matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma

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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 set "baseuri" "cic:/matita/CoRN-Decl/reals/OddPolyRootIR".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
  22
  23 include "reals/IVT.ma".
  24
  25 (*#* * Roots of polynomials of odd degree *)
  26
  27 (* UNEXPORTED
  28 Section CPoly_Big
  29 *)
  30
  31 (*#* ** Monic polynomials are positive near infinity
  32 %\begin{convention}% Let [R] be an ordered field.
  33 %\end{convention}%
  34 *)
  35
  36 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var".
  37
  38 (* begin hide *)
  39
  40 inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__".
  41
  42 (* end hide *)
  43
  44 inline "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con".
  45
  46 inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con".
  47
  48 inline "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con".
  49
  50 inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
  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 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var".
  66
  67 (* begin hide *)
  68
  69 inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__".
  70
  71 (* end hide *)
  72
  73 inline "cic:/CoRN/reals/OddPolyRootIR/flip.con".
  74
  75 inline "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con".
  76
  77 inline "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con".
  78
  79 (* UNEXPORTED
  80 Hint Resolve flip_coefficient: algebra.
  81 *)
  82
  83 inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
  84
  85 (* UNEXPORTED
  86 End Flip_Poly
  87 *)
  88
  89 (* UNEXPORTED
  90 Hint Resolve flip_poly: algebra.
  91 *)
  92
  93 (* UNEXPORTED
  94 Section OddPoly_Signs
  95 *)
  96
  97 (*#* ** Sign of a polynomial of odd degree
  98 %\begin{convention}% Let [R] be an ordered field.
  99 %\end{convention}%
 100 *)
 101
 102 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var".
 103
 104 (* begin hide *)
 105
 106 inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__".
 107
 108 (* end hide *)
 109
 110 inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con".
 111
 112 inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con".
 113
 114 inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
 115
 116 (* UNEXPORTED
 117 End OddPoly_Signs
 118 *)
 119
 120 (* UNEXPORTED
 121 Section Poly_Norm
 122 *)
 123
 124 (*#* ** The norm of a polynomial
 125 %\begin{convention}% Let [R] be a field, and [RX] the polynomials over
 126 this field.
 127 %\end{convention}%
 128 *)
 129
 130 alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var".
 131
 132 (* begin hide *)
 133
 134 inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__".
 135
 136 (* end hide *)
 137
 138 inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con".
 139
 140 inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con".
 141
 142 inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con".
 143
 144 inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
 145
 146 (* UNEXPORTED
 147 End Poly_Norm
 148 *)
 149
 150 (* UNEXPORTED
 151 Section OddPoly_Root
 152 *)
 153
 154 (*#* ** Roots of polynomials of odd degree
 155 Polynomials of odd degree over the reals always have a root. *)
 156
 157 inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con".
 158
 159 inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con".
 160
 161 inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
 162
 163 (* UNEXPORTED
 164 End OddPoly_Root
 165 *)
 166