package coq-core

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The Coq Proof Assistant -- Core Binaries and Tools

Install 

dune-project
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coq.inria.fr Readme Edit opam file Versions (11)

Authors

  1. T
    The Coq development team, INRIA, CNRS, and contributors

Maintainers

  1. T
    The Coq development team <coqdev@inria.fr>

Sources

coq-8.20.1.tar.gz
md5=0cfaa70f569be9494d24c829e6555d46
sha512=8ee967c636b67b22a4f34115871d8f9b9114df309afc9ddf5f61275251088c6e21f6cf745811df75554d30f4cebb6682f23eeb2e88b771330c4b60ce3f6bf5e2

doc/micromega_plugin/Micromega_plugin/Polynomial/LinPoly/index.html

Module Polynomial.LinPolySource

Linear(ised) polynomials represented as a Vect.t i.e a sorted association list. The constant is the coefficient of the variable 0

Each linear polynomial can be interpreted as a multi-variate polynomial. There is a bijection mapping between a linear variable and a monomial (see module MonT)

Sourcetype t = Vect.t

Each variable of a linear polynomial is mapped to a monomial. This is done using the monomial tables of the module MonT.

Sourcemodule MonT : sig ... end
Sourceval linpol_of_pol : Poly.t -> t

linpol_of_pol p linearise the polynomial p

Sourceval var : var -> t

var x

  • returns

    1.y where y is the variable index of the monomial x^1.

Sourceval of_monomial : Monomial.t -> t

of_monomial m

  • returns

    1.x where x is the variable (index) for monomial m

Sourceval of_vect : Vect.t -> t

of_vect v

  • returns

    a1.x1 + ... + an.xn This is not the identity because xi is the variable index of xi^1

variables p

  • returns

    the set of variables of the polynomial p interpreted as a multi-variate polynomial

Sourceval is_variable : t -> var option

is_variable p

  • returns

    Some x if p = a.x for a >= 0

Sourceval is_linear : t -> bool

is_linear p

  • returns

    whether the multi-variate polynomial is linear.

Sourceval is_linear_for : var -> t -> bool

is_linear_for x p

  • returns

    true if the polynomial is linear in x i.e can be written c*x+r where c is a constant and r is independent from x

constant c

  • returns

    the constant polynomial c

Sourceval search_all_linear : (Micromega_core_plugin.NumCompat.Q.t -> bool) -> t -> var list

search_all_linear pred p

  • returns

    all the variables x such p = a.x + b such that p is linear in x i.e x does not occur in b and a is a constant such that pred a

Sourceval product : t -> t -> t

product p q

  • returns

    the product of the polynomial p*q

Sourceval collect_square : t -> Monomial.t MonMap.t

collect_square p

  • returns

    a mapping m such that ms = s^2 for every s^2 that is a monomial of p

monomials p

  • returns

    the set of monomials.

Sourceval pp_var : Stdlib.out_channel -> var -> unit

pp_var o v pretty-prints a monomial indexed by v.

Sourceval pp : Stdlib.out_channel -> t -> unit

pp o p pretty-prints a polynomial.

Sourceval pp_goal : string -> Stdlib.out_channel -> (t * op) list -> unit

pp_goal typ o l pretty-prints the list of constraints as a Coq goal.