in reply to
I don't think you should use Perl for solving math. Rather use Perl as a glue to interact with some outside specialized math program.
R is a good program for statistics; Octave for matrix algebra. They are GNU software.
Omegahat (also free) offers R-Perl bidirectional interface.
Or, to interact with R, you can just do this in Perl:
my $Rpath = "\\user\\R\\rw\\bin\\" ;
my $Rcmd = $Rpath . "rterm --vanilla --quiet --slave" ;
my $Rscript = "whatever R commands";
$Rscript =~ s/(\r|;\r)/ ;/gm ;
$Rscript =~ s/<-/=/gm; # \r or <- will break "echo"
print `echo $Rscript | $Rcmd`; # execute R commands & print results
Update: an informative benchmark of various math packages at SciViews