Geometric algebra: Difference between revisions
Content added Content deleted
(→{{header|javascript}}: update) |
(→{{header|Perl 6}}: rephrasing + minor fix in the verification code) |
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}</lang> |
}</lang> |
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And here is the code |
And here is the code for verifying the solution: |
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<lang perl6>use MultiVector; |
<lang perl6>use MultiVector; |
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use Test; |
use Test; |
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plan 29; |
plan 29; |
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sub infix:<cdot>($x, $y) { ($x*$y + $y*$x)/2 } |
sub infix:<cdot>($x, $y) { ($x*$y + $y*$x)/2 } |
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my @e = map &e, ^5; |
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for ^5 X ^5 -> ($i, $j) { |
for ^5 X ^5 -> ($i, $j) { |
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my $s = $i == $j ?? 1 !! 0; |
my $s = $i == $j ?? 1 !! 0; |
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ok |
ok e($i) cdot e($j) == $s, "e$i cdot e$j = $s"; |
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} |
} |
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sub random { |
sub random { |
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MultiVector.new: |
MultiVector.new: |
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:blades(my Real %{UInt} = $_ => rand.round(.01)) |
:blades(my Real %{UInt} = $_ => rand.round(.01)) |
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}, |
}, ^32; |
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} |
} |
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my ($a, $b, $c) = random() xx 3; |
my ($a, $b, $c) = random() xx 3; |
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ok ($a*$b)*$c == $a*($b*$c), 'associativity'; |
ok ($a*$b)*$c == $a*($b*$c), 'associativity'; |
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ok $a*($b + $c) == $a*$b + $a*$c, 'left distributivity'; |
ok $a*($b + $c) == $a*$b + $a*$c, 'left distributivity'; |
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ok ($a + $b)*$c == $a*$c + $b*$c, 'right distributivity'; |
ok ($a + $b)*$c == $a*$c + $b*$c, 'right distributivity'; |
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my @coeff = (.5 - rand) xx |
my @coeff = (.5 - rand) xx 5; |
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my $v = [+] @coeff Z* map &e, ^ |
my $v = [+] @coeff Z* map &e, ^5; |
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ok ($v**2).narrow ~~ Real, 'contraction';</lang> |
ok ($v**2).narrow ~~ Real, 'contraction';</lang> |
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{{out}} |
{{out}} |
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