MANUAL DE USO DEL PACKAGE HYPERBOL

A continuación, y en el orden en el que aparecen a lo largo de esta memoria, damos ejemplos de uso de las distintas órdenes del package así como las descripciones que aparecen cuando se pregunta por cada una de ellas.

<< Geometry`Hyperbol`

?Angulo

Angulo[{1. , 0. }, {0. , 1. }]

?Cayley

Cayley[{0. , 1. }]

?InCayley

InCayley[{0. , 0. }]

?Hdist

Hdist[{2. , 1. }, {3. , 4. }]

?HDdist

HDdist[{0.1, 0.4}, {-0.2, 0.3}]

?Hrecta

Hrecta[{1. , 1. }, {1.1, 2.1}]

?GrHrecta

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[{1. , 2. }]}}], GrHrecta[{1. , 1. }, {1. , 2. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> 1];

?HDrecta

HDrecta[{1. , 0. }, {0. , 0.8}]

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0. }]}, {PointSize[0.03], 
              Point[{0.3, 0.5}]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDrecta[{0.1, 0. }, {0.3, 0.5}], PlotRange -> All, 
        AspectRatio -> Automatic, 
        DisplayFunction -> $DisplayFunction];

?GrHDrecta

Show[
        Graphics[{{PointSize[0.03], Point[{0.5, 0.3}]}, {PointSize[0.03], 
              Point[{1. , 0. }]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDrecta[{1. , 0. }, {0.5, 0.3}], PlotRange -> All, 
        AspectRatio -> Automatic, 
        DisplayFunction -> $DisplayFunction];

v = {1. , 0. }
v == {1. , 0. }

?GrHsegmento

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[{3. , 4. }]}}], GrHsegmento[{1. , 1. }, {3. , 4. }], 
        DisplayFunction -> $DisplayFunction];

?GrHDsegmento

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-0.6, 0.5}]}, {PointSize[0.03], Point[{0.8, 0.1}]}, 
            Circle[{0. , 0. }, 1. ]}], 
        GrHDsegmento[{-0.6, 0.5}, {0.8, 0.1}], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?Hmediatriz

Hmediatriz[{1. , 1. }, {2. , 2. }]

?GrHmediatriz

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[{2. , 1. }]}}], GrHmediatriz[{1. , 1. }, {2. , 1. }], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> 1];

?HDmediatriz

HDmediatriz[{0.1, 0.1}, {0.2, 0.2}]

?GrHDmediatriz

Show[
        Graphics[{{PointSize[0.03], Point[{0.5, 0.5}]}, {PointSize[0.03], 
              Point[{0.1, 0.5}]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDmediatriz[{0.5, 0.5}, {0.1, 0.5}], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

Show[
        Graphics[{{PointSize[0.03], Point[{0.5, 0. }]}, {PointSize[0.03], 
              Point[{0. , 0.5}]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDmediatriz[{0.5, 0. }, {0. , 0.5}], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?Hreflexion

Hreflexion[{1. , 1. }, {2. , 1. }, {2. , 2. }]

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[Hreflexion[{1. , 1. }, {2. , 1. }, {1. , 3. }]]}}], 
        GrHrecta[{2. , 1. }, {1. , 3. }], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?HDreflexion

HDreflexion[{0.1, 0.1}, {0.2, 0.1}, {0.2, 0.2}]

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0.1}]}, {PointSize[0.03], 
              Point[HDreflexion[{0.1, 0.1}, {0.2, 0.1}, {0.1, 0.3}]]}, 
            Circle[{0. , 0. }, 1. ]}], GrHDrecta[{0.2, 0.1}, {0.1, 0.3}], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?Htrasrec

Htrasrec[{4. , 2. }, {1. , 3. }, 2. ]

Show[
        Graphics[{{PointSize[0.03], Point[{4. , 2. }]}, {PointSize[0.03], 
              Point[Htrasrec[{4. , 2. }, {1. , 3. }, 2. ]]}}], 
        GrHrecta[{4. , 2. }, {1. , 3}], 
        AspectRatio -> Automatic];

?HDtrasrec

HDtrasrec[{0.4, 0.2}, {0.1, 0.3}, 2. ]

