functor (R : Ring.T) (X : Alphabet.T) ->
sig
module Ring :
sig
type t = Ring.Op(R).t
val eq : t -> t -> bool
val add : t -> t -> t
val zero : t
val neg : t -> t
val mul : t -> t -> t
val one : t
val to_string : t -> string
end
module E :
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 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 iter : (key -> 'a -> unit) -> 'a t -> unit
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 : key -> 'a t -> 'a
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 add : key -> Ring.Op(R).t -> Ring.Op(R).t t -> Ring.Op(R).t t
end
type r = Ring.Op(R).t
type t = r E.t
val zero : t
val inj : X.t -> t
val coeff : t -> X.t -> r
val included : t -> t -> bool
val eq : t -> t -> bool
val add_monomial : t -> r -> X.t -> t
val add : t -> t -> t
val neg : t -> t
val sub : t -> t -> t
val map : (X.t -> t) -> t -> t
val iter : (Ring.Op(R).t -> X.t -> unit) -> Ring.Op(R).t E.t -> unit
module Map :
sig
module E :
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 iter : (key -> 'a -> unit) -> 'a t -> unit
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 : key -> 'a t -> 'a
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
end
type map = t E.t
val set : map -> X.t -> t -> map
val app : map -> X.t -> t
val bind : map -> t -> t
val zero : map
val to_string : map -> string
type t = map
end
module Presentation :
sig
type pres = X.t array
type t = pres
val make : t -> t
val dim : t -> int
val presentation_to_string : X.t array -> string
module Map :
sig
module M :
sig
type t = Ring.Op(R).t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> Ring.Op(R).t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> Ring.Op(R).t
val to_string : t -> string
module Row :
sig
val is_zero : Ring.Op(R).t array array -> int -> bool
val replace : t -> int -> Ring.Op(R).t array -> t
val exchange : t -> int -> int -> t
val mult : t -> Ring.Op(R).t -> int -> t
val madd : t -> int -> Ring.Op(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 -> Ring.Op(R).t -> unit
val get : t -> X.t -> X.t -> Ring.Op(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 -> Ring.Op(R).t -> unit
val get : t -> X.t -> X.t -> Ring.Op(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 = L.t
type t = map
val app : t -> t -> t
val zero : X.t array -> X.t array -> t
val of_map : Map.map -> X.t array -> X.t array -> t
val to_map : t -> Map.map
val rank : t -> int
val nullity : t -> int
val to_string : t -> string
end
val iter : (X.t -> unit) -> t -> unit
module Complex :
sig
type t =
FreeLeft(Ring.Op(R))(X).Presentation.Complex.t = {
modules : pres array;
d : Map.t array;
}
val modules : t -> pres array
val maps : t -> Map.t array
val length : t -> int
val make : pres array -> Map.t array -> t
val valid : t -> bool
val to_string : t -> string
val homology : t -> int array
end
val to_string : X.t array -> string
end
val cinj : X.t -> Ring.Op(R).t -> t
val cmul : t -> Ring.Op(R).t -> t
val to_string : t -> string
end