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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="Li"></a>
Li
</h2>

Returns the value of the logarithmic integral.

<p><p>

<h3>
Syntax:
</h3>
<pre>a := Li(b);</pre>

<p>

<table>
<tr>
<td>real</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>real or integer</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
This function computes an approximation of the logarithmic
integral. It gives a good idea of the number of prime
ideals of norm less than or equal to the argument.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> Li(2);
1.045163780117492784844588889194613136522615578151
kash> Li(3);
2.163588594667191972876922367347721366542116212451
kash> Li(7.5);
5.009500143078375327886075408809948575232609368221
kash> Li(10000);
1246.137215899388459692771107529059792486534653513971
kash> l := []; p := 2;
[  ]
2
kash> while p <= 10000 do Add(l, p); p := NextPrime(p); od;
kash> Length(l);
1229
kash> o := OrderMaximal(x^2+164);;
kash> l := []; p := 2;
[  ]
2
kash> while p <= 10000 do
> pl := Filtered(Factor(p*o), x->IdealNorm(x[1]) <= 10000);
> Append(l, pl);
> p := NextPrime(p);
> od;
kash> Length(l);
> 1209

</pre>

<p>


<hr>

<p>
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