Singular Manual: map operations

| ### 4.12.3 map operations `( )` composition of maps. If, for example, `f` and `g` are maps, then `f(g)` is a map expression giving the composition 89#89 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) 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

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