Show[
        Graphics[{Circle[{0. , 0. }, 1. ], {PointSize[0.03], 
              Point[{0.4, 0.2}]}, 
{PointSize[0.03], 
              Point[HDtrasrec[{0.4, 0.2}, {0.1, 0.3}, 2. ]]}}], 
        GrHDrecta[{0.4, 0.2}, {0.1, 
            0.3}], 
AspectRatio -> Automatic, 
        PlotRange -> All];

?Hcirc

Hcirc[{1. , 1. }, 1. ]

?GrHcirc

Show[Graphics[{{PointSize[0.03], Point[{1. , 1. }]}}], 
        GrHcirc[{1. , 1. }, 1. ], DisplayFunction -> $DisplayFunction, 
        PlotRange -> All, AspectRatio -> Automatic];

?HDcirc

HDcirc[{0.1, 0.1}, 1. ]

?GrHDcirc

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0.1}]}, 
            Circle[{0. , 0. }, 1. ]}], GrHDcirc[{0.1, 0.1}, 1. ], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?Hgiro

Hgiro[{0. , 1. }, Pi/2. , {1. , 1. }]

Show[
        Graphics[{{PointSize[0.03], Point[{0. , 1. }]}, {PointSize[0.03], 
              Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[Hgiro[{0. , 1. }, Pi/2. , {1. , 1. }]]}}], 
        GrHcirc[{0. , 1. }, Hdist[{1. , 1. }, {0. , 1. }]], 
        GrHrecta[{0. , 1. }, {1. , 1. }], 
        GrHrecta[{0. , 1. }, Hgiro[{0. , 1. }, Pi/2. , {1. , 1. }]], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

?HDgiro

HDgiro[{0. , 0.4}, Pi/2. , {0.4, 0.4}]

Show[
        Graphics[{Circle[{0. , 0. }, 1. ], {PointSize[0.03], 
              Point[{0. , 0.4}]}, {PointSize[0.03], 
              Point[{0.4, 0.4}]}, {PointSize[0.03], 
              Point[HDgiro[{0. , 0.4}, Pi/2. , {0.4, 0.4}]]}}], 
        GrHDcirc[{0. , 0.4}, HDdist[{0.4, 0.4}, {0. , 0.4}]], 
        GrHDrecta[{0. , 0.4}, {0.4, 0.4}], 
        GrHDrecta[{0. , 0.4}, HDgiro[{0. , 0.4}, Pi/2. , {0.4, 0.4}]], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, Axes -> True, 
        PlotRange -> All];

?Htraslacion

Htraslacion[{1. , 1. }, {4. , 1. }]

?GrHtraslacion

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize[0.03], 
              Point[{4. , 1. }]}}], GrHtraslacion[{1. , 1. }, {4. , 1. }], 
        GrHrecta[{1. , 1}, {4. , 1. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

?HDtraslacion

HDtraslacion[{0.1, 0.1}, {0.4, 0.1}]

?GrHDtraslacion

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0.1}]}, {PointSize[0.03], 
              Point[{0.4, 0.1}]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDtraslacion[{0.1, 0.1}, {0.4, 0.1}], 
        GrHDrecta[{0.1, 0.1}, {0.4, 0.1}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

?Hperp

Hperp[{1. , 1. }, {-1. , 1. }]

?GrHperp

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 1. }]}, {PointSize [0.03], 
              Point[{-1. , 1. }]}}], 
        GrHperp[{1. , 1. }, {-1. , 1. }], 
        GrHrecta[{1. , 1. }, {-1. , 1. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

?HDperp

HDperp[{0.1, 0.1}, {-0.1, 0.1}]

?GrHDperp

Show[
        Graphics[{Circle[{0. , 0. }, 1. ], {PointSize[0.03], 
              Point[{0.1, 0.1}]}, {PointSize [0.03], 
              Point[{-0.1, 0.1}]}}], 
        GrHDperp[{0.1, 0.1}, {-0.1, 0.1}], 
        GrHDrecta[{0.1, 0.1}, {-0.1, 0.1}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

?Horociclo1

Horociclo1[{1. , 2. }, 2. ]

Horociclo1[{1. , 2. }, Infinity]

?GrHorociclo1

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 2. }]}, {PointSize[0.03], 
              Point[{2. , 0. }]}}], GrHorociclo1[{1. , 2. }, 2. ], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

Show[Graphics[{{PointSize[0.03], Point[{1. , 2. }]}}], 
        GrHorociclo1[{1. , 2. }, Infinity], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

