  | ### 7.3.19 oppose `Syntax:` `oppose (` ring_name, name `)` `Type:` poly, vector, ideal, module or matrix (the same type as the second argument) `Purpose:` for a given object in the given ring, creates its opposite object in the opposite ( opposite) ring (the last one is assumed to be the current ring). `Remark:` for any object .
      LIB "ncalg.lib";
      def R = makeUsl2();
      setring R;
      matrix m[3][4];
      poly   p  = (h^2-1)*f*e;
      vector v  = [1,e*h,0,p];
      ideal  i  = h*e, f^2*e,h*f*e;
      m         = e,f,h,1,0,h^2, p,0,0,1,e^2,e*f*h+1;
      module mm = module(m);
      def b     = opposite(R);
      setring b; b;
      ==> // coefficients: QQ
      ==> // number of vars : 3
      ==> //        block   1 : ordering a
      ==> //                  : names    H F E
      ==> //                  : weights  1 1 1
      ==> //        block   2 : ordering ls
      ==> //                  : names    H F E
      ==> //        block   3 : ordering C
      ==> // noncommutative relations:
      ==> //    FH=HF-2F
      ==> //    EH=HE+2E
      ==> //    EF=FE-H
      // we will oppose these objects: p,v,i,m,mm
      poly P    = oppose(R,p);
      vector V  = oppose(R,v);
      ideal  I  = oppose(R,i);
      matrix M  = oppose(R,m);
      module MM = oppose(R,mm);
      def c = opposite(b);
      setring c;   // now let's check the correctness:
      // print compact presentations of objects
      print(oppose(b,P)-imap(R,p));
      ==> 0
      print(oppose(b,V)-imap(R,v));
      ==> [0]
      print(matrix(oppose(b,I))-imap(R,i));
      ==> 0,0,0
      print(matrix(oppose(b,M))-imap(R,m));
      ==> 0,0,0,0,
      ==> 0,0,0,0,
      ==> 0,0,0,0
      print(matrix(oppose(b,MM))-imap(R,mm));
      ==> 0,0,0,0,
      ==> 0,0,0,0,
      ==> 0,0,0,0
See envelope; opposite.

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