Deck transformations
Deck transformations of a parametric polynomial system are the birational maps that fix the parameters of the polynomial system.
Computing deck transformations
DecomposingPolynomialSystems.symmetries_fixing_parameters
— Functionsymmetries_fixing_parameters(F::System; degree_bound=1, param_dep=true, kwargs...)
Given a polynomial system F returns the group of symmetries of F
that fix the parameters. The keyword argument degree_bound
is used to set the upper bound for the degrees of numerator and denominator polynomials in expressions for the symmetries. The param_dep
keyword argument specifies whether to consider functions of the symmetries to be dependent on the parameters of F
.
julia> @var x[1:2] p[1:2];
julia> F = System([x[1]^2 - x[2]^2 - p[1], 2*x[1]*x[2] - p[2]]; variables=x, parameters=p);
julia> symmetries_fixing_parameters(F; degree_bound=1, param_dep=false)
DeckTransformationGroup of order 4
structure: C2 x C2
action:
1st map:
x₁ ↦ x₁
x₂ ↦ x₂
2nd map:
x₁ ↦ -x₁
x₂ ↦ -x₂
3rd map:
x₁ ↦ im*x₂
x₂ ↦ -im*x₁
4th map:
x₁ ↦ -im*x₂
x₂ ↦ im*x₁
DeckTranfromationGroup
DecomposingPolynomialSystems.DeckTransformationGroup
— TypeDeckTransformationGroup
A DeckTransformationGroup
is the result of deck transformations computation.