functor (K : Field.T) (X : Alphabet.T) ->
sig
module M :
sig
type t = X.t array
type word = t
val mul : t -> t -> t
val one : t
val inj : X.t -> t
val length : t -> int
val sub : t -> int -> int -> t
val eq : t -> t -> bool
val compare : t -> t -> int
val peq : t -> int -> t -> int -> int -> bool
val to_string : t -> string
val included : t -> t -> bool
val unifier : ?i:int -> t -> t -> int
val ordered_unifiers : t -> t -> int list
val ordered_unifiers_bicontext : t -> t -> ((t * t) * (t * t)) list
val unifiers_bicontext : t -> t -> ((t * t) * (t * t)) list
module Order :
sig
val lexicographic : (X.t -> X.t -> bool) -> t -> t -> bool
val deglex : (X.t -> X.t -> bool) -> t -> t -> bool
end
module Anick :
sig
type t = word list
val empty : t
val singleton : X.t -> t
val singletons : X.t list -> t list
val hd : t -> word
val tl : t -> t
val weq : t -> t -> bool
val eq : t list -> t list -> bool
val compare : t list -> t list -> int
val extend : word list -> t list -> t list
val eval : t -> t
val length : t -> int
val to_string : t -> string
end
end
module A :
sig
module Ring :
sig
type t = K.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 = M.t
type 'a t = 'a Map.Make(M).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 -> K.t -> K.t t -> K.t t
end
type r = K.t
type t = r E.t
val zero : t
val cinj : K.t -> M.t -> t
val inj : M.t -> t
val coeff : t -> M.t -> r
val included : t -> t -> bool
val eq : t -> t -> bool
val add_monomial : t -> r -> M.t -> t
val add : t -> t -> t
val cmul : K.t -> t -> t
val neg : t -> t
val sub : t -> t -> t
val to_string : t -> string
val map : (M.t -> t) -> t -> t
val iter : (K.t -> M.t -> unit) -> K.t E.t -> unit
module Map :
sig
module E :
sig
type key = M.t
type 'a t = 'a Map.Make(M).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 -> M.t -> t -> map
val app : map -> M.t -> t
val bind : map -> t -> t
val zero : map
val to_string : map -> string
type t = map
end
module Presentation :
sig
type pres = M.t array
type t = pres
val make : t -> t
val dim : t -> int
val presentation_to_string : M.t array -> string
module Map :
sig
module M :
sig
type t = K.t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> K.t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> K.t
val to_string : t -> string
module Row :
sig
val is_zero : K.t array array -> int -> bool
val replace : t -> int -> K.t array -> t
val exchange : t -> int -> int -> t
val mult : t -> K.t -> int -> t
val madd : t -> int -> K.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 -> K.t -> unit
val get : t -> X.t -> X.t -> K.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 = M.t
type 'a t = 'a Map.Make(M).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 : M.t -> 'a t -> 'a
val iter : (M.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.t array -> int t
end
type map = int L.t
type t = map * map * M.matrix
val matrix : t -> M.matrix
val zero : M.t array -> M.t array -> t
val set : t -> M.t -> M.t -> K.t -> unit
val get : t -> M.t -> M.t -> K.t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.t -> unit) -> t -> unit
val iter_tgt : (M.t -> unit) -> t -> unit
val iter : (M.t -> M.t -> unit) -> t -> unit
end
type map = L.t
type t = map
val app : t -> t -> t
val zero : M.t array -> M.t array -> t
val of_map : Map.map -> M.t array -> M.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 : (M.t -> unit) -> t -> unit
module Complex :
sig
type t =
Module.FreeLeft(K)(M).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 : M.t array -> string
end
module Field :
sig
type t = K.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
val inv : t -> t
end
val one : t
val mul_monomial : t -> M.t -> t
