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[helm.git] / matita / contribs / CoRN-Decl / algebra / CPoly_ApZero.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_ApZero".
+
+include "CoRN.ma".
+
+(* $Id: CPoly_ApZero.v,v 1.3 2004/04/23 10:00:53 lcf Exp $ *)
+
+include "algebra/CPoly_Degree.ma".
+
+include "algebra/COrdFields2.ma".
+
+(*#* * Polynomials apart from zero *)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con".
+
+(* UNEXPORTED
+Implicit Arguments distinct1 [A].
+*)
+
+(* UNEXPORTED
+Section Poly_Representation
+*)
+
+(*#*
+** Representation of polynomials
+%\begin{convention}% Let [R] be a field, [RX] the ring of polynomials
+over [R], [a_ : nat->R] with [(distinct1 a_)] and let [f] be a
+polynomial over [R], [n] a natural with [(degree_le n f)], i.e. [f]
+has degree at most [n].
+%\end{convention}%
+*)
+
+alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var".
+
+alias id "a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var".
+
+alias id "distinct_a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var".
+
+alias id "f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var".
+
+alias id "n" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var".
+
+alias id "degree_f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var".
+
+(* begin hide *)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* end hide *)
+
+include "tactics/Transparent_algebra.ma".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con".
+
+include "tactics/Opaque_algebra.ma".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con".
+
+(* UNEXPORTED
+Hint Resolve poly_01_factor'_zero.
+*)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con".
+
+(* UNEXPORTED
+Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra.
+*)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con".
+
+(* UNEXPORTED
+Hint Resolve poly_01_zero poly_01_one: algebra.
+*)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con".
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con".
+
+(* UNEXPORTED
+Hint Resolve poly_representation: algebra.
+*)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con".
+
+(* UNEXPORTED
+End Poly_Representation
+*)
+
+(* UNEXPORTED
+Section Characteristic_zero
+*)
+
+(*#*
+If we are in a field of characteristic zero, the previous result can be
+strengthened.
+*)
+
+alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var".
+
+(* begin show *)
+
+alias id "H" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var".
+
+(* end show *)
+
+(* begin hide *)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* end hide *)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con".
+
+(*#*
+Also, in this situation polynomials are extensional functions.
+*)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con".
+
+(* UNEXPORTED
+End Characteristic_zero
+*)
+
+(*#*
+** Polynomials are nonzero on any interval
+*)
+
+(* UNEXPORTED
+Section Poly_ApZero_Interval
+*)
+
+alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var".
+
+(* begin hide *)
+
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
+(* end hide *)
+
+inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con".
+
+(* UNEXPORTED
+End Poly_ApZero_Interval
+*)
+