Merge pull request #839 from noudald/challenge-031-noud

Solutions to challenge 031 problem 1 and 2 in Perl 6

2 files changed, 53 insertions, 0 deletions

diff --git a/challenge-031/noud/perl6/ch1.p6 b/challenge-031/noud/perl6/ch1.p6
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+# Create a function to check divide by zero error without checking if the
+# denominator is zero.
+
+# Normally you would try to divide by zero, catch the exception that's
+# generated while dividing by zero.
+#
+# For fun, I'll try something else. Suppose we want to compute z = x / y. To
+# compute z we project x and y onto a one dimensional complex sphere with
+# center i / 2 and radius 1/2, and compute the division on the complex sphere.
+# This project is called the stereographic projects, also see
+# https://en.wikipedia.org/wiki/Stereographic_projection. The stereographic
+# projects of x is
+#
+#   x |---> \hat(x) = x / (1 + x^2) + x^2 / (1 + x^2) * i
+#
+# In the stereographic projection we can divide by zero. After dividing by
+# zero we end up in the north pole, which is the complex number i. Hence,
+# instead of checking if the denominator is zero, we check if in the
+# stereographic projection \hat(x / y) = i. Therefore, we don't check the if
+# the denominator is zero explicitly. A straightforward computation gives
+#
+#   \hat(x / y) = xy / (x^2 + y^2) + x^2 / (x^2 + y^2) * i
+
+sub infix:<%/>($x, $y) {
+    my $z = Complex.new($x * $y / ($x**2 + $y**2), $x**2 / ($x**2 + $y**2));
+    if ($z === i) {
+        # If z is the north pole, the inverse stereographic projection is
+        # not a number. (this is actually the perl weekly challenge)
+        NaN;
+    } else {
+        # For fun, use the inverse stereographic projection to compute x / y.
+        $z.re / (1 - $z.im);
+    }
+}
+
+say 1 %/ 2;
+say 3 %/ 7;
+say 1 %/ 0;
+say 0 %/ 0;
diff --git a/challenge-031/noud/perl6/ch2.p6 b/challenge-031/noud/perl6/ch2.p6
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+# Create a script to demonstrate creating dynamic variable name, assign a value
+# to the variable and finally print the variable. The variable name would be
+# passed as command line argument.
+
+# Example usage:
+#
+#   > perl6 ch2.p6 my_var 37
+#   $my_var = 37
+#
+
+sub MAIN($name, $value) {
+    GLOBAL::{'$' ~ $name} = $value;
+    say '$' ~ $name ~ " = " ~ GLOBAL::{'$' ~ $name};
+}