val mul : t -> t -> t
val leading : (M.t -> M.t -> bool) -> t -> K.t * M.t
end
type t = {
leq : Algebra.Presentation.M.t -> Algebra.Presentation.M.t -> bool;
generators : X.t list;
rules : (Algebra.Presentation.M.t * Algebra.Presentation.A.t) list;
}
val free :
(Algebra.Presentation.M.t -> Algebra.Presentation.M.t -> bool) ->
X.t list -> Algebra.Presentation.t
val orient :
Algebra.Presentation.t ->
Algebra.Presentation.A.t ->
Algebra.Presentation.M.t * Algebra.Presentation.A.t
val add_rule :
Algebra.Presentation.t ->
Algebra.Presentation.M.t * Algebra.Presentation.A.t ->
Algebra.Presentation.t
val add_relation :
Algebra.Presentation.t ->
Algebra.Presentation.A.t -> Algebra.Presentation.t
val make :
(Algebra.Presentation.M.t -> Algebra.Presentation.M.t -> bool) ->
X.t list -> Algebra.Presentation.A.t list -> Algebra.Presentation.t
val heads : Algebra.Presentation.t -> Algebra.Presentation.M.t list
val to_string : Algebra.Presentation.t -> string
val normalize :
Algebra.Presentation.t ->
Algebra.Presentation.A.t -> Algebra.Presentation.A.t
val buchberger : Algebra.Presentation.t -> Algebra.Presentation.t
val reduce : Algebra.Presentation.t -> Algebra.Presentation.t
module Algebra :
functor (P : sig val presentation : Algebra.Presentation.t end) ->
sig
type t = A.t
type r
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
module Field :
sig
val eq : r -> r -> bool
val add : r -> r -> r
val zero : r
val neg : r -> r
val mul : r -> r -> r
val one : r
val to_string : r -> string
val inv : r -> r
end
val cmul : r -> t -> t
end
module Augmentation :
sig
type t = Algebra.Presentation.A.t -> K.t
exception Invalid
val make :
Algebra.Presentation.Augmentation.t ->
(Algebra.Presentation.M.t -> K.t) ->
Algebra.Presentation.Augmentation.t
val graded :
Algebra.Presentation.Augmentation.t ->
Algebra.Presentation.Augmentation.t
val monoid :
Algebra.Presentation.Augmentation.t ->
Algebra.Presentation.Augmentation.t
end
module Anick :
sig
type chain = Algebra.Presentation.M.Anick.t
module AMod :
sig
module Mod :
sig
module Ring :
sig
type t = Ring.Op(A).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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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(A).t -> Ring.Op(A).t t -> Ring.Op(A).t t
end
type r = Ring.Op(A).t
type t = r E.t
val zero : t
val inj : M.Anick.t -> t
val coeff : t -> M.Anick.t -> r
val included : t -> t -> bool
val eq : t -> t -> bool
val add_monomial : t -> r -> M.Anick.t -> t
val add : t -> t -> t
val neg : t -> t
val sub : t -> t -> t
val map : (M.Anick.t -> t) -> t -> t
val iter :
(Ring.Op(A).t -> M.Anick.t -> unit) ->
Ring.Op(A).t E.t -> unit
module Map :
sig
module E :
sig
type key = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 -> M.Anick.t -> t -> map
val app : map -> M.Anick.t -> t
val bind : map -> t -> t
val zero : map
val to_string : map -> string
type t = map
end
module Presentation :
sig
type pres = M.Anick.t array
type t = pres
val make : t -> t
val dim : t -> int
val presentation_to_string : M.Anick.t array -> string
module Map :
sig
module M :
sig
type t = Ring.Op(A).t array array
type matrix = t
val zero : int -> int -> t
val init :
int -> int -> (int -> int -> Ring.Op(A).t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> Ring.Op(A).t
val to_string : t -> string
module Row :
sig
val is_zero :
Ring.Op(A).t array array -> int -> bool
val replace :
t -> int -> Ring.Op(A).t array -> t
val exchange : t -> int -> int -> t
val mult : t -> Ring.Op(A).t -> int -> t
val madd :
t -> int -> Ring.Op(A).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(A).t -> unit
