share/vector/rtest_vector_rebuild.mac

   1 (kill(all), 'done);
   2 'done$
   3
   4 (load("vector_rebuild"), 'done);
   5 'done;
   6
   7 [1,2]+t*[3,4], vector_simp;
   8 [3*t+1,4*t+2]$
   9
  10 vector_rebuild([3*t+1,4*t+2], [t]);
  11 t*[3,4]+[1,2]$
  12
  13 vector_rebuild([1,2]+t*[3,4]+[5,6]+(t/2-1)*[7,8], [t]);
  14 t*[13/2,8]+[-1,0]$
  15
  16 covect([1/2,1/3,1/4]), vector_factor;
  17 (1/12)*matrix([6],[4],[3])$
  18
  19 /*
  20 `vector_factor' returns
  21 ((MTIMES SIMP) -1 ((MTIMESQ SIMP) 2 ((MLIST SIMP) 1 2))) */
  22 block([vector_factor_minus:true],
  23   args(vector_factor([-2,-4])));
  24 [2*[1, 2]]$
  25
  26 extract_equations([1,2]+t*[3,4] = [4,3]+s*[2,1]);
  27 [3*t+1 = 2*s+4,4*t+2 = s+3]$
  28
  29 [1,0,0]~[0,1,0];
  30 [0,0,1]$
  31
  32 block([v: covect([1,2])], 1/|v|*v);
  33 (1/sqrt(5))*matrix([1],[2])$
  34
  35 (v([args]):= covect(args), 'done);
  36 done$
  37
  38 block([plane1, plane2, veq, sys, so, params],
  39   plane1: v(1,2,3)+p*v(4,5,6)+q*v(7,8,9),
  40   plane2: v(3,2,1)+r*v(6,5,4)+s*v(9,8,7),
  41   veq: plane1 = plane2,
  42   sys: extract_equations(veq),
  43   so: algsys(sys,[p,q,r,s]),
  44   params: subst([%rnum_list[1]=u, %rnum_list[2]=v], so),
  45   vector_rebuild(subst(params, plane2), [u, v]));
  46 v*matrix([7],[8],[9])+u*matrix([4],[5],[6])+matrix([1],[2],[3])$
  47
  48 block([n, a, plane],
  49   n: [1,2,3], a: [2,0,1],
  50   plane: x.n = a.n,
  51   plane: vector_simp(plane),
  52   plane: subst(x=[x1,x2,x3], plane),
  53   vector_simp(plane));
  54 3*x3+2*x2+x1 = 5$
  55
  56 block([n],
  57   n: v(1,2,3),
  58   1/|n|*n);
  59 (1/sqrt(14))*matrix([1],[2],[3])$
  60
  61 block([n, a, plane],
  62   n: v(1,2,3),
  63   a: v(2,0,1),
  64   plane: x.n = a.n,
  65   vector_simp(plane));
  66 x . matrix([1],[2],[3]) = 5$
  67
  68 block([point, a, n, en],
  69   point: v(0,1,2),
  70     a: v(2,0,1),
  71     n: v(1,2,3),
  72     en: 1/|n|*n,
  73     |(point-a)*en|);
  74   sqrt(17)/sqrt(14)$
  75
  76 block([a, n, en],
  77   a: v(2,0,1),
  78   n: v(1,2,3),
  79   en: 1/|n|*n,
  80   [vector_simp(a+t*en), vector_factor(vector_rebuild(a+t*en, [t]))]);
  81 [matrix([t/sqrt(14)+2],[(2*t)/sqrt(14)],[(3*t)/sqrt(14)+1]),
  82 (t/sqrt(14))*matrix([1],[2],[3])+matrix([2],[0],[1])]$
  83
  84 args(vector_factor(v(-2,-4)));
  85 [2,matrix([-1],[-2])]$
  86
  87 block([vector_factor_minus:true], args(vector_factor(v(-2,-4))));
  88 [2*matrix([1],[2])]$
  89
  90 block([vector_factor: true, M, M_1],
  91   M: matrix([1,2],[3,-1]),
  92   M_1: M^^-1,
  93   vector_simp(M.M_1));
  94 matrix([1,0],[0,1])$
  95
  96 (kill(v), 'done);
  97 'done$