### 7.8.3 freeAlgebra (letterplace)

`Syntax:`
  `freeAlgebra(` ring_expression r, int_expression d `)`
`Type:`
  ring
`Purpose:`
  Creates a free (letterplace) ring with the variables of the ring `r` up to the degree (length) bound `d`, with the monomial ordering, determined by those on the ring `r`.
`Note:`
  A letterplace ring has an attribute called `isLetterplaceRing`, which is zero for non-letterplace rings and contains the number of variables of the free algebra it encodes, otherwise.
`Example:`

      LIB "freegb.lib";
      ring r = 0,(x,y,z),dp;
      ring R = freeAlgebra(r, 7); // this ordering is degree right lex
      R;
      ==> // coefficients: QQ considered as a field
      ==> // number of vars : 21
      ==> //        block   1 : ordering dp
      ==> //                  : names    x y z x y z x y z x y z x y z x y z x y z
      ==> //        block   2 : ordering C
      ==> // letterplace ring (block size 3, ncgen count 0)
      attrib(R,"isLetterplaceRing");
      ==> 3
      ring r2 = 0,(x,y,z),lp;
      ring R2 = freeAlgebra(r2, 5); // note, that this ordering is NOT left or right lex
      R2;
      ==> // coefficients: QQ considered as a field
      ==> // number of vars : 15
      ==> //        block   1 : ordering a
      ==> //                  : names    x y z x y z x y z x y z x y z
      ==> //                  : weights  1 0 0 1 0 0 1 0 0 1 0 0 1 0 0
      ==> //        block   2 : ordering a
      ==> //                  : names    x y z x y z x y z x y z x y z
      ==> //                  : weights  0 1 0 0 1 0 0 1 0 0 1 0 0 1 0
      ==> //        block   3 : ordering a
      ==> //                  : names    x y z x y z x y z x y z x y z
      ==> //                  : weights  0 0 1 0 0 1 0 0 1 0 0 1 0 0 1
      ==> //        block   4 : ordering lp
      ==> //                  : names    x y z x y z x y z x y z x y z
      ==> //        block   5 : ordering C
      ==> // letterplace ring (block size 3, ncgen count 0)
      attrib(R2,"isLetterplaceRing");
      ==> 3

See Monomial orderings on free algebras.

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