1N/A#!./perl
1N/A
1N/A# $RCSfile: complex.t,v $
1N/A#
1N/A# Regression tests for the Math::Complex pacakge
1N/A# -- Raphael Manfredi since Sep 1996
1N/A# -- Jarkko Hietaniemi since Mar 1997
1N/A# -- Daniel S. Lewart since Sep 1997
1N/A
1N/ABEGIN {
1N/A chdir 't' if -d 't';
1N/A @INC = '../lib';
1N/A}
1N/A
1N/Ause Math::Complex;
1N/A
1N/Ause vars qw($VERSION);
1N/A
1N/A$VERSION = 1.92;
1N/A
1N/Amy ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
1N/A
1N/A$test = 0;
1N/A$| = 1;
1N/Amy @script = (
1N/A 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
1N/A "\n\n"
1N/A);
1N/Amy $eps = 1e-13;
1N/A
1N/Aif ($^O eq 'unicos') { # For some reason root() produces very inaccurate
1N/A $eps = 1e-10; # results in Cray UNICOS, and occasionally also
1N/A} # cos(), sin(), cosh(), sinh(). The division
1N/A # of doubles is the current suspect.
1N/A
1N/Awhile (<DATA>) {
1N/A s/^\s+//;
1N/A next if $_ eq '' || /^\#/;
1N/A chomp;
1N/A $test_set = 0; # Assume not a test over a set of values
1N/A if (/^&(.+)/) {
1N/A $op = $1;
1N/A next;
1N/A }
1N/A elsif (/^\{(.+)\}/) {
1N/A set($1, \@set, \@val);
1N/A next;
1N/A }
1N/A elsif (s/^\|//) {
1N/A $test_set = 1; # Requests we loop over the set...
1N/A }
1N/A my @args = split(/:/);
1N/A if ($test_set == 1) {
1N/A my $i;
1N/A for ($i = 0; $i < @set; $i++) {
1N/A # complex number
1N/A $target = $set[$i];
1N/A # textual value as found in set definition
1N/A $zvalue = $val[$i];
1N/A test($zvalue, $target, @args);
1N/A }
1N/A } else {
1N/A test($op, undef, @args);
1N/A }
1N/A}
1N/A
1N/A#
1N/A
1N/Asub test_mutators {
1N/A my $op;
1N/A
1N/A $test++;
1N/Apush(@script, <<'EOT');
1N/A{
1N/A my $z = cplx( 1, 1);
1N/A $z->Re(2);
1N/A $z->Im(3);
1N/A print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
1N/A print 'not ' unless Re($z) == 2 and Im($z) == 3;
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n"}\n));
1N/A
1N/A $test++;
1N/Apush(@script, <<'EOT');
1N/A{
1N/A my $z = cplx( 1, 1);
1N/A $z->abs(3 * sqrt(2));
1N/A print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
1N/A print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
1N/A (arg($z) - pi / 4 ) < $eps and
1N/A (Re($z) - 3 ) < $eps and
1N/A (Im($z) - 3 ) < $eps;
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n"}\n));
1N/A
1N/A $test++;
1N/Apush(@script, <<'EOT');
1N/A{
1N/A my $z = cplx( 1, 1);
1N/A $z->arg(-3 / 4 * pi);
1N/A print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
1N/A print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
1N/A (abs($z) - sqrt(2) ) < $eps and
1N/A (Re($z) + 1 ) < $eps and
1N/A (Im($z) + 1 ) < $eps;
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n"}\n));
1N/A}
1N/A
1N/Atest_mutators();
1N/A
1N/Amy $constants = '
1N/Amy $i = cplx(0, 1);
1N/Amy $pi = cplx(pi, 0);
1N/Amy $pii = cplx(0, pi);
1N/Amy $pip2 = cplx(pi/2, 0);
1N/Amy $zero = cplx(0, 0);
1N/A';
1N/A
1N/Apush(@script, $constants);
1N/A
1N/A
1N/A# test the divbyzeros
1N/A
1N/Asub test_dbz {
1N/A for my $op (@_) {
1N/A $test++;
1N/A push(@script, <<EOT);
1N/A eval '$op';
1N/A (\$bad) = (\$@ =~ /(.+)/);
1N/A print "# $test op = $op divbyzero? \$bad...\n";
1N/A print 'not ' unless (\$@ =~ /Division by zero/);
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n";\n));
1N/A }
1N/A}
1N/A
1N/A# test the logofzeros
1N/A
1N/Asub test_loz {
1N/A for my $op (@_) {
1N/A $test++;
1N/A push(@script, <<EOT);
1N/A eval '$op';
1N/A (\$bad) = (\$@ =~ /(.+)/);
1N/A print "# $test op = $op logofzero? \$bad...\n";
1N/A print 'not ' unless (\$@ =~ /Logarithm of zero/);
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n";\n));
1N/A }
1N/A}
1N/A
1N/Atest_dbz(
1N/A 'i/0',
1N/A 'acot(0)',
1N/A 'acot(+$i)',
1N/A# 'acoth(-1)', # Log of zero.