val get : t -> X.t -> X.t -> Ring.Op(A).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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 : M.Anick.t -> 'a t -> 'a
val iter :
(M.Anick.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.Anick.t array -> int t
end
type map = int L.t
type t = map * map * M.matrix
val matrix : t -> M.matrix
val zero :
M.Anick.t array -> M.Anick.t array -> t
val set :
t ->
M.Anick.t -> M.Anick.t -> Ring.Op(A).t -> unit
val get :
t -> M.Anick.t -> M.Anick.t -> Ring.Op(A).t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.Anick.t -> unit) -> t -> unit
val iter_tgt : (M.Anick.t -> unit) -> t -> unit
val iter :
(M.Anick.t -> M.Anick.t -> unit) -> t -> unit
end
type map = L.t
type t = map
val app : t -> t -> t
val zero : M.Anick.t array -> M.Anick.t array -> t
val of_map :
Map.map -> M.Anick.t array -> M.Anick.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 : (M.Anick.t -> unit) -> t -> unit
module Complex :
sig
type t =
Module.FreeLeft(Ring.Op(A))(M.Anick).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 : M.Anick.t array -> string
end
val cinj : M.Anick.t -> Ring.Op(A).t -> t
val cmul : t -> Ring.Op(A).t -> t
val to_string : t -> string
end
module Ring :
sig
type t = Ring.Op(A).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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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(A).t -> Ring.Op(A).t t -> Ring.Op(A).t t
end
type r = Ring.Op(A).t
type t = r E.t
val zero : t
val inj : M.Anick.t -> t
val coeff : t -> M.Anick.t -> r
val included : t -> t -> bool
val eq : t -> t -> bool
val add_monomial : t -> r -> M.Anick.t -> t
val add : t -> t -> t
val neg : t -> t
val sub : t -> t -> t
val map : (M.Anick.t -> t) -> t -> t
val iter :
(Ring.Op(A).t -> M.Anick.t -> unit) -> Ring.Op(A).t E.t -> unit
module Presentation :
sig
type pres = M.Anick.t array
type t = pres
val make : t -> t
val dim : t -> int
val presentation_to_string : M.Anick.t array -> string
module Map :
sig
module M :
sig
type t = Ring.Op(A).t array array
type matrix = t
val zero : int -> int -> t
val init :
int -> int -> (int -> int -> Ring.Op(A).t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> Ring.Op(A).t
val to_string : t -> string
module Row :
sig
val is_zero :
Ring.Op(A).t array array -> int -> bool
val replace : t -> int -> Ring.Op(A).t array -> t
val exchange : t -> int -> int -> t
val mult : t -> Ring.Op(A).t -> int -> t
val madd : t -> int -> Ring.Op(A).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(A).t -> unit
val get : t -> X.t -> X.t -> Ring.Op(A).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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 : M.Anick.t -> 'a t -> 'a
val iter :
(M.Anick.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.Anick.t array -> int t
end
type map = int L.t
type t = map * map * M.matrix
val matrix : t -> M.matrix
val zero : M.Anick.t array -> M.Anick.t array -> t
val set :
t -> M.Anick.t -> M.Anick.t -> Ring.Op(A).t -> unit
val get : t -> M.Anick.t -> M.Anick.t -> Ring.Op(A).t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.Anick.t -> unit) -> t -> unit
val iter_tgt : (M.Anick.t -> unit) -> t -> unit
val iter :
(M.Anick.t -> M.Anick.t -> unit) -> t -> unit
end
type map = L.t
type t = map
val app : t -> t -> t
val zero : M.Anick.t array -> M.Anick.t array -> t
val of_map :
Mod.Map.map -> M.Anick.t array -> M.Anick.t array -> t
val to_map : t -> Mod.Map.map
val rank : t -> int
val nullity : t -> int
val to_string : t -> string
end
val iter : (M.Anick.t -> unit) -> t -> unit
module Complex :
sig
type t =
Module.FreeLeft(Ring.Op(A))(M.Anick).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 : M.Anick.t array -> string
end
