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4.10.3 map operations

( )
composition of maps. If, for example, f and g are maps, then f(g) is a map expression giving the composition $f \circ g$ of f and g,
provided the target ring of g is the basering of f.

map_expression [ int_expressions ]
is a map entry (the image of the corresponding variable)


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