O16-C043
> restart;
> with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> a:=matrix(3,3,[1,0,-1,0,1,-1,-1,-1,1]);

                             [ 1     0    -1]
                             [              ]
                        a := [ 0     1    -1]
                             [              ]
                             [-1    -1     1]

> eigenvects(a);# C'est un hyperboloïde à une nappe

  [1 + sqrt(2), 1, {[1, 1, -sqrt(2)]}],

        [1 - sqrt(2), 1, {[1, 1, sqrt(2)]}], [1, 1, {[-1, 1, 0]}]

> with(plots);

  [animate, animate3d, animatecurve, changecoords, complexplot,

        complexplot3d, conformal, contourplot, contourplot3d,

        coordplot, coordplot3d, cylinderplot, densityplot, display,

        display3d, fieldplot, fieldplot3d, gradplot, gradplot3d,

        implicitplot, implicitplot3d, inequal, listcontplot,

        listcontplot3d, listdensityplot, listplot, listplot3d,

        loglogplot, logplot, matrixplot, odeplot, pareto, pointplot,

        pointplot3d, polarplot, polygonplot, polygonplot3d,

        polyhedra_supported, polyhedraplot, replot, rootlocus,

        semilogplot, setoptions, setoptions3d, spacecurve,

        sparsematrixplot, sphereplot, surfdata, textplot, textplot3d,

        tubeplot]

> v:=matrix(3,1,[x,y,z]);

                                    [x]
                                    [ ]
                               v := [y]
                                    [ ]
                                    [z]

> surf:=evalm(transpose(v)&*a&*v)[1,1]-1;

          surf := (x - z) x + (y - z) y + (-x - y + z) z - 1

> implicitplod3d(surf,x=-3..3,y=-3..3,z=-3..3);

  implicitplod3d((x - z) x + (y - z) y + (-x - y + z) z - 1,

        x = -3 .. 3, y = -3 .. 3, z = -3 .. 3)

> d1:=implicitplot3d( surf,x=-2..2,y=-2..2,
> z=-2..2,grid=[13,13,13]):
> g:=vector([diff(surf,x),diff(surf,y),diff(surf,z)]);h:=vector([x,y,z-1]);

            g := [2 x - 2 z, 2 y - 2 z, -2 x - 2 y + 2 z]


                          h := [x, y, z - 1]

> eq2:=dotprod(g,h,orthogonal);

  eq2 := (2 x - 2 z) x + (2 y - 2 z) y + (-2 x - 2 y + 2 z) (z - 1)

> solve({surf,eq2},{x,y});# Réunion de 2 droites

                {x = z - 1, y = 0}, {y = z - 1, x = 0}

> d2:=spacecurve({[z-1,0,z],[0,z-1,z]},z=-2..2):
> display({d1,d2});

>