val cinj : M.Anick.t -> Ring.Op(A).t -> t
val cmul : t -> Ring.Op(A).t -> t
val to_string : t -> string
val normalize :
Algebra.Presentation.t ->
Ring.Op(A).t E.t -> Algebra.Presentation.t
module Map :
sig
module E = Mod.Map.E
type map = Mod.t E.t
val set : map -> M.Anick.t -> Mod.t -> map
val app : map -> M.Anick.t -> Mod.t
val zero : map
val to_string : map -> string
type t = map
val bind :
Algebra.Presentation.t ->
map ->
Algebra.Presentation.Anick.AMod.Mod.t ->
Algebra.Presentation.t
end
end
module AKMod :
sig
type t = Algebra.Presentation.Anick.AMod.t
type r = K.t
val cinj :
K.t ->
Algebra.Presentation.M.Anick.t ->
Algebra.Presentation.M.t -> Algebra.Presentation.Anick.AMod.t
val inj :
Algebra.Presentation.Anick.AMod.t ->
Algebra.Presentation.M.t -> Algebra.Presentation.Anick.AMod.t
val cmul :
K.t ->
Algebra.Presentation.Anick.AMod.t ->
Algebra.Presentation.Anick.AMod.t
val iter :
(K.t ->
Algebra.Presentation.M.Anick.t ->
Algebra.Presentation.M.t -> unit) ->
Algebra.Presentation.Anick.AKMod.t -> unit
val map :
(Algebra.Presentation.M.Anick.t ->
Algebra.Presentation.M.t -> Algebra.Presentation.Anick.AMod.t) ->
Algebra.Presentation.Anick.AKMod.t ->
Algebra.Presentation.Anick.AMod.t
end
val chains :
Algebra.Presentation.t ->
int -> Algebra.Presentation.M.Anick.t list array
val resolution :
?augmentation:Algebra.Presentation.Augmentation.t ->
Algebra.Presentation.t ->
int -> Algebra.Presentation.Anick.AMod.Presentation.Complex.t
module KMod :
sig
module Ring :
sig
type t = K.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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 -> K.t -> K.t t -> K.t t
end
type r = K.t
type t = r E.t
val zero : t
val cinj : K.t -> M.Anick.t -> t
val inj : M.Anick.t -> t
val coeff : t -> M.Anick.t -> r
val included : t -> t -> bool
val eq : t -> t -> bool
val add_monomial : t -> r -> M.Anick.t -> t
val add : t -> t -> t
val cmul : K.t -> t -> t
val neg : t -> t
val sub : t -> t -> t
val to_string : t -> string
val map : (M.Anick.t -> t) -> t -> t
val iter : (K.t -> M.Anick.t -> unit) -> K.t E.t -> unit
module Map :
sig
module E :
sig
type key = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 -> M.Anick.t -> t -> map
val app : map -> M.Anick.t -> t
val bind : map -> t -> t
val zero : map
val to_string : map -> string
type t = map
end
module Presentation :
sig
type pres = M.Anick.t array
type t = pres
val make : t -> t
val dim : t -> int
val presentation_to_string : M.Anick.t array -> string
module Map :
sig
module M :
sig
type t = K.t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> K.t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> K.t
val to_string : t -> string
module Row :
sig
val is_zero : K.t array array -> int -> bool
val replace : t -> int -> K.t array -> t
val exchange : t -> int -> int -> t
val mult : t -> K.t -> int -> t
val madd : t -> int -> K.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 -> K.t -> unit
val get : t -> X.t -> X.t -> K.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 = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 : M.Anick.t -> 'a t -> 'a
val iter :
(M.Anick.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.Anick.t array -> int t
end
type map = int L.t
type t = map * map * M.matrix
val matrix : t -> M.matrix
val zero : M.Anick.t array -> M.Anick.t array -> t
val set : t -> M.Anick.t -> M.Anick.t -> K.t -> unit
val get : t -> M.Anick.t -> M.Anick.t -> K.t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.Anick.t -> unit) -> t -> unit
val iter_tgt : (M.Anick.t -> unit) -> t -> unit
val iter :
(M.Anick.t -> M.Anick.t -> unit) -> t -> unit
end
type map = L.t
type t = map
val app : t -> t -> t
