package prbnmcn-basic-structures

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Module Free_module.MakeSource

Make constructs an (OCaml) module to handle the free (algebraic) R-module generated by finite subsets of Basis. The implementation of free modules is backed by a map implementation M that must be provided by the user.

Parameters

module M : Map.S with type key = Basis.t

Signature

Sourcemodule R = R
Sourcetype t = R.t M.t
Sourceval zero : t
Sourceval add : t -> t -> t
Sourceval neg : t -> t
Sourceval compare : t -> t -> int
Sourceval equal : t -> t -> bool
Sourceval pp : Format.formatter -> t -> unit
Sourceval hash : t -> int
Sourceval smul : R.t -> t -> t
Sourcemodule Basis = Basis
Sourcetype basis = Basis.t
Sourceval delta : basis -> t

"Dirac" delta

Sourceval eval : t -> basis -> R.t

Project the coefficient corresponding to a basis vector.

Sourceval bind : t -> (basis -> t) -> t

bind = canonical, "multilinear" extension

Sourceval of_list : (basis * R.t) list -> t

of_list [(x1,r1);...;(xn,rn)] is equivalent to add (smul r1 (delta x1)) (add (smul r2 (delta x2)) (add ... (smul rn (delta xn))))

Sourceval fold : (basis -> R.t -> 'a -> 'a) -> t -> 'a -> 'a

Fold over the elements of a vector. Order is not specified.