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

Calculates the value of the Weierstrass \wp-function
related to the given lattice.

<p><p>

<h3>
Syntax:
</h3>
<pre>u := WeierstrassP(z, w1, w2);</pre>

<p>

<table>
<tr>
<td>complex</td>
<td><pre>  u  </pre></td>
<td></td>
</tr>
<tr>
<td>complex</td>
<td><pre>  z  </pre></td>
<td>a non-zero element of the complex  torus C/Zw_1oplusZw_2</td>
</tr>
<tr>
<td>complex</td>
<td><pre>  w1,w2  </pre></td>
<td>complex values with Im(w_1/w_2)>0</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let z, w_1 and w_2 be complex numbers with
Im(w_1/w_2)>0 and with z \notin
Zw_1oplusZw_2. The value of the Weierstrass
\wp-function \wp(z;Zw_1oplusZw_2) is then a
well-defined complex number. It is calculated by use of
the infinite q-expansion of \wp described in
cite[Chapt.~4.2, Prop.~3]{LangEF},
where the precision of the calculated
value depends on that of the defining complex field.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute \wp(\sqrt{-11}; (1+\sqrt{-11})Z oplus 12Z):
<pre>

kash> z := Sqrt(-11);
3.316624790355399849114932736670686683927088545589*i
kash> w1 := 1+Sqrt(-11);
1 + 3.316624790355399849114932736670686683927088545589*i
kash> w2 := Comp(12,0);
12
kash> WeierstrassP(z,w1,w2);
> 1.018219365756141747667075554911574076310206321785 + 0.03622971784813503226915\
102443845385206504756332*i

</pre>

<p>


<hr>

<p>
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