### 7.3.6 envelope

`Syntax:`
  `envelope (` ring_name `)`
`Type:`
  ring
`Purpose:`
  creates an enveloping algebra of a given algebra, that is , where is the opposite algebra of .
`Remark:`
  You have to activate the ring with the `setring` command. For the presentation, see explanation of `opposite` in opposite.

      LIB "ncalg.lib";
      def A = makeUsl2();
      setring A; A;
      ==> // coefficients: QQ considered as a field
      ==> // number of vars : 3
      ==> //        block   1 : ordering dp
      ==> //                  : names    e f h
      ==> //        block   2 : ordering C
      ==> // noncommutative relations:
      ==> //    fe=ef-h
      ==> //    he=eh+2e
      ==> //    hf=fh-2f
      def Aenv = envelope(A);
      setring Aenv;
      Aenv;
      ==> // coefficients: QQ considered as a field
      ==> // number of vars : 6
      ==> //        block   1 : ordering dp
      ==> //                  : names    e f h
      ==> //        block   2 : ordering a
      ==> //                  : names    H F E
      ==> //                  : weights  1 1 1
      ==> //        block   3 : ordering ls
      ==> //                  : names    H F E
      ==> //        block   4 : ordering C
      ==> // noncommutative relations:
      ==> //    fe=ef-h
      ==> //    he=eh+2e
      ==> //    hf=fh-2f
      ==> //    FH=HF-2F
      ==> //    EH=HE+2E
      ==> //    EF=FE-H

See oppose; opposite.

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