Geometric algebra: Difference between revisions
Added Go
m (→{{header|EchoLisp}}: corrected a typo (generationg ──► generating).) |
(Added Go) |
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Line 274:
<br> <b>e</b>1<b>e</b>2<b>e</b>3 * <b>e</b>2<b>e</b>3 = - <b>e</b>1
<br> <b>e</b>1<b>e</b>2<b>e</b>3 * <b>e</b>1<b>e</b>2<b>e</b>3 = - <b>1</b>
=={{header|Go}}==
{{trans|JavaScript}}
<lang go>package main
import (
"fmt"
"math/rand"
"time"
)
type vector []float64
func e(n uint) vector {
if n > 4 {
panic("n must be less than 5")
}
result := make(vector, 32)
result[1<<n] = 1.0
return result
}
func cdot(a, b vector) vector {
return mul(vector{0.5}, add(mul(a, b), mul(b, a)))
}
func neg(x vector) vector {
return mul(vector{-1}, x)
}
func bitCount(i int) int {
i = i - ((i >> 1) & 0x55555555)
i = (i & 0x33333333) + ((i >> 2) & 0x33333333)
i = (i + (i >> 4)) & 0x0F0F0F0F
i = i + (i >> 8)
i = i + (i >> 16)
return i & 0x0000003F
}
func reorderingSign(i, j int) float64 {
i >>= 1
sum := 0
for i != 0 {
sum += bitCount(i & j)
i >>= 1
}
cond := (sum & 1) == 0
if cond {
return 1.0
}
return -1.0
}
func add(a, b vector) vector {
result := make(vector, 32)
copy(result, a)
for i, _ := range b {
result[i] += b[i]
}
return result
}
func mul(a, b vector) vector {
result := make(vector, 32)
for i, _ := range a {
if a[i] != 0 {
for j, _ := range b {
if b[j] != 0 {
s := reorderingSign(i, j) * a[i] * b[j]
k := i ^ j
result[k] += s
}
}
}
}
return result
}
func randomVector() vector {
result := make(vector, 32)
for i := uint(0); i < 5; i++ {
result = add(result, mul(vector{rand.Float64()}, e(i)))
}
return result
}
func randomMultiVector() vector {
result := make(vector, 32)
for i := 0; i < 32; i++ {
result[i] = rand.Float64()
}
return result
}
func main() {
rand.Seed(time.Now().UnixNano())
for i := uint(0); i < 5; i++ {
for j := uint(0); j < 5; j++ {
if i < j {
if cdot(e(i), e(j))[0] != 0 {
fmt.Println("Unexpected non-null scalar product.")
return
}
} else if i == j {
if cdot(e(i), e(j))[0] == 0 {
fmt.Println("Unexpected null scalar product.")
