Can't create a date picker with an XWiki.JavaScriptExtension object

Steps to reproduce:
1: Install Date Picker Extension
http://maven.xwiki.org/releases/org/xwiki/contrib/xwiki-application-datepicker/1.1/xwiki-application-datepicker-1.1.xar

2: Create a page with this code or import the xar I post below:
{

{velocity}

}
#set($discard = $xwiki.jsfx.use("js/scriptaculous/scriptaculous.js"))
#set($discard = $xwiki.jsx.use("XWiki.DatePickerExtension",

{'defer':false}

))
#set($discard = $xwiki.ssx.use("XWiki.DatePickerExtension"))

{

{html clean="false"}

}
<h1>Working example</h1>
<input type="text" name="mydate" id="mydate_id" />
<script type="text/javascript">
var dpicker = new DatePicker(

{ relative : 'mydate_id', language: "$context.language" }

);
</script>
<h2>Issue</h2>
<input type="text" name="mydate2" id="mydate2_id" />
{

{/html}

}

{

{/velocity}

}

2bis: If you paste the code and you don't use my xar, add an XWiki.JavaScriptExtension object with this content:
var dpicker = new DatePicker({
relative : 'mydate2_id',
language: "$context.language",
dateFormat: [ ["dd","mm","yyyy"], "/" ]
});

Note that there is no datepicker on the second field.

Documentation: http://extensions.xwiki.org/xwiki/bin/view/Extension/Date+Picker+Application