The documentation for ->field() in WWW::Mechanize::Firefox says:

A selector prefixed with '#' must match the id attribute of the input. A selector prefixed with '.' matches the class attribute. A selector prefixed with '^' or with no prefix matches the name attribute.

I'm not sure how to make this clearer, but maybe an example helps:

$mech->field('#foo', 'bar'); # set value of element with id "foo" to "
+bar"
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I don't think that radio boxes are well-supported with WWW::Mechanize::Firefox though, because I've never needed them.