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2.2.11 Setting Up a Ring
A CoCoA session automatically starts with the default ring, R = QQ[x,y,z]. The command Use is used to change rings. The following example shows how to create the ring ZZ/(5)[a,b,c] (the coefficient ring is the integers mod 5). Once the ring has been declared, one may start to play with polynomials, ideals, modules, and other constructions in that ring. In the ring declaration, the indeterminates are optionally separated by commas, and note the use of two colons.

Some details on handling several rings is provided below in the section of the Tutorial entitled Using More Than One Ring and Ring Mapping Example.

  Use S ::= ZZ/(5)[a,b,c];
  F := a-b;
  I := Ideal(F^2,c);
Ideal(a^2 - 2ab + b^2, c)
  J := Ideal(a-b);
  I + J;
Ideal(a^2 - 2ab + b^2, c, a - b)
  Minimalized(It);  -- find a minimal set of generators for I+J
Ideal(a - b, c)