univpoly1 http://www.riaca.win.tue.nl/cds/poly1.ocd 2003-04-01 2001-07-14 experimental 1 0 quant1 logic1 relation1 alg1 polyr set1 arith1 We define univariate polynomials. univariate_polynomial Is used to define an univariate polynomial. univariate_polynomial( ring(), monomials( monomial(value1, order1), ..., monomial(valueN, orderN) ), (OMV)? ). Note that if we allow the ring to be a polynomial ring an then take value1, ..., valueN polynomial then we have also a multivariate polynomial. The OMV is optional and is meant just in case you want some presentation issues. The polynomial 1 + 2*x^2 is represented as 1 0 2 2 The polynomial 1-5*x+2*x^2 is represented as 1 0 5 1 2 2 The polynomial 1-(a+b)*z+2*z^2, a and b constants, is represented as 1 0 1 2 2 Presentation note: if you omit the indeterminate the XSLT stylesheet we use to get the MathML presentation assumes the indeterminate is X. 1 0 1 2 2 ring Used to define a ring constructor. monomials List of monomial terms. monomials(monomial(value1, order1),...,monomial(valueN, orderN)). order should be either an OMI or an OMV. monomial An specific monomial(value, order). order should be either an OMI or an OMV gcd The n-ary greatest commun divisor for univariate polynomials. The gcd(X,Y,Z). factor The action of factoring a polynomial into irreducible factors (I know this is field dependent but lets keep it simple by now). factors The action of returning a list composed of the irreducible factors of a polynomial. (I know this is field dependent but lets keep it simple by now). The gcd(X,Y,Z). expand Expands a polynomial. Acts as expand(expresion).