1N/A 'acoth(0)',
1N/A 'acoth(+1)',
1N/A 'acsc(0)',
1N/A 'acsch(0)',
1N/A 'asec(0)',
1N/A 'asech(0)',
1N/A 'atan($i)',
1N/A# 'atanh(-1)', # Log of zero.
1N/A 'atanh(+1)',
1N/A 'cot(0)',
1N/A 'coth(0)',
1N/A 'csc(0)',
1N/A 'csch(0)',
1N/A );
1N/A
1N/Atest_loz(
1N/A 'log($zero)',
1N/A 'atan(-$i)',
1N/A 'acot(-$i)',
1N/A 'atanh(-1)',
1N/A 'acoth(-1)',
1N/A );
1N/A
1N/A# test the bad roots
1N/A
1N/Asub test_broot {
1N/A for my $op (@_) {
1N/A $test++;
1N/A push(@script, <<EOT);
1N/A eval 'root(2, $op)';
1N/A (\$bad) = (\$@ =~ /(.+)/);
1N/A print "# $test op = $op badroot? \$bad...\n";
1N/A print 'not ' unless (\$@ =~ /root rank must be/);
1N/AEOT
1N/A push(@script, qq(print "ok $test\\n";\n));
1N/A }
1N/A}
1N/A
1N/Atest_broot(qw(-3 -2.1 0 0.99));
1N/A
1N/Asub test_display_format {
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# package display_format cartesian?\n";
1N/A print "not " unless Math::Complex->display_format eq 'cartesian';
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A push @script, <<EOS;
1N/A my \$j = (root(1,3))[1];
1N/A
1N/A \$j->display_format('polar');
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j display_format polar?\n";
1N/A print "not " unless \$j->display_format eq 'polar';
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j = \$j\n";
1N/A print "not " unless "\$j" eq "[1,2pi/3]";
1N/A print "ok $test\n";
1N/A
1N/A my %display_format;
1N/A
1N/A %display_format = \$j->display_format;
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# display_format{style} polar?\n";
1N/A print "not " unless \$display_format{style} eq 'polar';
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# keys %display_format == 2?\n";
1N/A print "not " unless keys %display_format == 2;
1N/A print "ok $test\n";
1N/A
1N/A \$j->display_format('style' => 'cartesian', 'format' => '%.5f');
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j = \$j\n";
1N/A print "not " unless "\$j" eq "-0.50000+0.86603i";
1N/A print "ok $test\n";
1N/A
1N/A %display_format = \$j->display_format;
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# display_format{format} %.5f?\n";
1N/A print "not " unless \$display_format{format} eq '%.5f';
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# keys %display_format == 3?\n";
1N/A print "not " unless keys %display_format == 3;
1N/A print "ok $test\n";
1N/A
1N/A \$j->display_format('format' => undef);
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j = \$j\n";
1N/A print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
1N/A print "ok $test\n";
1N/A
1N/A \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j = \$j\n";
1N/A print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
1N/A print "ok $test\n";
1N/A
1N/A \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j = \$j\n";
1N/A print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# j display_format cartesian?\n";
1N/A print "not " unless \$j->display_format eq 'cartesian';
1N/A print "ok $test\n";
1N/AEOS
1N/A}
1N/A
1N/Atest_display_format();
1N/A
1N/Asub test_remake {
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# remake 2+3i\n";
1N/A my \$z = cplx('2+3i');
1N/A print "not " unless \$z == Math::Complex->make(2,3);
