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1.1.9 Tutorial: polynomials

If you are new to CoCoA-5, we recommend that you read first the Tutorial: polynomial rings, use command .

A complete list of the functions and commands which operate on or return a polynomial can be obtained by looking up "RINGELEM" in the on-line manual.

In addition to the usual arithmetic operations, CoCoA-5 offers several functions for looking "inside" a polynomial. We give some examples here. Each non-zero polynomial has a leading monomial (see LM ), a leading coefficient (see LC ), and a leading term (see LT and LPP ).

One may also extract all monomials (see monomials ), all coefficients (see coefficients ), and all power-products (see support ). In each case the lists have the same order as in the polynomial itself.

There are more advanced functions for exploring the structure of a polynomial: see for instance CoefficientsWRT , CoeffListWRT , and CoeffOfTerm .

Example

/**/ use P ::= QQ[x,y]; // polys in x,y with coefficients in QQ /**/ f := (2*x^2+y)^3; f; 8*x^6 +12*x^4*y +6*x^2*y^2 +y^3 /**/ [LM(f), LC(f), LT(f)]; [8*x^6, 8, x^6] /**/ monomials(f); [8*x^6, 12*x^4*y, 6*x^2*y^2, y^3] /**/ coefficients(f); [8, 12, 6, 1] /**/ support(f); [x^6, x^4*y, x^2*y^2, y^3] /**/ CoeffListWRT(f,x); [y^3, 0, 6*y^2, 0, 12*y, 0, 8]