Singular Manual: ring declarations

| ### 4.20.2 ring declarations Syntax: `ring` name `= (` coefficients `),` `(` names_of_ring_variables `),` `(` ordering `);` or `ring` name `=` cring `[` names_of_ring_variables `]` Default: `(ZZ/32003)[x,y,z]` Purpose: declares a ring and sets it as the actual basering. The second form sets the ordering to `(dp,C)`. For the second form: `cring` stands currently for `QQ` (the rationals), `ZZ` (the integers) or `(ZZ/m)` (the field (m prime and <2147483648) resp. ring of the integers modulo m). The coefficients for the first form are given by one of the following: a `cring` as given above a non-negative int_expression less or equal 2147483647. an expression_list of an int_expression and one or more names. the name `real` an expression_list of the name `real` and an int_expression. an expression_list of the name `complex`, an optional int_expression and a name. an expression_list of the name `ZZ`. an expression_list of the name `integer` and following int_expressions. an expression_list of the name `integer` and two int_expressions. For the definition of the 'coefficients', see Rings and orderings. 'names_of_ring_variables' must be a list of names or (multi-)indexed names. 'ordering' is a list of block orderings where each block ordering is either `lp`, `dp`, `Dp`, `rp`, `ls`, `ds`, `Ds`, or `rs` optionally followed by a size parameter in parentheses. `wp`, `Wp`, `ws`, `Ws`, `am`, `aa`, or `a` followed by a weight vector given as an intvec_expression in parentheses. `M` followed by an intmat_expression in parentheses. `c` or `C`. For the definition of the orderings, see Term orderings, Monomial orderings. If one of coefficients, names_of_ring_variables, and ordering consists of only one entry, the parentheses around this entry may be omitted. See also Examples of ring declarations; ring; ringlist.

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