File r37/lisp/csl/html/r37_0625.html artifact f3ab6e75ec part of check-in d9e362f11e

<A NAME=Smithex_int>

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



<B>SMITHEX\_INT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The operator <em>smithex_int</em> performs the same task as <em>smithex</em> 
but on matrices containing only integer entries. Namely, 
<em>smithex_int</em> returns {S,P,P^-1} where S is the smith normal 
form of the input 
<A HREF=r37_0345.html>matrix</A> (A say), and P*S*P^-1 = A. 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>smithex_int</em>(&lt;matrix&gt;) 
<P>
<P>
&lt;matrix&gt; :- a rectangular 
<A HREF=r37_0345.html>matrix</A> of integer entries. 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
 a := mat((9,-36,30),(-36,192,-180),(30,-180,180)); 


       [ 9   -36    30 ]
       [               ]
  a := [-36  192   -180]
       [               ]
       [30   -180  180 ]



 smithex_int(a); 

    [3  0   0 ]    [-17  -5   -4 ]    [1   -24  30 ]
    [         ]    [             ]    [            ]
  { [0  12  0 ],   [64   19   15 ],   [-1  25   -30] }
    [         ]    [             ]    [            ] 
    [0  0   60]    [-50  -15  -12]    [0   -1    1 ] 

</TT></PRE><P>