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# remake 3i\n";
1N/A my \$z = Math::Complex->make('3i');
1N/A print "not " unless \$z == cplx(0,3);
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# remake [2,3]\n";
1N/A my \$z = cplxe('[2,3]');
1N/A print "not " unless \$z == Math::Complex->emake(2,3);
1N/A print "ok $test\n";
1N/AEOS
1N/A
1N/A $test++;
1N/A push @script, <<EOS;
1N/A print "# remake [2]\n";
1N/A my \$z = Math::Complex->emake('[2]');
1N/A print "not " unless \$z == cplxe(2);
1N/A print "ok $test\n";
1N/AEOS
1N/A}
1N/A
1N/Atest_remake();
1N/A
1N/Aprint "1..$test\n";
1N/Aeval join '', @script;
1N/Adie $@ if $@;
1N/A
1N/Asub abop {
1N/A my ($op) = @_;
1N/A
1N/A push(@script, qq(print "# $op=\n";));
1N/A}
1N/A
1N/Asub test {
1N/A my ($op, $z, @args) = @_;
1N/A my ($baop) = 0;
1N/A $test++;
1N/A my $i;
1N/A $baop = 1 if ($op =~ s/;=$//);
1N/A for ($i = 0; $i < @args; $i++) {
1N/A $val = value($args[$i]);
1N/A push @script, "\$z$i = $val;\n";
1N/A }
1N/A if (defined $z) {
1N/A $args = "'$op'"; # Really the value
1N/A $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
1N/A push @script, "\$res = $try; ";
1N/A push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
1N/A } else {
1N/A my ($try, $args);
1N/A if (@args == 2) {
1N/A $try = "$op \$z0";
1N/A $args = "'$args[0]'";
1N/A } else {
1N/A $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
1N/A $args = "'$args[0]', '$args[1]'";
1N/A }
1N/A push @script, "\$res = $try; ";
1N/A push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
1N/A if (@args > 2 and $baop) { # binary assignment ops
1N/A $test++;
1N/A # check the op= works
1N/A push @script, <<EOB;
1N/A{
1N/A my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
1N/A
1N/A my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
1N/A
1N/A my \$zb = cplx(\$z1r, \$z1i);
1N/A
1N/A \$za $op= \$zb;
1N/A my (\$zbr, \$zbi) = \@{\$zb->cartesian};
1N/A
1N/A check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
1N/AEOB
1N/A $test++;
1N/A # check that the rhs has not changed
1N/A push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
1N/A push @script, qq(print "ok $test\\n";\n);
1N/A push @script, "}\n";
1N/A }
1N/A }
1N/A}
1N/A
1N/Asub set {
1N/A my ($set, $setref, $valref) = @_;
1N/A @{$setref} = ();
1N/A @{$valref} = ();
1N/A my @set = split(/;\s*/, $set);
1N/A my @res;
1N/A my $i;
1N/A for ($i = 0; $i < @set; $i++) {
1N/A push(@{$valref}, $set[$i]);
1N/A my $val = value($set[$i]);
1N/A push @script, "\$s$i = $val;\n";
1N/A push @{$setref}, "\$s$i";
1N/A }
1N/A}
1N/A
1N/Asub value {
1N/A local ($_) = @_;
1N/A if (/^\s*\((.*),(.*)\)/) {
1N/A return "cplx($1,$2)";
1N/A }
1N/A elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
1N/A return "cplx($1,0)";
1N/A }
1N/A elsif (/^\s*\[(.*),(.*)\]/) {
1N/A return "cplxe($1,$2)";
1N/A }
1N/A elsif (/^\s*'(.*)'/) {
1N/A my $ex = $1;
1N/A $ex =~ s/\bz\b/$target/g;
1N/A $ex =~ s/\br\b/abs($target)/g;
1N/A $ex =~ s/\bt\b/arg($target)/g;
1N/A $ex =~ s/\ba\b/Re($target)/g;
1N/A $ex =~ s/\bb\b/Im($target)/g;
1N/A return $ex;
1N/A }
1N/A elsif (/^\s*"(.*)"/) {
1N/A return "\"$1\"";
1N/A }
1N/A return $_;
1N/A}
1N/A
1N/Asub check {
1N/A my ($test, $try, $got, $expected, @z) = @_;
1N/A
1N/A print "# @_\n";
1N/A
1N/A if ("$got" eq "$expected"
