: 2 * F)
• Omega: The infinitesimal generator of the reference frame rotation (default: 0)
• denominator: The denominator of the potential (default: x)

The following is an example of a TOML file defining a problem:

symmetry_name = "2d_cyclic_2"
NOB = 3
dim = 2
m = [1, 1, 1]

# Group generators
kern = "TrivialKerTau(2)"
action_type = 0
rotV = "[[-1, 0], [0, -1] ]"
rotS = "(2,3)"

# Other configs
F = 24
Omega = [
    [0, 0],
    [0, 0]
]

Load the problem

A problem can be loaded using the initialize function. The function receives the path to the TOML file and returns a Problem object.

julia> P = initialize("example.toml")N: 		3
dim: 		2
F: 		24
steps: 		48
masses: 	[1.0, 1.0, 1.0]
denominator: 	f(x) = x

Symmetry group: SymmetryGroup of type Cyclic

*  ker(τ): Subgroup of order 1

*  g = GroupElement:
	σ: [2, 3, 1]
	M: [1.0 0.0; 0.0 1.0]

*  Cyclic order = 3