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Quaternion type: Difference between revisions

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Quaternion type (view source)

Revision as of 17:46, 14 March 2020

16 bytes added ,  4 years ago
Rename Perl 6 -> Raku, alphabetize, minor clean-up
(Rename Perl 6 -> Raku, alphabetize, minor clean-up)
Line 791:
(13) true
Type: Boolean</lang>
 
=={{header|BBC BASIC}}==
Although BBC BASIC doesn't have native support for quaternions its array arithmetic provides all of the required operations either directly or very straightforwardly.
Line 1,043 ⟶ 1,044:
return EXIT_SUCCESS;
}</lang>
 
=={{header|C sharp}}==
<lang csharp>using System;
 
struct Quaternion : IEquatable<Quaternion>
{
public readonly double A, B, C, D;
 
public Quaternion(double a, double b, double c, double d)
{
this.A = a;
this.B = b;
this.C = c;
this.D = d;
}
 
public double Norm()
{
return Math.Sqrt(A * A + B * B + C * C + D * D);
}
 
public static Quaternion operator -(Quaternion q)
{
return new Quaternion(-q.A, -q.B, -q.C, -q.D);
}
 
public Quaternion Conjugate()
{
return new Quaternion(A, -B, -C, -D);
}
 
// implicit conversion takes care of real*quaternion and real+quaternion
public static implicit operator Quaternion(double d)
{
return new Quaternion(d, 0, 0, 0);
}
 
public static Quaternion operator +(Quaternion q1, Quaternion q2)
{
return new Quaternion(q1.A + q2.A, q1.B + q2.B, q1.C + q2.C, q1.D + q2.D);
}
 
public static Quaternion operator *(Quaternion q1, Quaternion q2)
{
return new Quaternion(
q1.A * q2.A - q1.B * q2.B - q1.C * q2.C - q1.D * q2.D,
q1.A * q2.B + q1.B * q2.A + q1.C * q2.D - q1.D * q2.C,
q1.A * q2.C - q1.B * q2.D + q1.C * q2.A + q1.D * q2.B,
q1.A * q2.D + q1.B * q2.C - q1.C * q2.B + q1.D * q2.A);
}
 
public static bool operator ==(Quaternion q1, Quaternion q2)
{
return q1.A == q2.A && q1.B == q2.B && q1.C == q2.C && q1.D == q2.D;
}
 
public static bool operator !=(Quaternion q1, Quaternion q2)
{
return !(q1 == q2);
}
 
#region Object Members
 
public override bool Equals(object obj)
{
if (obj is Quaternion)
return Equals((Quaternion)obj);
 
return false;
}
 
public override int GetHashCode()
{
return A.GetHashCode() ^ B.GetHashCode() ^ C.GetHashCode() ^ D.GetHashCode();
}
 
public override string ToString()
{
return string.Format("Q({0}, {1}, {2}, {3})", A, B, C, D);
}
 
#endregion
 
#region IEquatable<Quaternion> Members
 
public bool Equals(Quaternion other)
{
return other == this;
}
 
#endregion
}</lang>
 
Demonstration:
<lang csharp>using System;
 
static class Program
{
static void Main(string[] args)
{
Quaternion q = new Quaternion(1, 2, 3, 4);
Quaternion q1 = new Quaternion(2, 3, 4, 5);
Quaternion q2 = new Quaternion(3, 4, 5, 6);
double r = 7;
 
Console.WriteLine("q = {0}", q);
Console.WriteLine("q1 = {0}", q1);
Console.WriteLine("q2 = {0}", q2);
Console.WriteLine("r = {0}", r);
 
Console.WriteLine("q.Norm() = {0}", q.Norm());
Console.WriteLine("q1.Norm() = {0}", q1.Norm());
Console.WriteLine("q2.Norm() = {0}", q2.Norm());
 
Console.WriteLine("-q = {0}", -q);
Console.WriteLine("q.Conjugate() = {0}", q.Conjugate());
 
Console.WriteLine("q + r = {0}", q + r);
Console.WriteLine("q1 + q2 = {0}", q1 + q2);
Console.WriteLine("q2 + q1 = {0}", q2 + q1);
 
Console.WriteLine("q * r = {0}", q * r);
Console.WriteLine("q1 * q2 = {0}", q1 * q2);
Console.WriteLine("q2 * q1 = {0}", q2 * q1);
 
Console.WriteLine("q1*q2 {0} q2*q1", (q1 * q2) == (q2 * q1) ? "==" : "!=");
}
}</lang>
 
