X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FOddPolyRootIR.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FOddPolyRootIR.ma;h=ebcef6dac859d71d773ec4bd6125a891dddd03cc;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma b/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma new file mode 100644 index 000000000..ebcef6dac --- /dev/null +++ b/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma @@ -0,0 +1,166 @@ +(**************************************************************************) +(* ___ *) +(* ||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 +*) +