sig
module M :
sig
type t = R.t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> R.t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> R.t
val to_string : t -> string
module Row :
sig
val is_zero : R.t array array -> int -> bool
val replace : t -> int -> R.t array -> t
val exchange : t -> int -> int -> t
val mult : t -> R.t -> int -> t
val madd : t -> int -> R.t -> int -> t
end
val row_echelon : t -> t
val rank : t -> int
val nullity : t -> int
module Labeled :
functor (X : Alphabet.T) ->
sig
module L :
sig
type key = X.t
type 'a t = 'a Map.Make(X).t
val empty : 'a t
val is_empty : 'a t -> bool
val mem : key -> 'a t -> bool
val add : key -> 'a -> 'a t -> 'a t
val update : key -> ('a option -> 'a option) -> 'a t -> 'a t
val singleton : key -> 'a -> 'a t
val remove : key -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val union :
(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val for_all : (key -> 'a -> bool) -> 'a t -> bool
val exists : (key -> 'a -> bool) -> 'a t -> bool
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val cardinal : 'a t -> int
val bindings : 'a t -> (key * 'a) list
val min_binding : 'a t -> key * 'a
val min_binding_opt : 'a t -> (key * 'a) option
val max_binding : 'a t -> key * 'a
val max_binding_opt : 'a t -> (key * 'a) option
val choose : 'a t -> key * 'a
val choose_opt : 'a t -> (key * 'a) option
val split : key -> 'a t -> 'a t * 'a option * 'a t
val find_opt : key -> 'a t -> 'a option
val find_first : (key -> bool) -> 'a t -> key * 'a
val find_first_opt :
(key -> bool) -> 'a t -> (key * 'a) option
val find_last : (key -> bool) -> 'a t -> key * 'a
val find_last_opt :
(key -> bool) -> 'a t -> (key * 'a) option
val map : ('a -> 'b) -> 'a t -> 'b t
val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t
val to_seq : 'a t -> (key * 'a) Seq.t
val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
val of_seq : (key * 'a) Seq.t -> 'a t
val find : X.t -> 'a t -> 'a
val iter : (X.t -> 'a -> unit) -> 'a t -> unit
val of_array : X.t array -> int t
end
type map = int L.t
type t = map * map * matrix
val matrix : t -> matrix
val zero : X.t array -> X.t array -> t
val set : t -> X.t -> X.t -> R.t -> unit
val get : t -> X.t -> X.t -> R.t
val rank : t -> int
val nullity : t -> int
val iter_src : (X.t -> unit) -> t -> unit
val iter_tgt : (X.t -> unit) -> t -> unit
val iter : (X.t -> X.t -> unit) -> t -> unit
end
end
module L :
sig
module L :
sig
type key = X.t
type 'a t = 'a Map.Make(X).t
val empty : 'a t
val is_empty : 'a t -> bool
val mem : key -> 'a t -> bool
val add : key -> 'a -> 'a t -> 'a t
val update : key -> ('a option -> 'a option) -> 'a t -> 'a t
val singleton : key -> 'a -> 'a t
val remove : key -> 'a t -> 'a t
val merge :
(key -> 'a option -> 'b option -> 'c option) ->
'a t -> 'b t -> 'c t
val union : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val fold : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val for_all : (key -> 'a -> bool) -> 'a t -> bool
val exists : (key -> 'a -> bool) -> 'a t -> bool
val filter : (key -> 'a -> bool) -> 'a t -> 'a t
val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val cardinal : 'a t -> int
val bindings : 'a t -> (key * 'a) list
val min_binding : 'a t -> key * 'a
val min_binding_opt : 'a t -> (key * 'a) option
val max_binding : 'a t -> key * 'a
val max_binding_opt : 'a t -> (key * 'a) option
val choose : 'a t -> key * 'a
val choose_opt : 'a t -> (key * 'a) option
val split : key -> 'a t -> 'a t * 'a option * 'a t
val find_opt : key -> 'a t -> 'a option
val find_first : (key -> bool) -> 'a t -> key * 'a
val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) option
val find_last : (key -> bool) -> 'a t -> key * 'a
val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) option
val map : ('a -> 'b) -> 'a t -> 'b t
val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t
val to_seq : 'a t -> (key * 'a) Seq.t
val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
val of_seq : (key * 'a) Seq.t -> 'a t
val find : X.t -> 'a t -> 'a
val iter : (X.t -> 'a -> unit) -> 'a t -> unit
val of_array : X.t array -> int t
end
type map = int L.t
type t = map * map * M.matrix
val matrix : t -> M.matrix
val zero : X.t array -> X.t array -> t
val set : t -> X.t -> X.t -> R.t -> unit
val get : t -> X.t -> X.t -> R.t
val rank : t -> int
val nullity : t -> int
val iter_src : (X.t -> unit) -> t -> unit
val iter_tgt : (X.t -> unit) -> t -> unit
val iter : (X.t -> X.t -> unit) -> t -> unit
end
type map = Module.FreeLeft.Presentation.Map.L.t
type t = Module.FreeLeft.Presentation.Map.map
val app :
Module.FreeLeft.Presentation.Map.t ->
Module.FreeLeft.Presentation.Map.t -> Module.FreeLeft.Presentation.Map.t
val zero : X.t array -> X.t array -> Module.FreeLeft.Presentation.Map.t
val of_map :
Module.FreeLeft.Map.map ->
X.t array -> X.t array -> Module.FreeLeft.Presentation.Map.t
val to_map : Module.FreeLeft.Presentation.Map.t -> Module.FreeLeft.Map.map
val rank : Module.FreeLeft.Presentation.Map.t -> int
val nullity : Module.FreeLeft.Presentation.Map.t -> int
val to_string : Module.FreeLeft.Presentation.Map.t -> string
end