16.40 LISTVECOPS: Vector operations on lists

Author: Eberhard Schrüfer

This package implements vector operations on lists.. Addition, multiplication, division, and exponentiation work elementwise. For example, after

  A := {a1,a2,a3,a4};
  B := {b1,b2,b3,b4};

c*A will simplify to {c*a1,..,c*a4}, A + B to {a1+b1,...,a4+b4}, and A*B to {a1*b1,...,a4*b4}. Linear operations work as expected:

c1*A + c2*B;
{a1*c1 + b1*c2,
  a2*c1 + b2*c2,
  a3*c1 + b3*c2,
  a4*c1 + b4*c2}

A division and an exponentation example:

{a,b,c}/{3,g,5};
  a   b   c
{---,---,---}
  3   g   5
ws^3;
   3    3    3
  a    b    c
{----,----,-----}
  27    3   125
       g

The new operator *. (ldot) implements the dot product:

{a,b,c,d} *. {5,7,9,11/d};
5*a + 7*b + 9*c + 11

For accessing list elements, the new operator _ (lnth) can be used instead of the PART operator:

l := {1,{2,3},4}$
lnth(l,3);
4
l _2*3;
{6,9}
l _2 _2;
3

It can also be used to modify a list (unlike PART, which returns a modified list):

part(l,2,2):=three;
{1,{2,three},4}
l;
{1,{2,3},4}
l _ 2 _2 :=three;
three
l;
{1,{2,three},4}

Operators are distributed over lists:

a *. log b;
log(b1)*a1 + log(b2)*a2 + log(b3)*a3 + log(b4)*a4
df({sin x*y,x^3*cos y},x,2,y);
{ - sin(x), - 6*sin(y)*x}
int({sin x,cos x},x);
{ - cos(x),sin(x)}

By using the keyword listproc, an algebraic procedure can be declared to return a list:

listproc spat3(u,v,w);
   begin scalar x,y;
     x := u *. w;
     y := u *. v;
     return v*x - w*y
   end;