4.8.3 map operations

( )

composition of maps. If, for example, f and g are maps, then f(g) is a map expression giving the composition of f and g.

map_expression [ int_expressions ]

is a map entry (the image of the corresponding variable)

Example:

  ring r=0,(x,y),dp;
  map f=r,y,x;    // the map f permutes the variables
  f;
→ f[1]=y
→ f[2]=x
  poly p=x+2y3;
  f(p);
→ 2x3+y
  map g=f(f);    // the map g defined as  f^2 is the identity
  g;
→ g[1]=x
→ g[2]=y
  g(p) == p;
→ 1