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About: About this document ring declarations (plural)

ring name = ( coefficient_field ), ( names_of_ring_variables ), ( ordering );
declares a ring and sets it as the actual basering.

The coefficient_field is given by one of the following:

  1. a non-negative int_expression less or equal 2147483647.
  2. an expression_list of an int_expression and one or more names.
  3. the name real.
  4. an expression_list of the name real and an int_expression.
  5. an expression_list of the name complex, an optional int_expression and a name.

'names_of_ring_variables' must be a list of names or indexed names.

'ordering' is a list of block orderings where each block ordering is either

  1. lp, dp, Dp, optionally followed by a size parameter in parentheses.

  2. wp, Wp, or a followed by a weight vector given as an intvec_expression in parentheses.

  3. M followed by an intmat_expression in parentheses.

  4. c or C.

As long as all non-commuting variables are global, any ordering may be used. In graded commutative algebras, one may also use ls, ds, Ds, ws, and Ws.

If one of coefficient_field, names_of_ring_variables, and ordering consists of only one entry, the parentheses around this entry may be omitted.

In order to create a non-commutative structure over a commutative ring, use nc_algebra.