Tutorial: polynomial rings, use command

1.1.8 Tutorial: polynomial rings, use command

When you want to do a computation in CoCoA-5, the first thing you need to do is tell CoCoA-5 in which ring to compute. The use command informs CoCoA-5 about this. The most convenient method does two things at once: it creates the polynomial ring, and then chooses that ring as the "current ring".

Once the correct current ring has been selected, you may type in polynomials using a natural syntax; note that you must use * to denote all products (e.g. between coefficients and indeterminates, or even between powers of indeterminates).

The most common coefficient fields are the rationals (denoted by QQ) and small prime finite fields (denoted by ZZ/(p)).

Example

/**/ use P ::= QQ[x,y];  // polys in x,y with coefficients in QQ
/**/ (x+y)^2;
x^2 + 2*x*y + y^2
/**/ use ZZ/(2)[a,b];    // polys in a,b with coefficients in ZZ/(2)
/**/ (a+b)^2;
a^2 + b^2
/**/ use QQ[x,y,z],lex;  // polys in x,y,z, coeffs in QQ, term order "lex"
/**/ x+y^2;
x + y^2