archive/share/trash/differ.dem

   1 /*  Sample usage of difference equation package  -*-Macsyma-*- */
   2 if get('differ,'version)=false then load(differ)$
   3
   4 a:matrix([1,-1],[-5,5]);
   5 eigenvalues(a);
   6 eigenvector(a,0);
   7 eigenvector(a,6);
   8 normalize:true$
   9 eigenvector(a,0);
  10
  11 /*  First order equations  */
  12
  13 f[n+1]=f[n];
  14 difference(%,f[n]);
  15
  16 g[0]:1$
  17 g[n+1]=2*g[n];
  18 difference(%,g[n]);
  19
  20 h[n+1]=3*h[n]+2;
  21 difference(%,h[n]);
  22
  23 /*  Systems of homogeneous first order equations  */
  24
  25 differverbose:true$
  26 eqn1:y[k+1]+z[k]-3*y[k]=0;
  27 eqn2:3*y[k]+z[k+1]-5*z[k]=0;
  28 difference([eqn1,eqn2],[y[k],z[k]]);
  29
  30 /*  Second order equations */
  31
  32 y[k+2]-6*y[k+1]+8*y[k]=0;
  33 difference(%,y[k]);
  34
  35 differverbose:false$
  36
  37 y[0]:3$
  38 y[1]:2$
  39 y[k+2]-6*y[k+1]+8*y[k]=0;
  40 difference(%,y[k]);
  41 part(%,2),k=5;
  42
  43 /*  Fibonacci Numbers:   1, 1, 2, 3, 5, 8, 13, 21, ...  */
  44
  45 f[0]:1$
  46 f[1]:1$
  47 f[n+2]=f[n+1]+f[n];
  48 difference(%,f[n]);
  49 ratsimp(ev(part(%,2),n=7));
  50
  51 /* Cleanup */
  52
  53 remvalue(a);