}
}
}
}
a := randomMultiVector()
b := randomMultiVector()
c := randomMultiVector()
x := randomVector()
// (ab)c == a(bc)
fmt.Println(mul(mul(a, b), c))
fmt.Println(mul(a, mul(b, c)))
// a(b + c) == ab + ac
fmt.Println(mul(a, add(b, c)))
fmt.Println(add(mul(a, b), mul(a, c)))
// (a + b)c == ac + bc
fmt.Println(mul(add(a, b), c))
fmt.Println(add(mul(a, c), mul(b, c)))
// x² is real
fmt.Println(mul(x, x))
}</lang>
{{out}}
<pre>
[1.6282881498413662 0.2490818261523896 -0.8936755921478269 -1.555477163901491 6.47589688756284 8.705633181089887 -1.28416798750558 -3.0984267307080446 -14.384954438859133 -13.511137120485879 6.071767421804147 1.099627765550034 -0.40641746354718655 -3.3593459129408076 -2.8089033176352967 -3.003641914720827 4.223517526463662 5.7807271315990185 -4.921271185053852 -5.698203073886508 -0.5449956221104395 3.2199941835007997 -0.4168598688210261 -1.6164380014352773 -13.447900615475964 -11.892642419707807 5.484071302025009 2.781324432176212 5.237445180167182 0.4643791234551212 -7.986755945938485 -2.9272187129576714]
[1.628288149841367 0.24908182615239083 -0.8936755921478254 -1.5554771639014895 6.475896887562836 8.705633181089889 -1.2841679875055805 -3.0984267307080433 -14.384954438859129 -13.51113712048588 6.071767421804145 1.099627765550032 -0.40641746354718755 -3.359345912940806 -2.8089033176352958 -3.003641914720825 4.223517526463663 5.7807271315990185 -4.921271185053855 -5.698203073886506 -0.5449956221104393 3.2199941835008032 -0.4168598688210253 -1.6164380014352775 -13.44790061547596 -11.89264241970781 5.484071302025003 2.781324432176209 5.237445180167183 0.464379123455121 -7.986755945938484 -2.9272187129576706]
[-4.652496095413123 -6.651741805769786 -0.18044192849719706 -1.118756694503706 -1.4545868044605725 0.10199724090664991 0.5018587820915257 2.3004721822960024 -1.813996268087529 0.38357415506855985 7.882236705126414 4.377167004918281 0.338317137066833 1.0631923204534859 5.08861779773926 4.611434580371178 -5.277764644396049 -7.961720991272197 -1.27063408303169 -1.2002120748969933 -0.3251154212726659 2.005000622005424 1.0505371909084391 1.9822320823801767 -2.271503682913346 -0.2403902213900877 6.6269980604812275 4.006018365857085 -0.15074367863748028 -0.48557428903338595 5.291057793190274 2.7751733146879394]
[-4.652496095413124 -6.651741805769786 -0.18044192849719662 -1.1187566945037064 -1.454586804460573 0.10199724090665008 0.5018587820915265 2.3004721822960037 -1.8139962680875295 0.38357415506856163 7.882236705126415 4.377167004918281 0.338317137066834 1.0631923204534859 5.088617797739261 4.611434580371178 -5.277764644396049 -7.9617209912721965 -1.2706340830316898 -1.200212074896994 -0.3251154212726654 2.0050006220054257 1.050537190908438 1.9822320823801762 -2.2715036829133437 -0.24039022139008648 6.626998060481226 4.006018365857084 -0.15074367863747984 -0.4855742890333855 5.291057793190275 2.7751733146879403]
[-4.682894668443622 -7.686899263290272 -0.2500585680601418 -0.8779897639638435 2.579501108403806 2.901924320921563 -0.4542430696469483 1.0374201754917136 -2.588607371991848 -3.229485794697976 7.444924967244714 4.93089687101153 -2.0124785310408284 0.46939350205418884 6.568153651157447 5.710192967946121 -1.41530169954937 -4.536345225213684 0.5240731948596796 1.5123734256564463 1.767786974613905 2.9960861930917018 0.969306657461082 1.036924529835111 -1.456640437477983 -1.3085896429723467 2.9678738261068895 1.3051596528834055 -3.8197616441989037 -1.3030506523824616 4.7818448875243895 4.122121121578954]
[-4.682894668443622 -7.686899263290271 -0.2500585680601421 -0.877989763963844 2.5795011084038055 2.9019243209215633 -0.4542430696469487 1.0374201754917127 -2.5886073719918494 -3.2294857946979736 7.444924967244715 4.93089687101153 -2.0124785310408275 0.46939350205418884 6.568153651157447 5.710192967946121 -1.415301699549369 -4.536345225213685 0.5240731948596802 1.512373425656447 1.7677869746139057 2.9960861930917013 0.9693066574610807 1.036924529835109 -1.456640437477983 -1.3085896429723465 2.9678738261068895 1.305159652883405 -3.819761644198904 -1.3030506523824616 4.781844887524388 4.122121121578957]
[2.1206022437357284 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|J}}==
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