1N/A ||
1N/A ($expected =~ /^-?\d/ && $got == $expected)
1N/A ||
1N/A (abs($got - $expected) < $eps)
1N/A ) {
1N/A print "ok $test\n";
1N/A } else {
1N/A print "not ok $test\n";
1N/A my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
1N/A print "# '$try' expected: '$expected' got: '$got' for $args\n";
1N/A }
1N/A}
1N/A
1N/Asub addsq {
1N/A my ($z1, $z2) = @_;
1N/A return ($z1 + i*$z2) * ($z1 - i*$z2);
1N/A}
1N/A
1N/Asub subsq {
1N/A my ($z1, $z2) = @_;
1N/A return ($z1 + $z2) * ($z1 - $z2);
1N/A}
1N/A
1N/A__END__
1N/A&+;=
1N/A(3,4):(3,4):(6,8)
1N/A(-3,4):(3,-4):(0,0)
1N/A(3,4):-3:(0,4)
1N/A1:(4,2):(5,2)
1N/A[2,0]:[2,pi]:(0,0)
1N/A
1N/A&++
1N/A(2,1):(3,1)
1N/A
1N/A&-;=
1N/A(2,3):(-2,-3)
1N/A[2,pi/2]:[2,-(pi)/2]
1N/A2:[2,0]:(0,0)
1N/A[3,0]:2:(1,0)
1N/A3:(4,5):(-1,-5)
1N/A(4,5):3:(1,5)
1N/A(2,1):(3,5):(-1,-4)
1N/A
1N/A&--
1N/A(1,2):(0,2)
1N/A[2,pi]:[3,pi]
1N/A
1N/A&*;=
1N/A(0,1):(0,1):(-1,0)
1N/A(4,5):(1,0):(4,5)
1N/A[2,2*pi/3]:(1,0):[2,2*pi/3]
1N/A2:(0,1):(0,2)
1N/A(0,1):3:(0,3)
1N/A(0,1):(4,1):(-1,4)
1N/A(2,1):(4,-1):(9,2)
1N/A
1N/A&/;=
1N/A(3,4):(3,4):(1,0)
1N/A(4,-5):1:(4,-5)
1N/A1:(0,1):(0,-1)
1N/A(0,6):(0,2):(3,0)
1N/A(9,2):(4,-1):(2,1)
1N/A[4,pi]:[2,pi/2]:[2,pi/2]
1N/A[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
1N/A
1N/A&**;=
1N/A(2,0):(3,0):(8,0)
1N/A(3,0):(2,0):(9,0)
1N/A(2,3):(4,0):(-119,-120)
1N/A(0,0):(1,0):(0,0)
1N/A(0,0):(2,3):(0,0)
1N/A(1,0):(0,0):(1,0)
1N/A(1,0):(1,0):(1,0)
1N/A(1,0):(2,3):(1,0)
1N/A(2,3):(0,0):(1,0)
1N/A(2,3):(1,0):(2,3)
1N/A(0,0):(0,0):(1,0)
1N/A
1N/A&Re
1N/A(3,4):3
1N/A(-3,4):-3
1N/A[1,pi/2]:0
1N/A
1N/A&Im
1N/A(3,4):4
1N/A(3,-4):-4
1N/A[1,pi/2]:1
1N/A
1N/A&abs
1N/A(3,4):5
1N/A(-3,4):5
1N/A
1N/A&arg
1N/A[2,0]:0
1N/A[-2,0]:pi
1N/A
1N/A&~
1N/A(4,5):(4,-5)
1N/A(-3,4):(-3,-4)
1N/A[2,pi/2]:[2,-(pi)/2]
1N/A
1N/A&<
1N/A(3,4):(1,2):0
1N/A(3,4):(3,2):0
1N/A(3,4):(3,8):1
1N/A(4,4):(5,129):1
1N/A
1N/A&==
1N/A(3,4):(4,5):0
1N/A(3,4):(3,5):0
1N/A(3,4):(2,4):0
1N/A(3,4):(3,4):1
1N/A
1N/A&sqrt
1N/A-9:(0,3)
1N/A(-100,0):(0,10)
1N/A(16,-30):(5,-3)
1N/A
1N/A&stringify_cartesian
1N/A(-100,0):"-100"
1N/A(0,1):"i"
1N/A(4,-3):"4-3i"
1N/A(4,0):"4"
1N/A(-4,0):"-4"
1N/A(-2,4):"-2+4i"
1N/A(-2,-1):"-2-i"
1N/A
1N/A&stringify_polar
1N/A[-1, 0]:"[1,pi]"
1N/A[1, pi/3]:"[1,pi/3]"
1N/A[6, -2*pi/3]:"[6,-2pi/3]"
1N/A[0.5, -9*pi/11]:"[0.5,-9pi/11]"
1N/A
1N/A{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
1N/A
1N/A|'z + ~z':'2*Re(z)'
1N/A|'z - ~z':'2*i*Im(z)'
1N/A|'z * ~z':'abs(z) * abs(z)'
1N/A
1N/A{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
1N/A
1N/A|'(root(z, 4))[1] ** 4':'z'
1N/A|'(root(z, 5))[3] ** 5':'z'
1N/A|'(root(z, 8))[7] ** 8':'z'
1N/A|'abs(z)':'r'
1N/A|'acot(z)':'acotan(z)'
1N/A|'acsc(z)':'acosec(z)'
1N/A|'acsc(z)':'asin(1 / z)'
1N/A|'asec(z)':'acos(1 / z)'
1N/A|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
1N/A|'cos(acos(z))':'z'
1N/A|'addsq(cos(z), sin(z))':1
1N/A|'cos(z)':'cosh(i*z)'
1N/A|'subsq(cosh(z), sinh(z))':1
1N/A|'cot(acot(z))':'z'
1N/A|'cot(z)':'1 / tan(z)'
1N/A|'cot(z)':'cotan(z)'
1N/A|'csc(acsc(z))':'z'
1N/A|'csc(z)':'1 / sin(z)'
1N/A|'csc(z)':'cosec(z)'
1N/A|'exp(log(z))':'z'
1N/A|'exp(z)':'exp(a) * exp(i * b)'
1N/A|'ln(z)':'log(z)'
1N/A|'log(exp(z))':'z'
1N/A|'log(z)':'log(r) + i*t'
1N/A|'log10(z)':'log(z) / log(10)'
