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in-package search v0.1.0
Library
Module
Module type
Parameter
Class
Class type
Parameters
Signature
type species_system =
K.t Smol.Polynomial.Make(Literal.Variable).p Species.s
Map.Make(Literal.Class).t
type solution_kind =
| Poly of species_system
| Seq of K.t
| Tree of K.t * K.t Map.Make(Literal.Class).t
val translate :
Literal.Class.t ->
'a Combi.Make(K).class_tree ->
species_system
Translate a class_tree
into a system of equations
val translate_class : 'a Combi.Make(K).combi_class -> species_system
Note for both translations: variables in h
are prefixed with "T_", while in sampler_mapping
they are prefixed with "s_"
val is_well_founded :
species_system ->
K.t Smol.Polynomial.Make(Literal.Variable).p Species.s
Smol.Matrix.Make(Literal.Class).m ->
bool
Algorithm isWellFounded Characterization of well-founded systems See Definition 5.3 and Theorem 5.5. This condition is sufficient to use Newton's iteration to evaluate the generating function of the combinatorial system.
val newton_iteration :
species_system ->
K.t Smol.Polynomial.Make(Literal.Variable).p Species.s
Smol.Matrix.Make(Literal.Class).m ->
K.t ->
K.t ->
K.t Map.Make(Literal.Class).t option
Newton iteration
val eval_convergence_radius :
species_system ->
K.t Smol.Polynomial.Make(Literal.Variable).p Species.s
Smol.Matrix.Make(Literal.Class).m ->
K.t ->
K.t * K.t Map.Make(Literal.Class).t option
Estimation of the convergence radius. Since the system is well founded, it exists and is between 0 and 1. Uses a bisection method: the newtown iteration method converges for a certain value iff it is inside the convergence disk (TODO: citation needed).
val classify :
species_system ->
K.t Smol.Polynomial.Make(Literal.Variable).p Species.s
Smol.Matrix.Make(Literal.Class).m ->
K.t ->
solution_kind
val solve :
species_system ->
Literal.Class.t ->
K.t ->
int ->
K.t * K.t Map.Make(Literal.Class).t option
val solve_class :
'a Combi.Make(K).combi_class ->
K.t ->
int ->
K.t * K.t Map.Make(Literal.Class).t option