IDEAL PARAMETERS

Most operators of the Groebner package compute expressions in a polynomial ring which given as <R>[<var>,<var>,...] where <R> is the current REDUCE coefficient domain. All algebraically exact domains of REDUCE are supported. The package can operate over rings and fields. The operation mode is distinguished automatically. In general the ring mode is a bit faster than the field mode. The factoring variant can be applied only over domains which allow you factoring of multivariate polynomials.

The variable sequence <var> is either declared explicitly as argument in form of a list in torder, or it is extracted automatically from the expressions. In the second case the current REDUCE system order is used (see korder) for arranging the variables. If some kernels should play the role of formal parameters (the ground domain <R> then is the polynomial ring over these), the variable sequences must be given explicitly.

All REDUCE kernels can be used as variables. But please note, that all variables are considered as independent. E.g. when using sin(a) and cos(a) as variables, the basic relation sin(a)^2+cos(a)^2-1=0 must be explicitly added to an equation set because the Groebner operators don't include such knowledge automatically.

The terms (monomials) in polynomials are arranged according to the current term order. Note that the algebraic properties of the computed results only are valid as long as neither the ordering nor the variable sequence changes.

The input expressions <exp> can be polynomials <p>, rational functions <n>/<d> or equations <lh>=<rh> built from polynomials or rational functions. Apart from the tracing algorithms groebnert and preducet, where the equations have a specific meaning, equations are converted to simple expressions by taking the difference of the left-hand and right-hand sides <lh>-<rh>=><p>. Rational functions are converted to polynomials by converting the expression to a common denominator form first, and then using the numerator only <n>=><p>. So eventual zeros of the denominators are ignored.

A basis on input or output of an algorithm is coded as list of expressions {<exp>,<exp>,...} .