1N/A|'logn(z, 2)':'log(z) / log(2)'
1N/A|'logn(z, 3)':'log(z) / log(3)'
1N/A|'sec(asec(z))':'z'
1N/A|'sec(z)':'1 / cos(z)'
1N/A|'sin(asin(z))':'z'
1N/A|'sin(i * z)':'i * sinh(z)'
1N/A|'sqrt(z) * sqrt(z)':'z'
1N/A|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
1N/A|'tan(atan(z))':'z'
1N/A|'z**z':'exp(z * log(z))'
1N/A
1N/A{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
1N/A
1N/A|'cosh(acosh(z))':'z'
1N/A|'coth(acoth(z))':'z'
1N/A|'coth(z)':'1 / tanh(z)'
1N/A|'coth(z)':'cotanh(z)'
1N/A|'csch(acsch(z))':'z'
1N/A|'csch(z)':'1 / sinh(z)'
1N/A|'csch(z)':'cosech(z)'
1N/A|'sech(asech(z))':'z'
1N/A|'sech(z)':'1 / cosh(z)'
1N/A|'sinh(asinh(z))':'z'
1N/A|'tanh(atanh(z))':'z'
1N/A
1N/A{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
1N/A
1N/A|'acos(cos(z)) ** 2':'z * z'
1N/A|'acosh(cosh(z)) ** 2':'z * z'
1N/A|'acoth(z)':'acotanh(z)'
1N/A|'acoth(z)':'atanh(1 / z)'
1N/A|'acsch(z)':'acosech(z)'
1N/A|'acsch(z)':'asinh(1 / z)'
1N/A|'asech(z)':'acosh(1 / z)'
1N/A|'asin(sin(z))':'z'
1N/A|'asinh(sinh(z))':'z'
1N/A|'atan(tan(z))':'z'
1N/A|'atanh(tanh(z))':'z'
1N/A
1N/A&log
1N/A(-2.0,0):( 0.69314718055995, 3.14159265358979)
1N/A(-1.0,0):( 0 , 3.14159265358979)
1N/A(-0.5,0):( -0.69314718055995, 3.14159265358979)
1N/A( 0.5,0):( -0.69314718055995, 0 )
1N/A( 1.0,0):( 0 , 0 )
1N/A( 2.0,0):( 0.69314718055995, 0 )
1N/A
1N/A&log
1N/A( 2, 3):( 1.28247467873077, 0.98279372324733)
1N/A(-2, 3):( 1.28247467873077, 2.15879893034246)
1N/A(-2,-3):( 1.28247467873077, -2.15879893034246)
1N/A( 2,-3):( 1.28247467873077, -0.98279372324733)
1N/A
1N/A&sin
1N/A(-2.0,0):( -0.90929742682568, 0 )
1N/A(-1.0,0):( -0.84147098480790, 0 )
1N/A(-0.5,0):( -0.47942553860420, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.47942553860420, 0 )
1N/A( 1.0,0):( 0.84147098480790, 0 )
1N/A( 2.0,0):( 0.90929742682568, 0 )
1N/A
1N/A&sin
1N/A( 2, 3):( 9.15449914691143, -4.16890695996656)
1N/A(-2, 3):( -9.15449914691143, -4.16890695996656)
1N/A(-2,-3):( -9.15449914691143, 4.16890695996656)
1N/A( 2,-3):( 9.15449914691143, 4.16890695996656)
1N/A
1N/A&cos
1N/A(-2.0,0):( -0.41614683654714, 0 )
1N/A(-1.0,0):( 0.54030230586814, 0 )
1N/A(-0.5,0):( 0.87758256189037, 0 )
1N/A( 0.0,0):( 1 , 0 )
1N/A( 0.5,0):( 0.87758256189037, 0 )
1N/A( 1.0,0):( 0.54030230586814, 0 )
1N/A( 2.0,0):( -0.41614683654714, 0 )
1N/A
1N/A&cos
1N/A( 2, 3):( -4.18962569096881, -9.10922789375534)
1N/A(-2, 3):( -4.18962569096881, 9.10922789375534)
1N/A(-2,-3):( -4.18962569096881, -9.10922789375534)
1N/A( 2,-3):( -4.18962569096881, 9.10922789375534)
1N/A
1N/A&tan
1N/A(-2.0,0):( 2.18503986326152, 0 )
1N/A(-1.0,0):( -1.55740772465490, 0 )
1N/A(-0.5,0):( -0.54630248984379, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.54630248984379, 0 )
1N/A( 1.0,0):( 1.55740772465490, 0 )
1N/A( 2.0,0):( -2.18503986326152, 0 )
1N/A
1N/A&tan
1N/A( 2, 3):( -0.00376402564150, 1.00323862735361)
1N/A(-2, 3):( 0.00376402564150, 1.00323862735361)
1N/A(-2,-3):( 0.00376402564150, -1.00323862735361)
1N/A( 2,-3):( -0.00376402564150, -1.00323862735361)
1N/A
1N/A&sec
1N/A(-2.0,0):( -2.40299796172238, 0 )
1N/A(-1.0,0):( 1.85081571768093, 0 )
1N/A(-0.5,0):( 1.13949392732455, 0 )
1N/A( 0.0,0):( 1 , 0 )
1N/A( 0.5,0):( 1.13949392732455, 0 )
1N/A( 1.0,0):( 1.85081571768093, 0 )
