helm/software/matita/contribs/procedural/CoRN/reals/OddPolyRootIR.mma

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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 (* UNEXPORTED
  35 cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var
  36 *)
  37
  38 (* begin hide *)
  39
  40 inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__" as definition.
  41
  42 (* end hide *)
  43
  44 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con" as lemma.
  45
  46 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con" as lemma.
  47
  48 inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con" as lemma.
  49
  50 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con" as lemma.
  51
  52 (* UNEXPORTED
  53 End CPoly_Big
  54 *)
  55
  56 (* UNEXPORTED
  57 Section Flip_Poly
  58 *)
  59
  60 (*#* **Flipping a polynomial
  61 %\begin{convention}% Let [R] be a ring.
  62 %\end{convention}%
  63 *)
  64
  65 (* UNEXPORTED
  66 cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var
  67 *)
  68
  69 (* begin hide *)
  70
  71 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__" as definition.
  72
  73 (* end hide *)
  74
  75 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con" as definition.
  76
  77 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con" as lemma.
  78
  79 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con" as lemma.
  80
  81 (* UNEXPORTED
  82 Hint Resolve flip_coefficient: algebra.
  83 *)
  84
  85 inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con" as lemma.
  86
  87 (* UNEXPORTED
  88 End Flip_Poly
  89 *)
  90
  91 (* UNEXPORTED
  92 Hint Resolve flip_poly: algebra.
  93 *)
  94
  95 (* UNEXPORTED
  96 Section OddPoly_Signs
  97 *)
  98
  99 (*#* ** Sign of a polynomial of odd degree
 100 %\begin{convention}% Let [R] be an ordered field.
 101 %\end{convention}%
 102 *)
 103
 104 (* UNEXPORTED
 105 cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var
 106 *)
 107
 108 (* begin hide *)
 109
 110 inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__" as definition.
 111
 112 (* end hide *)
 113
 114 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con" as lemma.
 115
 116 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con" as lemma.
 117
 118 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con" as lemma.
 119
 120 (* UNEXPORTED
 121 End OddPoly_Signs
 122 *)
 123
 124 (* UNEXPORTED
 125 Section Poly_Norm
 126 *)
 127
 128 (*#* ** The norm of a polynomial
 129 %\begin{convention}% Let [R] be a field, and [RX] the polynomials over
 130 this field.
 131 %\end{convention}%
 132 *)
 133
 134 (* UNEXPORTED
 135 cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var
 136 *)
 137
 138 (* begin hide *)
 139
 140 inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__" as definition.
 141
 142 (* end hide *)
 143
 144 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con" as lemma.
 145
 146 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con" as definition.
 147
 148 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con" as lemma.
 149
 150 inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con" as lemma.
 151
 152 (* UNEXPORTED
 153 End Poly_Norm
 154 *)
 155
 156 (* UNEXPORTED
 157 Section OddPoly_Root
 158 *)
 159
 160 (*#* ** Roots of polynomials of odd degree
 161 Polynomials of odd degree over the reals always have a root. *)
 162
 163 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con" as lemma.
 164
 165 inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con" as lemma.
 166
 167 inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con" as lemma.
 168
 169 (* UNEXPORTED
 170 End OddPoly_Root
 171 *)
 172