
<A NAME=CRAMER>

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



<B>CRAMER</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>switch</B><P>
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When the <em>cramer</em> switch is on, 
<A HREF=r37_0345.html>matrix</A> inversion 
and linear equation 
solving (operator 
<A HREF=r37_0179.html>solve</A>) is done by Cramer's rule, through exterior 
multiplication. Default is <em>off</em>. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
on time; 

  Time: 80 ms 


off output; 

  Time: 100 ms 


mm := mat((a,b,c,d,f),(a,a,c,f,b),(b,c,a,c,d), (c,c,a,b,f),
          (d,a,d,e,f));
 

  Time: 300 ms 


inverse := 1/mm; 

  Time: 18460 ms 


on cramer; 

  Time: 80 ms 


cramersinv := 1/mm; 

  Time: 9260 ms

</TT></PRE><P>Your time readings will vary depending on the REDUCE version you u
se. 
After you invert the matrix, turn on 
<A HREF=r37_0314.html>output</A> and ask for one of 
the elements of the inverse matrix, such as <em>cramersinv(3,2)</em>, so that 
you can see the size of the expressions produced. 
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Inversion of matrices and the solution of linear equations with dense 
symbolic entries in many variables is generally considerably faster with 
<em>cramer</em> on. However, inversion of numeric-valued matrices is 
slower. Consider the matrices you're inverting before deciding whether to 
turn <em>cramer</em> on or off. A substantial portion of the time in matrix 
inversion is given to formatting the results for printing. To save this 
time, turn <em>output</em> off, as shown in this example or terminate the 
expression with a dollar sign instead of a semicolon. The results are 
still available to you in the workspace associated with your prompt 
number, or you can assign them to an identifier for further use. 
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