1N/A( 2.0,0):( -2.40299796172238, 0 )
1N/A
1N/A&sec
1N/A( 2, 3):( -0.04167496441114, 0.09061113719624)
1N/A(-2, 3):( -0.04167496441114, -0.09061113719624)
1N/A(-2,-3):( -0.04167496441114, 0.09061113719624)
1N/A( 2,-3):( -0.04167496441114, -0.09061113719624)
1N/A
1N/A&csc
1N/A(-2.0,0):( -1.09975017029462, 0 )
1N/A(-1.0,0):( -1.18839510577812, 0 )
1N/A(-0.5,0):( -2.08582964293349, 0 )
1N/A( 0.5,0):( 2.08582964293349, 0 )
1N/A( 1.0,0):( 1.18839510577812, 0 )
1N/A( 2.0,0):( 1.09975017029462, 0 )
1N/A
1N/A&csc
1N/A( 2, 3):( 0.09047320975321, 0.04120098628857)
1N/A(-2, 3):( -0.09047320975321, 0.04120098628857)
1N/A(-2,-3):( -0.09047320975321, -0.04120098628857)
1N/A( 2,-3):( 0.09047320975321, -0.04120098628857)
1N/A
1N/A&cot
1N/A(-2.0,0):( 0.45765755436029, 0 )
1N/A(-1.0,0):( -0.64209261593433, 0 )
1N/A(-0.5,0):( -1.83048772171245, 0 )
1N/A( 0.5,0):( 1.83048772171245, 0 )
1N/A( 1.0,0):( 0.64209261593433, 0 )
1N/A( 2.0,0):( -0.45765755436029, 0 )
1N/A
1N/A&cot
1N/A( 2, 3):( -0.00373971037634, -0.99675779656936)
1N/A(-2, 3):( 0.00373971037634, -0.99675779656936)
1N/A(-2,-3):( 0.00373971037634, 0.99675779656936)
1N/A( 2,-3):( -0.00373971037634, 0.99675779656936)
1N/A
1N/A&asin
1N/A(-2.0,0):( -1.57079632679490, 1.31695789692482)
1N/A(-1.0,0):( -1.57079632679490, 0 )
1N/A(-0.5,0):( -0.52359877559830, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.52359877559830, 0 )
1N/A( 1.0,0):( 1.57079632679490, 0 )
1N/A( 2.0,0):( 1.57079632679490, -1.31695789692482)
1N/A
1N/A&asin
1N/A( 2, 3):( 0.57065278432110, 1.98338702991654)
1N/A(-2, 3):( -0.57065278432110, 1.98338702991654)
1N/A(-2,-3):( -0.57065278432110, -1.98338702991654)
1N/A( 2,-3):( 0.57065278432110, -1.98338702991654)
1N/A
1N/A&acos
1N/A(-2.0,0):( 3.14159265358979, -1.31695789692482)
1N/A(-1.0,0):( 3.14159265358979, 0 )
1N/A(-0.5,0):( 2.09439510239320, 0 )
1N/A( 0.0,0):( 1.57079632679490, 0 )
1N/A( 0.5,0):( 1.04719755119660, 0 )
1N/A( 1.0,0):( 0 , 0 )
1N/A( 2.0,0):( 0 , 1.31695789692482)
1N/A
1N/A&acos
1N/A( 2, 3):( 1.00014354247380, -1.98338702991654)
1N/A(-2, 3):( 2.14144911111600, -1.98338702991654)
1N/A(-2,-3):( 2.14144911111600, 1.98338702991654)
1N/A( 2,-3):( 1.00014354247380, 1.98338702991654)
1N/A
1N/A&atan
1N/A(-2.0,0):( -1.10714871779409, 0 )
1N/A(-1.0,0):( -0.78539816339745, 0 )
1N/A(-0.5,0):( -0.46364760900081, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.46364760900081, 0 )
1N/A( 1.0,0):( 0.78539816339745, 0 )
1N/A( 2.0,0):( 1.10714871779409, 0 )
1N/A
1N/A&atan
1N/A( 2, 3):( 1.40992104959658, 0.22907268296854)
1N/A(-2, 3):( -1.40992104959658, 0.22907268296854)
1N/A(-2,-3):( -1.40992104959658, -0.22907268296854)
1N/A( 2,-3):( 1.40992104959658, -0.22907268296854)
1N/A
1N/A&asec
1N/A(-2.0,0):( 2.09439510239320, 0 )
1N/A(-1.0,0):( 3.14159265358979, 0 )
1N/A(-0.5,0):( 3.14159265358979, -1.31695789692482)
1N/A( 0.5,0):( 0 , 1.31695789692482)
1N/A( 1.0,0):( 0 , 0 )
1N/A( 2.0,0):( 1.04719755119660, 0 )
1N/A
1N/A&asec
1N/A( 2, 3):( 1.42041072246703, 0.23133469857397)
1N/A(-2, 3):( 1.72118193112276, 0.23133469857397)
1N/A(-2,-3):( 1.72118193112276, -0.23133469857397)
1N/A( 2,-3):( 1.42041072246703, -0.23133469857397)
1N/A
1N/A&acsc
1N/A(-2.0,0):( -0.52359877559830, 0 )
1N/A(-1.0,0):( -1.57079632679490, 0 )