{{out}}
<pre>q = Q(1, 2, 3, 4)
q1 = Q(2, 3, 4, 5)
q2 = Q(3, 4, 5, 6)
r = 7
q.Norm() = 5.47722557505166
q1.Norm() = 7.34846922834953
q2.Norm() = 9.2736184954957
-q = Q(-1, -2, -3, -4)
q.Conjugate() = Q(1, -2, -3, -4)
q + r = Q(8, 2, 3, 4)
q1 + q2 = Q(5, 7, 9, 11)
q2 + q1 = Q(5, 7, 9, 11)
q * r = Q(7, 14, 21, 28)
q1 * q2 = Q(-56, 16, 24, 26)
q2 * q1 = Q(-56, 18, 20, 28)
q1*q2 != q2*q1</pre>
 
=={{header|C++}}==
Line 1,240 ⟶ 1,387:
6 + 0i + 0j + 0k
</pre>
 
=={{header|C sharp}}==
<lang csharp>using System;
 
struct Quaternion : IEquatable<Quaternion>
{
public readonly double A, B, C, D;
 
public Quaternion(double a, double b, double c, double d)
{
this.A = a;
this.B = b;
this.C = c;
this.D = d;
}
 
public double Norm()
{
return Math.Sqrt(A * A + B * B + C * C + D * D);
}
 
public static Quaternion operator -(Quaternion q)
{
return new Quaternion(-q.A, -q.B, -q.C, -q.D);
}
 
public Quaternion Conjugate()
{
return new Quaternion(A, -B, -C, -D);
}
 
// implicit conversion takes care of real*quaternion and real+quaternion
public static implicit operator Quaternion(double d)
{
return new Quaternion(d, 0, 0, 0);
}
 
public static Quaternion operator +(Quaternion q1, Quaternion q2)
{
return new Quaternion(q1.A + q2.A, q1.B + q2.B, q1.C + q2.C, q1.D + q2.D);
}
 
public static Quaternion operator *(Quaternion q1, Quaternion q2)
{
return new Quaternion(
q1.A * q2.A - q1.B * q2.B - q1.C * q2.C - q1.D * q2.D,
q1.A * q2.B + q1.B * q2.A + q1.C * q2.D - q1.D * q2.C,
q1.A * q2.C - q1.B * q2.D + q1.C * q2.A + q1.D * q2.B,
q1.A * q2.D + q1.B * q2.C - q1.C * q2.B + q1.D * q2.A);
}
 
public static bool operator ==(Quaternion q1, Quaternion q2)
{
return q1.A == q2.A && q1.B == q2.B && q1.C == q2.C && q1.D == q2.D;
}
 
public static bool operator !=(Quaternion q1, Quaternion q2)
{
return !(q1 == q2);
}
 
#region Object Members
 
public override bool Equals(object obj)
{
if (obj is Quaternion)
return Equals((Quaternion)obj);
 
return false;
}
 
public override int GetHashCode()
{
return A.GetHashCode() ^ B.GetHashCode() ^ C.GetHashCode() ^ D.GetHashCode();
}
 
public override string ToString()
{
return string.Format("Q({0}, {1}, {2}, {3})", A, B, C, D);
}
 
#endregion
 
#region IEquatable<Quaternion> Members
 
public bool Equals(Quaternion other)
{
return other == this;
}
 
#endregion
}</lang>
 
Demonstration:
<lang csharp>using System;
 
static class Program
{
static void Main(string[] args)
{
Quaternion q = new Quaternion(1, 2, 3, 4);
Quaternion q1 = new Quaternion(2, 3, 4, 5);
Quaternion q2 = new Quaternion(3, 4, 5, 6);
double r = 7;
 
Console.WriteLine("q = {0}", q);
Console.WriteLine("q1 = {0}", q1);
Console.WriteLine("q2 = {0}", q2);
Console.WriteLine("r = {0}", r);
 
Console.WriteLine("q.Norm() = {0}", q.Norm());
Console.WriteLine("q1.Norm() = {0}", q1.Norm());
Console.WriteLine("q2.Norm() = {0}", q2.Norm());
 
Console.WriteLine("-q = {0}", -q);
Console.WriteLine("q.Conjugate() = {0}", q.Conjugate());
 
Console.WriteLine("q + r = {0}", q + r);
Console.WriteLine("q1 + q2 = {0}", q1 + q2);
Console.WriteLine("q2 + q1 = {0}", q2 + q1);
 
Console.WriteLine("q * r = {0}", q * r);
Console.WriteLine("q1 * q2 = {0}", q1 * q2);
Console.WriteLine("q2 * q1 = {0}", q2 * q1);
 