?HDhorociclo1

HDhorociclo1[{0.1, 0.2}, {0.6, 0.8}]

?GrHDhorociclo1

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0.2}]}, {PointSize[0.03], 
              Point[{0.6, 0.8}]}}], GrHDhorociclo1[{0.1, 0.2}, {0.6, 0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

?Horociclo2

Horociclo2[{1. , 2. }, {2. , 3. }]

Horociclo2[{1. , 2. }, {2. , 2. }]

?GrHorociclo2

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 2. }]}, {PointSize[0.03], 
              Point[{2. , 3. }]}}], GrHorociclo2[{1. , 2. }, {2. , 3. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

Show[
        Graphics[{{PointSize[0.03], Point[{1. , 2. }]}, {PointSize[0.03], 
              Point[{2. , 2. }]}}], GrHorociclo2[{1. , 2. }, {2. , 2. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

?HDhorociclo2

HDhorociclo2[{0.1, 0.2}, {0.3, 0.4}]

HDhorociclo2[Cayley[{1. , 2. }], Cayley[{2. , 2. }]]

HDhorociclo2[Cayley[{1. , 2. }], Cayley[{2. , 3. }]]

?GrHDhorociclo2

Show[
        Graphics[{{PointSize[0.03], Point[{0.1, 0.2}]}, {PointSize[0.03], 
              Point[{0.3, 0.4}]}}], GrHDhorociclo2[{0.1, 0.2}, {0.3, 0.4}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

Show[
        Graphics[{{PointSize[0.03], 
              Point[Cayley[{1. , 2. }]]}, {PointSize[0.03], 
              Point[Cayley[{2, 3. }]]}}], 
        GrHDhorociclo2[Cayley[{1. , 2. }], Cayley[{2. , 3. }]], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

Show[
        Graphics[{{PointSize[0.03], 
              Point[Cayley[{1. , 2. }]]}, {PointSize[0.03], 
              Point[Cayley[{2, 2. }]]}}], 
        GrHDhorociclo2[Cayley[{1. , 2. }], Cayley[{2. , 2. }]], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic];

?HperpComun

p = 
      HperpComun[{2. , 1. }, {3. , 2. }, {-3. , 2. }, {-1. , 
          1. }]

Show[
        Graphics[{{PointSize[0.03], Point[{2. , 1. }]}, {PointSize[0.03], 
              Point[{3. , 2. }]}, {PointSize[0.03], 
              Point[{-3. , 2. }]}, {PointSize[0.03], 
              Point[{-1. , 1. }]}}], GrHrecta[{2. , 1. }, {3. , 2. }], 
        GrHrecta[{-3. , 2. }, {-1. , 1. }], 
        GrHrecta[{p[[1]] - p[[2]], 0. }, {p[[1]] + p[[2]], 
            0. }], AspectRatio -> Automatic, 
        DisplayFunction -> $DisplayFunction, 
        PlotRange -> All];

?HDperpComun

p = 
      HDperpComun[{0.2, 0.1}, {0.3, 
          0.6}, {-0.3, -0.2}, {-0.1, -0.8}]

Show [
        Graphics[{Circle[{0. , 0. }, 1. ], {PointSize[0.03], 
              Point[{0.2, 0.1}]}, {PointSize[0.03], 
              Point[{0.3, 0.6}]}, {PointSize[0.03], 
              Point[{-0.3, -0.2}]}, {PointSize[0.03], 
              Point[{-0.1, -0.8}]}}], 
        GrHDrecta[{0.2, 0.1}, {0.3, 0.6}], 
        GrHDrecta[{-0.3, -0.2}, {-0.1, -0.8}], 
        GrHDrecta[p[[1]], p[[2]]], 
        DisplayFunction -> $DisplayFunction, PlotRange -> All, 
        AspectRatio -> Automatic];

?Hiperciclo

Hiperciclo[-1. , 1. , {0. , 3. }]

?GrHiperciclo

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-1. , 0. }]}, {PointSize[0.03], 
              Point[{1. , 0. }]}, {PointSize[0.03], Point[{0. , 3. }]}}], 
        GrHrecta[{-1. , 0. }, {1. , 0. }], 
        GrHiperciclo[-1. , 1. , {0. , 3. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

Hiperciclo[-2. , 2. , {0. , 19. }]