1N/A(-0.5,0):( -1.57079632679490, 1.31695789692482)
1N/A( 0.5,0):( 1.57079632679490, -1.31695789692482)
1N/A( 1.0,0):( 1.57079632679490, 0 )
1N/A( 2.0,0):( 0.52359877559830, 0 )
1N/A
1N/A&acsc
1N/A( 2, 3):( 0.15038560432786, -0.23133469857397)
1N/A(-2, 3):( -0.15038560432786, -0.23133469857397)
1N/A(-2,-3):( -0.15038560432786, 0.23133469857397)
1N/A( 2,-3):( 0.15038560432786, 0.23133469857397)
1N/A
1N/A&acot
1N/A(-2.0,0):( -0.46364760900081, 0 )
1N/A(-1.0,0):( -0.78539816339745, 0 )
1N/A(-0.5,0):( -1.10714871779409, 0 )
1N/A( 0.5,0):( 1.10714871779409, 0 )
1N/A( 1.0,0):( 0.78539816339745, 0 )
1N/A( 2.0,0):( 0.46364760900081, 0 )
1N/A
1N/A&acot
1N/A( 2, 3):( 0.16087527719832, -0.22907268296854)
1N/A(-2, 3):( -0.16087527719832, -0.22907268296854)
1N/A(-2,-3):( -0.16087527719832, 0.22907268296854)
1N/A( 2,-3):( 0.16087527719832, 0.22907268296854)
1N/A
1N/A&sinh
1N/A(-2.0,0):( -3.62686040784702, 0 )
1N/A(-1.0,0):( -1.17520119364380, 0 )
1N/A(-0.5,0):( -0.52109530549375, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.52109530549375, 0 )
1N/A( 1.0,0):( 1.17520119364380, 0 )
1N/A( 2.0,0):( 3.62686040784702, 0 )
1N/A
1N/A&sinh
1N/A( 2, 3):( -3.59056458998578, 0.53092108624852)
1N/A(-2, 3):( 3.59056458998578, 0.53092108624852)
1N/A(-2,-3):( 3.59056458998578, -0.53092108624852)
1N/A( 2,-3):( -3.59056458998578, -0.53092108624852)
1N/A
1N/A&cosh
1N/A(-2.0,0):( 3.76219569108363, 0 )
1N/A(-1.0,0):( 1.54308063481524, 0 )
1N/A(-0.5,0):( 1.12762596520638, 0 )
1N/A( 0.0,0):( 1 , 0 )
1N/A( 0.5,0):( 1.12762596520638, 0 )
1N/A( 1.0,0):( 1.54308063481524, 0 )
1N/A( 2.0,0):( 3.76219569108363, 0 )
1N/A
1N/A&cosh
1N/A( 2, 3):( -3.72454550491532, 0.51182256998738)
1N/A(-2, 3):( -3.72454550491532, -0.51182256998738)
1N/A(-2,-3):( -3.72454550491532, 0.51182256998738)
1N/A( 2,-3):( -3.72454550491532, -0.51182256998738)
1N/A
1N/A&tanh
1N/A(-2.0,0):( -0.96402758007582, 0 )
1N/A(-1.0,0):( -0.76159415595576, 0 )
1N/A(-0.5,0):( -0.46211715726001, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.46211715726001, 0 )
1N/A( 1.0,0):( 0.76159415595576, 0 )
1N/A( 2.0,0):( 0.96402758007582, 0 )
1N/A
1N/A&tanh
1N/A( 2, 3):( 0.96538587902213, -0.00988437503832)
1N/A(-2, 3):( -0.96538587902213, -0.00988437503832)
1N/A(-2,-3):( -0.96538587902213, 0.00988437503832)
1N/A( 2,-3):( 0.96538587902213, 0.00988437503832)
1N/A
1N/A&sech
1N/A(-2.0,0):( 0.26580222883408, 0 )
1N/A(-1.0,0):( 0.64805427366389, 0 )
1N/A(-0.5,0):( 0.88681888397007, 0 )
1N/A( 0.0,0):( 1 , 0 )
1N/A( 0.5,0):( 0.88681888397007, 0 )
1N/A( 1.0,0):( 0.64805427366389, 0 )
1N/A( 2.0,0):( 0.26580222883408, 0 )
1N/A
1N/A&sech
1N/A( 2, 3):( -0.26351297515839, -0.03621163655877)
1N/A(-2, 3):( -0.26351297515839, 0.03621163655877)
1N/A(-2,-3):( -0.26351297515839, -0.03621163655877)
1N/A( 2,-3):( -0.26351297515839, 0.03621163655877)
1N/A
1N/A&csch
1N/A(-2.0,0):( -0.27572056477178, 0 )
1N/A(-1.0,0):( -0.85091812823932, 0 )
1N/A(-0.5,0):( -1.91903475133494, 0 )
1N/A( 0.5,0):( 1.91903475133494, 0 )
1N/A( 1.0,0):( 0.85091812823932, 0 )
1N/A( 2.0,0):( 0.27572056477178, 0 )
1N/A
1N/A&csch
1N/A( 2, 3):( -0.27254866146294, -0.04030057885689)
1N/A(-2, 3):( 0.27254866146294, -0.04030057885689)
1N/A(-2,-3):( 0.27254866146294, 0.04030057885689)
1N/A( 2,-3):( -0.27254866146294, 0.04030057885689)
