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Geometric algebra: Difference between revisions
→{{header|Nim}}
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=={{header|Nim}}==
{{trans|Go}}
<lang Nim>import bitops, random, sequtils, strutils
type Vector = seq[float]
func reorderingSign(i, j: int): float =
var i = i shr 1
var sum = 0
while i != 0:
sum += countSetBits(i and j)
i = i shr 1
result = if (sum and 1) == 0: 1 else: -1
func e(n: Natural): Vector =
result.setLen(32)
assert n < 5, "index must be less than 5; got $#.".format(n)
result[1 shl n] = 1
func `+`(a, b: Vector): Vector =
result.setLen(32)
for i in 0..b.high:
result[i] = a[i] + b[i]
func `*`(a, b: Vector): Vector =
result.setLen(32)
for i in 0..a.high:
if a[i] != 0:
for j in 0..b.high:
if b[j] != 0:
let s = reorderingSign(i, j) * a[i] * b[j]
let k = i xor j
result[k] += s
func dot(a, b: Vector): Vector =
(a * b + b * a) * @[0.5]
proc randomVector(): Vector =
result.setLen(32)
for i in 0..4:
result = result + @[rand(1.0)] * e(i)
proc randomMultiVector(): Vector =
newSeqWith(32, rand(1.0))
when isMainModule:
randomize()
for i in 0..4:
for j in 0..4:
if i < j:
if dot(e(i), e(j))[0] != 0:
raise newException(ValueError, "Unexpected non-null scalar product.")
elif i == j:
if dot(e(i), e(j))[0] == 0:
raise newException(ValueError, "Unexpected null scalar product.")
let a = randomMultiVector()
let b = randomMultiVector()
let c = randomMultiVector()
let x = randomVector()
# (ab)c == a(bc).
echo (a * b) * c
echo a * (b * c)
echo()
# a(b + c) == ab + ac.
echo a * (b + c)
echo a * b + a * c
echo()
# (a + b)c == ac + bc.
echo (a + b) * c
echo a * c + b * c
echo()
# x² is real.
echo x * x</lang>
{{out}}
<pre>@[-9.297288337196365, -13.59127999209494, 0.8722218109740326, 1.226935672314977, 7.508102247367465, 4.724948516329687, -5.033061024827017, -1.610503728288931, -3.33431529299565, 0.3532979194154671, 4.301275797990844, 0.515295984242726, 4.687736789474281, 2.172013218653572, 1.231492215423554, 0.3536950472866263, -2.327900412362799, -9.527999065273885, -1.555602751234329, 5.382767377500711, 6.267283581472086, 2.76910363753004, -2.301420318996988, 3.652383163769268, 1.752589228395532, 5.939099169023176, 4.479735695808257, 0.01446097776030125, -2.363384273037976, -5.720151847201447, -0.9397636030508162, -6.25507506195876]
@[-9.297288337196365, -13.59127999209493, 0.872221810974033, 1.226935672314978, 7.508102247367463, 4.72494851632969, -5.033061024827017, -1.610503728288931, -3.334315292995649, 0.3532979194154663, 4.301275797990842, 0.5152959842427232, 4.687736789474281, 2.172013218653572, 1.231492215423554, 0.3536950472866283, -2.327900412362798, -9.527999065273882, -1.55560275123433, 5.382767377500712, 6.267283581472084, 2.76910363753004, -2.301420318996988, 3.652383163769271, 1.752589228395533, 5.939099169023176, 4.47973569580826, 0.01446097776030148, -2.363384273037971, -5.720151847201445, -0.9397636030508175, -6.255075061958758]
@[-2.586487554821921, -2.653533704207625, 2.766021230656747, 2.036067471647896, 3.190493529679435, 2.42809912090021, 0.6900349473229486, 2.878934763823856, -3.935215841511595, -0.7288825987300381, 6.463778612248242, 4.417536841852129, 0.636912176867748, 4.413110019589562, 2.623393232840747, 1.608010580836939, -0.5328933745526506, -3.058074932298209, 2.178373565254037, 2.495618455562951, 4.609639873172126, 2.906729883514136, -0.934662696267724, 0.1369174733899857, 0.7572410282960323, 2.600596775217479, 4.079925278716743, 2.378076954647832, -1.529999013986847, 4.451662845891456, 0.07968415835836305, 0.7302442935297417]
@[-2.586487554821921, -2.653533704207625, 2.766021230656746, 2.036067471647896, 3.190493529679435, 2.42809912090021, 0.6900349473229492, 2.878934763823857, -3.935215841511596, -0.7288825987300391, 6.463778612248241, 4.417536841852128, 0.6369121768677473, 4.413110019589563, 2.623393232840748, 1.60801058083694, -0.5328933745526511, -3.058074932298209, 2.178373565254037, 2.495618455562951, 4.609639873172125, 2.906729883514135, -0.9346626962677241, 0.1369174733899854, 0.7572410282960332, 2.600596775217479, 4.079925278716742, 2.378076954647831, -1.529999013986847, 4.451662845891456, 0.0796841583583624, 0.7302442935297415]
@[-4.043970500041602, -6.87480031917386, 2.141017248170762, 0.3993395131802852, 0.8031440447491957, 3.401648770759057, 1.607243807621857, 3.522447744273161, -1.991055803046583, -0.7625625003549232, 6.536037328177198, 3.860062375500871, 2.237849358894385, 4.651754451010404, 8.300896571599077, 4.846096568587825, -2.0442907200416, -4.305082016141705, -0.9716874582456112, 0.214856705219781, 3.6445786747822, 2.050775132011032, -2.303468928921437, -1.111677463505033, 2.776551776801528, 1.829715078662076, 4.565478899003429, 1.874485695211426, -2.682597285575913, 1.056667802512815, 4.075588220758377, 1.609677009616234]
@[-4.043970500041601, -6.874800319173863, 2.141017248170761, 0.3993395131802844, 0.8031440447491961, 3.401648770759058, 1.607243807621859, 3.522447744273161, -1.991055803046583, -0.7625625003549237, 6.536037328177197, 3.860062375500871, 2.237849358894385, 4.651754451010405, 8.300896571599079, 4.846096568587828, -2.044290720041601, -4.305082016141704, -0.9716874582456119, 0.2148567052197807, 3.6445786747822, 2.050775132011031, -2.303468928921436, -1.111677463505034, 2.776551776801528, 1.829715078662075, 4.565478899003429, 1.874485695211426, -2.682597285575913, 1.056667802512815, 4.075588220758375, 1.609677009616233]
@[2.298735784397904, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]</pre>
=={{header|Phix}}==
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