File r37/lisp/csl/html/r37_0390.html artifact 68597c53b8 part of check-in b7c3de82ef

<A NAME=groebnerf>

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



<B>GROEBNERF</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P> <H3> 
syntax: </H3>
<P>
<P>
<em>groebnerf</em>({&lt;exp&gt;, ...}[,{},{&lt;nz&gt;, ... }]); 
<P>
<P>
<P>
<P>
where {&lt;exp&gt;, ... } is a list of expressions or 
equations, and {&lt;nz&gt;,... } is 
an optional list of polynomials to be considered as non zero 
for this calculation. An empty list must be passed as second argument 
if the non-zero list is specified. 
<P>
<P>
<em>groebnerf</em>tries to separate polynomials into individual factors and 
to branch the computation in a recursive manner (factorization tree). 
The result is a list of partial Groebner bases. 
Multiplicities (one factor with a higher power, the same partial basis 
twice) are deleted as early as possible in order to speed up the 
calculation. 
<P>
<P>
The third parameter of <em>groebnerf</em> declares some polynomials 
nonzero. If any of these is found in a branch of the calculation 
the branch is canceled. 
<P>
<P>
 <P> <H3> 
example: </H3>
<P><PRE><TT>
groebnerf({ 3*x**2*y+2*x*y+y+9*x**2+5*x = 3,  
            2*x**3*y-x*y-y+6*x**3-2*x**2-3*x = -3, 
            x**3*y+x**2*y+3*x**3+2*x**2 }, {y,x});

       {{Y - 3,X},

                      2
    {2*Y + 2*X - 1,2*X  - 5*X - 5}}
</TT></PRE><P> <P> <H3> 
related: </H3>
<P>
 _ _ _ 
<A HREF=r37_0392.html>groebresmax</A>variable 
<P>
 _ _ _  
<A HREF=r37_0391.html>groebmonfac</A> variable 
<P>
 _ _ _  
<A HREF=r37_0393.html>groebrestriction</A> variable 
<P>
 _ _ _  
<A HREF=r37_0382.html>groebner</A> operator 
<P>
 _ _ _  
<A HREF=r37_0371.html>gvarslast</A> variable 
<P>
 _ _ _  
<A HREF=r37_0370.html>groebopt</A> switch 
<P>
 _ _ _  
<A HREF=r37_0372.html>groebprereduce</A> switch 
<P>
 _ _ _  
<A HREF=r37_0373.html>groebfullreduction</A> switch 
<P>
 _ _ _  
<A HREF=r37_0374.html>gltbasis</A> switch 
<P>
 _ _ _  
<A HREF=r37_0375.html>gltb</A> variable 
<P>
 _ _ _  
<A HREF=r37_0376.html>glterms</A> variable 
<P>
 _ _ _  
<A HREF=r37_0377.html>groebstat</A> switch 
<P>
 _ _ _  
<A HREF=r37_0378.html>trgroeb</A> switch 
<P>
 _ _ _  
<A HREF=r37_0379.html>trgroebs</A> switch 
<P>
 _ _ _  
<A HREF=r37_0397.html>groebnert</A> operator 
<P>
<P>
<P>