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Tutorial-06: rings, polynomials, use command

Tutorial-06: rings, polynomials, use command

Syntax
?tutorial

Description
Tutorial-06 for CoCoA-5

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 (with the caveat 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

See Also