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[helm.git] / matita / contribs / CoRN-Decl / reals / OddPolyRootIR.ma

diff --git a/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma b/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.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/reals/OddPolyRootIR".
+
+include "CoRN.ma".
+
+(* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
+
+include "reals/IVT.ma".
+
+(*#* * Roots of polynomials of odd degree *)
+
+(* UNEXPORTED
+Section CPoly_Big
+*)
+
+(*#* ** Monic polynomials are positive near infinity
+%\begin{convention}% Let [R] be an ordered field.
+%\end{convention}%
+*)
+
+alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var".
+
+(* begin hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__".
+
+(* end hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
+
+(* UNEXPORTED
+End CPoly_Big
+*)
+
+(* UNEXPORTED
+Section Flip_Poly
+*)
+
+(*#* **Flipping a polynomial
+%\begin{convention}% Let [R] be a ring.
+%\end{convention}%
+*)
+
+alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var".
+
+(* begin hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__".
+
+(* end hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/flip.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con".
+
+(* UNEXPORTED
+Hint Resolve flip_coefficient: algebra.
+*)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
+
+(* UNEXPORTED
+End Flip_Poly
+*)
+
+(* UNEXPORTED
+Hint Resolve flip_poly: algebra.
+*)
+
+(* UNEXPORTED
+Section OddPoly_Signs
+*)
+
+(*#* ** Sign of a polynomial of odd degree
+%\begin{convention}% Let [R] be an ordered field.
+%\end{convention}%
+*)
+
+alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var".
+
+(* begin hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__".
+
+(* end hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
+
+(* UNEXPORTED
+End OddPoly_Signs
+*)
+
+(* UNEXPORTED
+Section Poly_Norm
+*)
+
+(*#* ** The norm of a polynomial
+%\begin{convention}% Let [R] be a field, and [RX] the polynomials over
+this field.
+%\end{convention}%
+*)
+
+alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var".
+
+(* begin hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__".
+
+(* end hide *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
+
+(* UNEXPORTED
+End Poly_Norm
+*)
+
+(* UNEXPORTED
+Section OddPoly_Root
+*)
+
+(*#* ** Roots of polynomials of odd degree
+Polynomials of odd degree over the reals always have a root. *)
+
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con".
+
+inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
+
+(* UNEXPORTED
+End OddPoly_Root
+*)
+