lib/Math/Complex.pm

48 	      pi
214 	    $theta = ($theta <= 0) ? $theta + pi() : $theta - pi();
249 # pi
251 # The number defined as pi = 180 degrees
253 sub pi () { 4 * CORE::atan2(1, 1) }
260 sub pit2 () { 2 * pi }
267 sub pip2 () { pi / 2 }
275 sub deg1 () { pi / 180 }
394 	    if    ($t >   pi()) { $t -= pit2 }
395 	    elsif ($t <= -pi()) { $t += pit2 }
448 		if    ($t >   pi()) { $t -= pit2 }
449 		elsif ($t <= -pi()) { $t += pit2 }
454 		if    ($t >   pi()) { $t -= pit2 }
455 		elsif ($t <= -pi()) { $t += pit2 }
541 		$t = ($t <= 0) ? $t + pi : $t - pi;
590     if    ($$theta >   pi()) { $$theta -= pit2 }
591     elsif ($$theta <= -pi()) { $$theta += pit2 }
679 # z^(1/n) = r^(1/n) (cos ((t+2 k pi)/n) + i sin ((t+2 k pi)/n))
685 	    @{$z->polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
793 	    return $z > 0 ? CORE::log($z) : cplx(CORE::log(-$z), pi);
797 	if    ($t >   pi()) { $t -= pit2 }
798 	elsif ($t <= -pi()) { $t += pit2 }
1286 	$u += pi   if $re2 < 0;
1287 	$u -= pit2 if $u > pi;
1435 	} elsif ($t == pi) {
1436 	    $theta = "pi";
1444 	# Try to identify pi/n and friends.
1452 		$b = $t * $a / pi;
1455 		    $theta = "${b}pi/$a";
1486 	$j = cplxe(1, 2*pi/3);
1571 axis, and therefore I<theta> is zero or I<pi>.
1594 Indeed, a negative real number can be noted C<[x,pi]> (the modulus
1595 I<x> is always non-negative, so C<[x,pi]> is really C<-x>, a negative
1598 	sqrt([x,pi]) = sqrt(x) * exp(i*pi/2) = [sqrt(x),pi/2] = sqrt(x)*i
1727 	(root(z, n))[k] = r**(1/n) * exp(i * (t + 2*k*pi)/n)
1748 	$z = Math::Complex->emake(5, pi/3);
1749 	$x = cplxe(5, pi/3);
1752 (in radians, the full circle is 2*pi).  (Mnemonic: C<e> is used as a
1757 	$x = cplxe(-3, pi/4);
1759 but that will be silently converted into C<[3,-3pi/4]>, since the
1804 	print "j = $j\n";		# Prints "j = [1,2pi/3]"
1808 The polar style attempts to emphasize arguments like I<k*pi/n>
1860 	$j = cplxe(1, 2*pi/3);	# $j ** 3 == 1
1867 	$k = exp(i * 2*pi/3);
1904 C<sec>, C<tanh>, the argument cannot be I<pi/2 + k * pi>, where I<k>