helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma

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   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
  20
  21 include "reals/IVT.ma".
  22
  23 (*#* * Roots of polynomials of odd degree *)
  24
  25 (* UNEXPORTED
  26 Section CPoly_Big
  27 *)
  28
  29 (*#* ** Monic polynomials are positive near infinity
  30 %\begin{convention}% Let [R] be an ordered field.
  31 %\end{convention}%
  32 *)
  33
  34 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var".
  35
  36 (* begin hide *)
  37
  38 inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__".
  39
  40 (* end hide *)
  41
  42 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con".
  43
  44 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con".
  45
  46 inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con".
  47
  48 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
  49
  50 (* UNEXPORTED
  51 End CPoly_Big
  52 *)
  53
  54 (* UNEXPORTED
  55 Section Flip_Poly
  56 *)
  57
  58 (*#* **Flipping a polynomial
  59 %\begin{convention}% Let [R] be a ring.
  60 %\end{convention}%
  61 *)
  62
  63 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var".
  64
  65 (* begin hide *)
  66
  67 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__".
  68
  69 (* end hide *)
  70
  71 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con".
  72
  73 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con".
  74
  75 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con".
  76
  77 (* UNEXPORTED
  78 Hint Resolve flip_coefficient: algebra.
  79 *)
  80
  81 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
  82
  83 (* UNEXPORTED
  84 End Flip_Poly
  85 *)
  86
  87 (* UNEXPORTED
  88 Hint Resolve flip_poly: algebra.
  89 *)
  90
  91 (* UNEXPORTED
  92 Section OddPoly_Signs
  93 *)
  94
  95 (*#* ** Sign of a polynomial of odd degree
  96 %\begin{convention}% Let [R] be an ordered field.
  97 %\end{convention}%
  98 *)
  99
 100 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var".
 101
 102 (* begin hide *)
 103
 104 inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__".
 105
 106 (* end hide *)
 107
 108 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con".
 109
 110 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con".
 111
 112 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
 113
 114 (* UNEXPORTED
 115 End OddPoly_Signs
 116 *)
 117
 118 (* UNEXPORTED
 119 Section Poly_Norm
 120 *)
 121
 122 (*#* ** The norm of a polynomial
 123 %\begin{convention}% Let [R] be a field, and [RX] the polynomials over
 124 this field.
 125 %\end{convention}%
 126 *)
 127
 128 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var".
 129
 130 (* begin hide *)
 131
 132 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__".
 133
 134 (* end hide *)
 135
 136 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con".
 137
 138 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con".
 139
 140 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con".
 141
 142 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
 143
 144 (* UNEXPORTED
 145 End Poly_Norm
 146 *)
 147
 148 (* UNEXPORTED
 149 Section OddPoly_Root
 150 *)
 151
 152 (*#* ** Roots of polynomials of odd degree
 153 Polynomials of odd degree over the reals always have a root. *)
 154
 155 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con".
 156
 157 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con".
 158
 159 inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
 160
 161 (* UNEXPORTED
 162 End OddPoly_Root
 163 *)
 164