### 7.3.7 fetch (plural)

`Syntax:`
  `fetch (` ring_name`,` name `)`
`Type:`
  number, poly, vector, ideal, module, matrix or list (the same type as the second argument)
`Purpose:`
  maps objects between rings. `fetch` is the identity map between rings and qrings, the i-th variable of the source ring is mapped to the i-th variable of the basering. The coefficient fields must be compatible. (See map (plural) for a description of possible mappings between different ground fields).
  `fetch` offers a convenient way to change variable names or orderings, or to map objects from a ring to a quotient ring of that ring or vice versa.
`Note:`
  Compared with `imap`, `fetch` uses the position of the ring variables, not their names.
`Example:`

      LIB "ncalg.lib";
      def Usl2 = makeUsl2(); // this algebra is U(sl_2)
      setring Usl2;
      option(redSB);
      option(redTail);
      poly  C  = 4*e*f+h^2-2*h; // the central element of Usl2
      ideal I  = e^3,f^3,h^3-4*h;
      ideal J  = twostd(I);
       // print a compact presentation of J:
      print(matrix(ideal(J[1..5]))); // first 5 generators
      ==> h3-4h,fh2-2fh,eh2+2eh,f2h-2f2,2efh-h2-2h
      print(matrix(ideal(J[6..size(J)]))); // last generators
      ==> e2h+2e2,f3,ef2-fh,e2f-eh-2e,e3
      ideal QC = twostd(C-8);
      qring Q  = QC;
      ideal QJ = fetch(Usl2,J);
      QJ = std(QJ);
      // thus QJ is the image of I in the factor-algebra QC
      print(matrix(QJ)); // print QJ compactly
      ==> h3-4h,fh2-2fh,eh2+2eh,f2h-2f2,e2h+2e2,f3,e3

See imap (plural); map (plural); qring (plural); ring (plural).

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