
<A NAME=Ideal_Parameters>

<TITLE>Ideal_Parameters</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>IDEAL PARAMETERS</B><P>
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Most operators of the <em>Groebner</em> package compute expressions in a 
polynomial ring which given as &lt;R&gt;[&lt;var&gt;,&lt;var&gt;,...] where 
&lt;R&gt; 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. 
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The variable sequence &lt;var&gt; is either declared explicitly as argument 
in form of a 
<A HREF=r37_0053.html>list</A> in 
<A HREF=r37_0354.html>torder</A>, or it is extracted 
automatically from the expressions. In the second case the current REDUCE 
system order is used (see 
<A HREF=r37_0198.html>korder</A>) for arranging the variables. 
If some kernels should play the role of formal parameters (the ground 
domain &lt;R&gt; then is the polynomial ring over these), the variable 
sequences must be given explicitly. 
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All REDUCE 
<A HREF=r37_0002.html>kernel</A>s can be used as variables. But please note, 
that all variables are considered as independent. E.g. when using 
<em>sin(a)</em> and <em>cos(a)</em> as variables, the basic relation 
<em>sin(a)^2+cos(a)^2-1=0</em> must be explicitly added to an equation set 
because the Groebner operators don't include such knowledge automatically. 
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The terms (monomials) in polynomials are arranged according to the current 

<A HREF=r37_0353.html>term order</A>. Note that the algebraic properties of the 
computed 
results only are valid as long as neither the ordering nor the variable 
sequence changes. 
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The input expressions &lt;exp&gt; can be polynomials &lt;p&gt;, rational 
functions &lt;n&gt;/&lt;d&gt; or equations &lt;lh&gt;=&lt;rh&gt; built from 
polynomials or rational functions. Apart from the <em>tracing</em> 
algorithms 
<A HREF=r37_0397.html>groebnert</A> and 
<A HREF=r37_0398.html>preducet</A>, 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 
&lt;lh&gt;-&lt;rh&gt;=&gt;&lt;p&gt;. Rational functions are converted to 
polynomials by converting the expression to a common denominator form 
first, and then using the numerator only &lt;n&gt;=&gt;&lt;p&gt;. So eventual 
zeros of the denominators are ignored. 
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A basis on input or output of an algorithm is coded as 
<A HREF=r37_0053.html>list</A> of 
expressions {&lt;exp&gt;,&lt;exp&gt;,...} . 
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