[libmath-prime-util-perl] 28/54: Add xt ispower test and some more PE examples

[Partha P. Mukherjee]

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ppm-guest pushed a commit to annotated tag v0.38
in repository libmath-prime-util-perl.

commit 759e933fe14a70dfab6023ca68aa01a2392a780a
Author: Dana Jacobsen <dana at acm.org>
Date:   Thu Feb 13 12:26:24 2014 -0800

    Add xt ispower test and some more PE examples
---
 MANIFEST                      |  3 +++
 examples/project_euler_131.pl | 18 ++++++++++++++++++
 examples/project_euler_142.pl | 42 ++++++++++++++++++++++++++++++++++++++++++
 xt/test-ispower.pl            | 34 ++++++++++++++++++++++++++++++++++
 4 files changed, 97 insertions(+)

diff --git a/MANIFEST b/MANIFEST
index 399f926..5121185 100644
--- a/MANIFEST
+++ b/MANIFEST
@@ -77,6 +77,8 @@ examples/project_euler_069.pl
 examples/project_euler_070.pl
 examples/project_euler_072.pl
 examples/project_euler_095.pl
+examples/project_euler_131.pl
+examples/project_euler_142.pl
 examples/project_euler_211.pl
 examples/project_euler_214.pl
 examples/project_euler_342.pl
@@ -141,4 +143,5 @@ xt/test-primes-script.pl
 xt/test-primes-script2.pl
 xt/test-factor-yafu.pl
 xt/test-nextprime-yafu.pl
+xt/test-ispower.pl
 .travis.yml
diff --git a/examples/project_euler_131.pl b/examples/project_euler_131.pl
new file mode 100644
index 0000000..05b3d5b
--- /dev/null
+++ b/examples/project_euler_131.pl
@@ -0,0 +1,18 @@
+#!/usr/bin/env perl
+use warnings;
+use strict;
+use Math::Prime::Util qw/is_prime/;
+
+my $limit = shift || 1000000;
+
+# Any prime p where n^3 + n^2*p = m^3 must be the difference of (i+1)^3 - i^3.
+# So we'll just walk them looking for primes.
+
+my $sum = 0;
+foreach my $i (1 .. 2650070) {
+  my $j = $i+1;
+  my $p = $j*$j*$j - $i*$i*$i;
+  last if $p > $limit;
+  $sum++ if is_prime($p);
+}
+print "$sum\n";
diff --git a/examples/project_euler_142.pl b/examples/project_euler_142.pl
new file mode 100644
index 0000000..4d0ab12
--- /dev/null
+++ b/examples/project_euler_142.pl
@@ -0,0 +1,42 @@
+#!/usr/bin/env perl
+use warnings;
+use strict;
+use Math::Prime::Util qw/:all/;
+
+# x+y = a^2    x = a^2 - y
+# x-y = b^2    a^2-y-y = b^2  2y = b^2-a^2  y = (b^2-a^2)/2
+# x+z = c^2    z = c^2 - z
+# x-z = d^2    c^2-z-z=d^2    2z = c^2-d^2  z = (c^2-d^2)/2
+# y+z = e^2
+# y-z = f^2                                 x = (e^2-f^2)/2
+
+# x+y = a^2   x-y = b^2     ===>   2x = a^2+b^2   x=(a^2+b^2)/2
+# x+z = c^2   x-z = d^2     ===>   2z = c^2-d^2   z=(c^2-d^2)/2
+# y+z = e^2   y-z = f^2     ===>   2y = e^2+f^2   y=(e^2+f^2)/2
+
+# a^2 = x+y = x+y+z-z = x+z + y-z  = c^2 + f^2
+# e^2 = y+z = y+z+x-x = y+x -(x-z) = a^2 - d^2
+# b^2 = x-y = x-y+z-z = x+z -(y+z) = c^2 - e^2
+
+foreach my $a (4 .. 1000000) {
+  my $a2 = $a*$a;
+  foreach my $c (3 .. $a-1) {
+    my $c2 = $c*$c;
+    my $f2 = $a2 - $c2;
+    next unless $f2 >= 0 && is_power($f2,2);
+    foreach my $d (1 .. $c-1) {
+      next if ($d ^ $c) & 1;   # c and d must have same parity
+      my $d2 = $d*$d;
+      my $e2 = $a2 - $d2;
+      my $b2 = $c2 - $e2;
+      next if $e2 <= 0 || $b2 <= 0;
+      #next if (($a2+$b2) & 1) || (($e2+$f2) & 1) || (($c2-$d2) & 1);
+      next unless is_power($e2,2) && is_power($b2,2);
+      my $x = ($a2+$b2) >> 1;
+      my $y = ($e2+$f2) >> 1;
+      my $z = ($c2-$d2) >> 1;
+      my $result = $x+$y+$z;
+      die "$result  [$x $y $z]\n";
+    }
+  }
+}
diff --git a/xt/test-ispower.pl b/xt/test-ispower.pl
new file mode 100755
index 0000000..234b099
--- /dev/null
+++ b/xt/test-ispower.pl
@@ -0,0 +1,34 @@
+#!/usr/bin/env perl
+use strict;
+use warnings;
+$| = 1;  # fast pipes
+
+use Math::Prime::Util qw/is_prime is_power/;
+use Math::GMPz;
+
+foreach my $e (5 .. 37) {
+  next unless is_prime($e);
+  print "$e ";
+  for (3..1000000) {
+    my $n = Math::GMPz->new($_) ** $e;
+    last if $n > ~0;
+    die "$n\n" unless is_power($n);
+    foreach my $o (-10..10) {
+      my $m = $n+$o;
+      next if $m==$n;
+      die "$m\n" if is_power($m) && int(sqrt($m))**2 != $m && $m!=2197;
+    }
+  }
+}
+print "\n";
+
+my $int = 100000;
+foreach my $i (1 .. 80*$int) {
+  print "." unless $i % $int;
+  my @iroots = (0,0,map { int($i ** (1.0/$_) + 0.00001) ** $_ } 2 .. 12);
+  foreach my $e (2 .. 12) {
+    if (is_power($i,$e)) { die "$i $e" unless $iroots[$e] == $i; }
+    else                 { die "$i $e" unless $iroots[$e] != $i; }
+  }
+}
+print "\n";

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