1N/A
1N/A&coth
1N/A(-2.0,0):( -1.03731472072755, 0 )
1N/A(-1.0,0):( -1.31303528549933, 0 )
1N/A(-0.5,0):( -2.16395341373865, 0 )
1N/A( 0.5,0):( 2.16395341373865, 0 )
1N/A( 1.0,0):( 1.31303528549933, 0 )
1N/A( 2.0,0):( 1.03731472072755, 0 )
1N/A
1N/A&coth
1N/A( 2, 3):( 1.03574663776500, 0.01060478347034)
1N/A(-2, 3):( -1.03574663776500, 0.01060478347034)
1N/A(-2,-3):( -1.03574663776500, -0.01060478347034)
1N/A( 2,-3):( 1.03574663776500, -0.01060478347034)
1N/A
1N/A&asinh
1N/A(-2.0,0):( -1.44363547517881, 0 )
1N/A(-1.0,0):( -0.88137358701954, 0 )
1N/A(-0.5,0):( -0.48121182505960, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.48121182505960, 0 )
1N/A( 1.0,0):( 0.88137358701954, 0 )
1N/A( 2.0,0):( 1.44363547517881, 0 )
1N/A
1N/A&asinh
1N/A( 2, 3):( 1.96863792579310, 0.96465850440760)
1N/A(-2, 3):( -1.96863792579310, 0.96465850440761)
1N/A(-2,-3):( -1.96863792579310, -0.96465850440761)
1N/A( 2,-3):( 1.96863792579310, -0.96465850440760)
1N/A
1N/A&acosh
1N/A(-2.0,0):( 1.31695789692482, 3.14159265358979)
1N/A(-1.0,0):( 0, 3.14159265358979)
1N/A(-0.5,0):( 0, 2.09439510239320)
1N/A( 0.0,0):( 0, 1.57079632679490)
1N/A( 0.5,0):( 0, 1.04719755119660)
1N/A( 1.0,0):( 0 , 0 )
1N/A( 2.0,0):( 1.31695789692482, 0 )
1N/A
1N/A&acosh
1N/A( 2, 3):( 1.98338702991654, 1.00014354247380)
1N/A(-2, 3):( 1.98338702991653, 2.14144911111600)
1N/A(-2,-3):( 1.98338702991653, -2.14144911111600)
1N/A( 2,-3):( 1.98338702991654, -1.00014354247380)
1N/A
1N/A&atanh
1N/A(-2.0,0):( -0.54930614433405, 1.57079632679490)
1N/A(-0.5,0):( -0.54930614433405, 0 )
1N/A( 0.0,0):( 0 , 0 )
1N/A( 0.5,0):( 0.54930614433405, 0 )
1N/A( 2.0,0):( 0.54930614433405, 1.57079632679490)
1N/A
1N/A&atanh
1N/A( 2, 3):( 0.14694666622553, 1.33897252229449)
1N/A(-2, 3):( -0.14694666622553, 1.33897252229449)
1N/A(-2,-3):( -0.14694666622553, -1.33897252229449)
1N/A( 2,-3):( 0.14694666622553, -1.33897252229449)
1N/A
1N/A&asech
1N/A(-2.0,0):( 0 , 2.09439510239320)
1N/A(-1.0,0):( 0 , 3.14159265358979)
1N/A(-0.5,0):( 1.31695789692482, 3.14159265358979)
1N/A( 0.5,0):( 1.31695789692482, 0 )
1N/A( 1.0,0):( 0 , 0 )
1N/A( 2.0,0):( 0 , 1.04719755119660)
1N/A
1N/A&asech
1N/A( 2, 3):( 0.23133469857397, -1.42041072246703)
1N/A(-2, 3):( 0.23133469857397, -1.72118193112276)
1N/A(-2,-3):( 0.23133469857397, 1.72118193112276)
1N/A( 2,-3):( 0.23133469857397, 1.42041072246703)
1N/A
1N/A&acsch
1N/A(-2.0,0):( -0.48121182505960, 0 )
1N/A(-1.0,0):( -0.88137358701954, 0 )
1N/A(-0.5,0):( -1.44363547517881, 0 )
1N/A( 0.5,0):( 1.44363547517881, 0 )
1N/A( 1.0,0):( 0.88137358701954, 0 )
1N/A( 2.0,0):( 0.48121182505960, 0 )
1N/A
1N/A&acsch
1N/A( 2, 3):( 0.15735549884499, -0.22996290237721)
1N/A(-2, 3):( -0.15735549884499, -0.22996290237721)
1N/A(-2,-3):( -0.15735549884499, 0.22996290237721)
1N/A( 2,-3):( 0.15735549884499, 0.22996290237721)
1N/A
1N/A&acoth
1N/A(-2.0,0):( -0.54930614433405, 0 )
1N/A(-0.5,0):( -0.54930614433405, 1.57079632679490)
1N/A( 0.5,0):( 0.54930614433405, 1.57079632679490)
1N/A( 2.0,0):( 0.54930614433405, 0 )
1N/A
1N/A&acoth
1N/A( 2, 3):( 0.14694666622553, -0.23182380450040)
1N/A(-2, 3):( -0.14694666622553, -0.23182380450040)
1N/A(-2,-3):( -0.14694666622553, 0.23182380450040)
1N/A( 2,-3):( 0.14694666622553, 0.23182380450040)
1N/A
1N/A# eof