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-2. , 0. }]}, {PointSize[0.03], 
              Point[{2. , 0. }]}, {PointSize[0.03], Point[{0. , 19. }]}}], 
        GrHrecta[{-2. , 0. }, {2. , 0. }], 
        GrHiperciclo[-2. , 2. , {0. , 19. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

Hiperciclo[-1. , 1. , {0. , 1. }]

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-1. , 0. }]}, {PointSize[0.03], 
              Point[{1. , 0. }]}, {PointSize[0.03], Point[{0. , 1. }]}}], 
        GrHrecta[{-1. , 0. }, {1. , 0. }], 
        GrHiperciclo[-1. , 1. , {0. , 1. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

Hiperciclo[-1. , Infinity, {2. , 3. }]

Show[
        Graphics[{Line[{{-2. , 0. }, {4. , 0. }}], {PointSize[0.03], 
              Point[{-1. , 0. }]}, {PointSize[0.03], 
              Point[{2. , 3. }]}}], 
        GrHrecta[{-1. , 0. }, {-1. , 3. }], 
        GrHiperciclo[-1. , Infinity, {2. , 3. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

Hiperciclo[-1. , Infinity, {-1. , 3. }]

Show[
        Graphics[{Line[{{-2. , 0. }, {0. , 0. }}], {PointSize[0.09], 
              Point[{-1. , 0. }]}, {PointSize[0.09], 
              Point[{-1. , 3. }]}}], 
        GrHrecta[{-1. , 0. }, {-1. , 3. }], 
        GrHiperciclo[-1. , Infinity, {-1. , 3. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

?HDhiperciclo

HDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , 0.8}]

?GrHDhiperciclo

Show[
        Graphics[{{PointSize[0.03], Point[{0.6, 0.8}]}, {PointSize[0.03], 
              Point[{-0.6, 0.8}]}, {PointSize[0.03], Point[{0. , 0.1}]}, 
            Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , 0.1}], 
        GrHDrecta[{0.6, 0.8}, {-0.6, 0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

HDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , 0.1}]

Show[
        Graphics[{{PointSize[0.03], Point[{0.6, 0.8}]}, {PointSize[0.03], 
              Point[{-0.6, 0.8}]}, {PointSize[0.03], Point[{0. , 0.8}]}, 
            Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , 0.8}], 
        GrHDrecta[{0.6, 0.8}, {-0.6, 0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

HDhiperciclo[{-0.6, 0.8}, {0.6, 0.8}, {-0.1, 0. }]

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-0.6, 0.8}]}, {PointSize[0.03], 
              Point[{0.6, 0.8}]}, {PointSize[0.03], Point[{0. , 0.9}]}, 
            Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , 0.9}], 
        GrHDrecta[{-0.6, 0.8}, {0.6, 0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

HDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , -0.95}]

Show[
        Graphics[{{PointSize[0.03], Point[{0.6, 0.8}]}, {PointSize[0.03], 
              Point[{-0.6, 0.8}]}, {PointSize[0.03], 
              Point[{0. , -0.95}]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{0.6, 0.8}, {-0.6, 0.8}, {0. , -0.95}], 
        GrHDrecta[{0.6, 0.8}, {-0.6, 0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

HDhiperciclo[{-0.6, 0.8}, {0.6, 0.8}, {0. , 0.1}]

Show[
        Graphics[{{PointSize[0.03], 
              Point[{-0.6, 0.8}]}, {PointSize[0.03], 
              Point[{-0.6, -0.8}]}, {PointSize[0.03], 
              Point[{-0.6, 0. }]}, Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{-0.6, 0.8}, {-0.6, -0.8}, {-0.6, 
            0. }], GrHDrecta[{-0.6, 0.8}, {-0.6, -0.8}], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];

HDhiperciclo[{0.6, 0.8}, {1. , 0. }, {0. , 0.5}]

Show[
        Graphics[{{PointSize[0.03], Point[{0.6, 0.8}]}, {PointSize[0.03], 
              Point[{1. , 0. }]}, {PointSize[0.03], Point[{0. , 0.5}]}, 
            Circle[{0. , 0. }, 1. ]}], 
        GrHDhiperciclo[{0.6, 0.8}, {1. , 0. }, {0. , 0.5}], 
        GrHDrecta[{0.6, 0.8}, {1. , 0. }], 
        DisplayFunction -> $DisplayFunction, 
        AspectRatio -> Automatic, PlotRange -> All];