X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Freals%2FOddPolyRootIR.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Freals%2FOddPolyRootIR.ma;h=21a487409b23ac60121ea64b480b8f381eccb8ee;hb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;hp=0000000000000000000000000000000000000000;hpb=438a29376390222b94c1fe9772917c3aad50d42e;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma b/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma new file mode 100644 index 000000000..21a487409 --- /dev/null +++ b/helm/software/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". + +(* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *) + +(* INCLUDE +IVT +*) + +(*#* * 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}% +*) + +inline cic:/CoRN/reals/OddPolyRootIR/R.var. + +(* begin hide *) + +inline cic:/CoRN/reals/OddPolyRootIR/RX.con. + +(* 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}% +*) + +inline cic:/CoRN/reals/OddPolyRootIR/R.var. + +(* begin hide *) + +inline cic:/CoRN/reals/OddPolyRootIR/RX.con. + +(* 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}% +*) + +inline cic:/CoRN/reals/OddPolyRootIR/R.var. + +(* begin hide *) + +inline cic:/CoRN/reals/OddPolyRootIR/RX.con. + +(* 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}% +*) + +inline cic:/CoRN/reals/OddPolyRootIR/R.var. + +(* begin hide *) + +inline cic:/CoRN/reals/OddPolyRootIR/RX.con. + +(* 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. +*) +