### 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:

1. a `cring` as given above
2. a non-negative int_expression less or equal 2147483647.
3. an expression_list of an int_expression and one or more names.
4. the name `real`
5. an expression_list of the name `real` and an int_expression.
6. an expression_list of the name `complex`, an optional int_expression and a name.
7. an expression_list of the name `ZZ`.
8. an expression_list of the name `integer` and following int_expressions.
9. 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

1. `lp`, `dp`, `Dp`, `rp`, `ls`, `ds`, `Ds`, or `rs` optionally followed by a size parameter in parentheses.

2. `wp`, `Wp`, `ws`, `Ws`, `am`, `aa`, 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`.

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.

User manual for Singular version 4.4.1, 2025, generated by texi2html.