val zero : M.Anick.t array -> M.Anick.t array -> t
val of_map :
Map.map -> M.Anick.t array -> M.Anick.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 : (M.Anick.t -> unit) -> t -> unit
module Complex :
sig
type t =
Module.FreeLeft(K)(M.Anick).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 : M.Anick.t array -> string
end
end
module MF :
sig
module M :
sig
type t = A.t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> A.t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> A.t
val to_string : t -> string
module Row :
sig
val is_zero : A.t array array -> int -> bool
val replace : t -> int -> A.t array -> t
val exchange : t -> int -> int -> t
val mult : t -> A.t -> int -> t
val madd : t -> int -> A.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 -> A.t -> unit
val get : t -> X.t -> X.t -> A.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 M' :
sig
type t = K.t array array
type matrix = t
val zero : int -> int -> t
val init : int -> int -> (int -> int -> K.t) -> t
val rows : t -> int
val cols : t -> int
val get : t -> int -> int -> K.t
val to_string : t -> string
module Row :
sig
val is_zero : K.t array array -> int -> bool
val replace : t -> int -> K.t array -> t
val exchange : t -> int -> int -> t
val mult : t -> K.t -> int -> t
val madd : t -> int -> K.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 -> K.t -> unit
val get : t -> X.t -> X.t -> K.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
val map : (A.t -> K.t) -> M.t -> M'.t
module Labeled :
functor (X : Alphabet.T) (X' : Alphabet.T) ->
sig
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 -> A.t -> unit
val get : t -> X.t -> X.t -> A.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
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 -> K.t -> unit
val get : t -> X'.t -> X'.t -> K.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
val map :
(X.t -> X'.t) ->
(X.t -> X'.t) -> (A.t -> K.t) -> L.t -> L'.t
end
end
module MFL :
sig
module L :
sig
module L :
sig
type key = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 : M.Anick.t -> 'a t -> 'a
val iter : (M.Anick.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.Anick.t array -> int t
end
type map = int L.t
type t = map * map * MF.M.matrix
val matrix : t -> MF.M.matrix
val zero : M.Anick.t array -> M.Anick.t array -> t
val set : t -> M.Anick.t -> M.Anick.t -> A.t -> unit
val get : t -> M.Anick.t -> M.Anick.t -> A.t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.Anick.t -> unit) -> t -> unit
val iter_tgt : (M.Anick.t -> unit) -> t -> unit
val iter : (M.Anick.t -> M.Anick.t -> unit) -> t -> unit
end
module L' :
sig
module L :
sig
type key = M.Anick.t
type 'a t = 'a Map.Make(M.Anick).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 : M.Anick.t -> 'a t -> 'a
val iter : (M.Anick.t -> 'a -> unit) -> 'a t -> unit
val of_array : M.Anick.t array -> int t
end
type map = int L.t
type t = map * map * MF.M'.matrix
val matrix : t -> MF.M'.matrix
val zero : M.Anick.t array -> M.Anick.t array -> t
val set : t -> M.Anick.t -> M.Anick.t -> K.t -> unit
val get : t -> M.Anick.t -> M.Anick.t -> K.t
val rank : t -> int
val nullity : t -> int
val iter_src : (M.Anick.t -> unit) -> t -> unit
val iter_tgt : (M.Anick.t -> unit) -> t -> unit
val iter : (M.Anick.t -> M.Anick.t -> unit) -> t -> unit
end
val map :
(M.Anick.t -> M.Anick.t) ->
(M.Anick.t -> M.Anick.t) -> (A.t -> K.t) -> L.t -> L'.t
end
val complex :
?augmentation:Algebra.Presentation.Augmentation.t ->
Algebra.Presentation.t ->
int -> Algebra.Presentation.Anick.KMod.Presentation.Complex.t
val homology :
?augmentation:Algebra.Presentation.Augmentation.t ->
Algebra.Presentation.t -> int -> int array
end
end