<A NAME=LCM>
<TITLE>LCM</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>
<B>LCM</B> _ _ _ _ _ _ _ _ _ _ _ _ <B>switch</B><P>
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The <em>lcm</em> switch instructs REDUCE to compute the least common multiple
of denominators whenever rational expressions occur. Default is <em>on</em>.
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examples: </H3>
<P><PRE><TT>
off lcm;
z := 1/(x**2 - y**2) + 1/(x-y)**2;
2*X*(X - Y)
Z := -------------------------
4 3 3 4
X - 2*X *Y + 2*X*Y - Y
on lcm;
z;
2*X*(X - Y)
-------------------------
4 3 3 4
X - 2*X *Y + 2*X*Y - Y
zz := 1/(x**2 - y**2) + 1/(x-y)**2;
2*X
ZZ := ---------------------
3 2 2 3
X - X *Y - X*Y + Y
on gcd;
z;
2*X
----------------------
3 2 2 3
X - X *Y - X*Y + Y
</TT></PRE><P>Note that <em>lcm</em> has effect only when rational expressions a
re first
combined. It does not examine existing structures for simplifications on
display. That is shown above when z is entered with
<em>lcm</em> off. It remains unsimplified even after <em>lcm</em> is turned
back on. However, a new variable containing the same expression is
simplified on entry. The switch
<A HREF=r37_0086.html>gcd</A> does examine existing
structures, as shown in the last example line above.
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Full greatest common divisor calculations become expensive if work with
large rational expressions is required. A considerable savings of time
can be had if a full gcd check is made only when denominators are combined,
and only a partial check for numerators. This is the effect of the <em>lcm</em>
switch.
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