X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Freals%2FOddPolyRootIR.ma;h=ebcef6dac859d71d773ec4bd6125a891dddd03cc;hb=db235934efa41a0f38e79747f6db4f468367410b;hp=21a487409b23ac60121ea64b480b8f381eccb8ee;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;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 index 21a487409..ebcef6dac 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma @@ -16,16 +16,16 @@ 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 -IVT -*) +include "reals/IVT.ma". (*#* * Roots of polynomials of odd degree *) (* UNEXPORTED -Section CPoly_Big. +Section CPoly_Big *) (*#* ** Monic polynomials are positive near infinity @@ -33,28 +33,28 @@ Section CPoly_Big. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +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/Cbigger.con". -inline cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con. +inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con". -inline cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con. +inline "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con". -inline cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con. +inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con". (* UNEXPORTED -End CPoly_Big. +End CPoly_Big *) (* UNEXPORTED -Section Flip_Poly. +Section Flip_Poly *) (*#* **Flipping a polynomial @@ -62,28 +62,28 @@ Section Flip_Poly. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +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.con". -inline cic:/CoRN/reals/OddPolyRootIR/flip_poly.con. +inline "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con". -inline cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con. +inline "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con". (* UNEXPORTED Hint Resolve flip_coefficient: algebra. *) -inline cic:/CoRN/reals/OddPolyRootIR/flip_odd.con. +inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con". (* UNEXPORTED -End Flip_Poly. +End Flip_Poly *) (* UNEXPORTED @@ -91,7 +91,7 @@ Hint Resolve flip_poly: algebra. *) (* UNEXPORTED -Section OddPoly_Signs. +Section OddPoly_Signs *) (*#* ** Sign of a polynomial of odd degree @@ -99,26 +99,26 @@ Section OddPoly_Signs. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +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_pos'.con. +inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con". -inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con. +inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con". (* UNEXPORTED -End OddPoly_Signs. +End OddPoly_Signs *) (* UNEXPORTED -Section Poly_Norm. +Section Poly_Norm *) (*#* ** The norm of a polynomial @@ -127,40 +127,40 @@ this field. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +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_aux.con". -inline cic:/CoRN/reals/OddPolyRootIR/poly_norm.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_monic.con". -inline cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con. +inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con". (* UNEXPORTED -End Poly_Norm. +End Poly_Norm *) (* UNEXPORTED -Section OddPoly_Root. +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/oddpoly_root.con. +inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con". -inline cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con. +inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con". (* UNEXPORTED -End OddPoly_Root. +End OddPoly_Root *)