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lib/Math/Algebra/Symbols/Sum.pm  view on Meta::CPAN

#_______________________________________________________________________

    my %S = ();
    for my $t(@s)
     {my $s = $t->Sqrt;
      my $S = $s->signature;
      push @{$S{$S}}, $t;
     }

#_______________________________________________________________________
# Square each partitions, as required by the formulae below.
#_______________________________________________________________________

    my @t;
    push @t, sigma(@n)->power($two) if scalar(@n);  # Non sqrt partition
    for my $s(keys(%S))
     {push @t, sigma(@{$S{$s}})->power($two);       # Sqrt partition
     }

#_______________________________________________________________________
# I can multiply out upto 4 square roots using the formulae below.
# There are formula to multiply out more than 4 sqrts, but they are big.
# These formulae are obtained by squaring out and rearranging:
# sqrt(a)+sqrt(b)+sqrt(c)+sqrt(d) == 0 until no sqrts remain, and
# then matching terms to produce optimal execution.
# This remarkable result was obtained with the help of this package:
# demonstrating its utility in optimizing complex calculations written
# in Perl: which in of itself cannot optimize broadly.
#_______________________________________________________________________

    my $ns = scalar(@t);
# 2016/01/26 12:29:28 No need to die
#   $ns < 5 or die "There are $ns square roots present.  I can handle less than 5";

t/bug_2004_6_1.t  view on Meta::CPAN

# Convert miles per gallon to liters per 100 kilometers symbolically.
# PhilipRBrenan@yahoo.com, 2004                                      
#______________________________________________________________________

($gallons, $miles) = symbols(qw(gallons miles));

$liters      = $gallons * 3.8;                       # 4: Have to use fraction, not decimal, improvement needed.
$kilometers  = $miles   * 1.6;                       # 5: Have to use fraction, not decimal, improvement needed.
$consumption = $liters / $kilometers * 100;          # 6: Correct precedence

print "Liters per 100 kilometers = $consumption\n";  # 7: As a general formula.

$miles       = 40;                                   # 8:  This expresses that the mileage is 40. Mike points out that 
$gallons     =  1;                                   # it would be more natural to express this as $miles/$gallons == 40,

print
  "$miles miles per $gallons gallon = ",
  eval "$consumption",                               # 9: Evaluate for a specific example
  " liters per 100 kilometers\n";

# Liters per 100 kilometers = 475/2*$gallons/$miles         # 10: The general formula
# 40 miles per 1 gallon = 5.9375 liters per 100 kilometers  # 11: A specific example

ok("$consumption" eq '475/2*$gallons/$miles');
ok(eval "$consumption" == 5.9375);

my ($gallons, $miles) = symbols(qw(gallons miles));
ok($gallons/$miles == 1/($miles/$gallons));          # 12: Check inverse of $miles/$gallon