Console.WriteLine("q1*q2 {0} q2*q1", (q1 * q2) == (q2 * q1) ? "==" : "!=");
}
}</lang>
 
{{out}}
<pre>q = Q(1, 2, 3, 4)
q1 = Q(2, 3, 4, 5)
q2 = Q(3, 4, 5, 6)
r = 7
q.Norm() = 5.47722557505166
q1.Norm() = 7.34846922834953
q2.Norm() = 9.2736184954957
-q = Q(-1, -2, -3, -4)
q.Conjugate() = Q(1, -2, -3, -4)
q + r = Q(8, 2, 3, 4)
q1 + q2 = Q(5, 7, 9, 11)
q2 + q1 = Q(5, 7, 9, 11)
q * r = Q(7, 14, 21, 28)
q1 * q2 = Q(-56, 16, 24, 26)
q2 * q1 = Q(-56, 18, 20, 28)
q1*q2 != q2*q1</pre>
 
=={{header|Common Lisp}}==
Line 2,124 ⟶ 2,125:
2013-09-04 16:40:29.822 a.out[2170:507] q1 * q2 = (-56.0, 16.0, 24.0, 26.0)
2013-09-04 16:40:29.822 a.out[2170:507] q2 * q1 = (-56.0, 18.0, 20.0, 28.0)</pre>
 
=={{header|Elena}}==
{{trans|C#}}
Line 4,238 ⟶ 4,240:
True
True</pre>
 
=={{header|Maple}}==
<lang Maple>
Line 4,438 ⟶ 4,441:
 
</pre>
 
=={{header|Mathematica}}==
<lang Mathematica><<Quaternions`
Line 4,761 ⟶ 4,765:
> q1 == q2
ans = 0</lang>
 
 
=={{header|Oforth}}==
Line 5,127 ⟶ 5,130:
print "a * b = ", $a * $b, "\n";
print "b * a = ", $b * $a, "\n";</lang>
 
=={{header|Perl 6}}==
<lang perl6>class Quaternion {
has Real ( $.r, $.i, $.j, $.k );
multi method new ( Real $r, Real $i, Real $j, Real $k ) {
self.bless: :$r, :$i, :$j, :$k;
}
multi qu(*@r) is export { Quaternion.new: |@r }
sub postfix:<j>(Real $x) is export { qu 0, 0, $x, 0 }
sub postfix:<k>(Real $x) is export { qu 0, 0, 0, $x }
method Str () { "$.r + {$.i}i + {$.j}j + {$.k}k" }
method reals () { $.r, $.i, $.j, $.k }
method conj () { qu $.r, -$.i, -$.j, -$.k }
method norm () { sqrt [+] self.reals X** 2 }
multi infix:<eqv> ( Quaternion $a, Quaternion $b ) is export { $a.reals eqv $b.reals }
multi infix:<+> ( Quaternion $a, Real $b ) is export { qu $b+$a.r, $a.i, $a.j, $a.k }
multi infix:<+> ( Real $a, Quaternion $b ) is export { qu $a+$b.r, $b.i, $b.j, $b.k }
multi infix:<+> ( Quaternion $a, Complex $b ) is export { qu $b.re + $a.r, $b.im + $a.i, $a.j, $a.k }
multi infix:<+> ( Complex $a, Quaternion $b ) is export { qu $a.re + $b.r, $a.im + $b.i, $b.j, $b.k }
multi infix:<+> ( Quaternion $a, Quaternion $b ) is export { qu $a.reals Z+ $b.reals }
multi prefix:<-> ( Quaternion $a ) is export { qu $a.reals X* -1 }
multi infix:<*> ( Quaternion $a, Real $b ) is export { qu $a.reals X* $b }
multi infix:<*> ( Real $a, Quaternion $b ) is export { qu $b.reals X* $a }
multi infix:<*> ( Quaternion $a, Complex $b ) is export { $a * qu $b.reals, 0, 0 }
multi infix:<*> ( Complex $a, Quaternion $b ) is export { $b R* qu $a.reals, 0, 0 }
multi infix:<*> ( Quaternion $a, Quaternion $b ) is export {
my @a_rijk = $a.reals;
my ( $r, $i, $j, $k ) = $b.reals;
return qu [+]( @a_rijk Z* $r, -$i, -$j, -$k ), # real
[+]( @a_rijk Z* $i, $r, $k, -$j ), # i
[+]( @a_rijk Z* $j, -$k, $r, $i ), # j
[+]( @a_rijk Z* $k, $j, -$i, $r ); # k
}
}
import Quaternion;
my $q = 1 + 2i + 3j + 4k;
my $q1 = 2 + 3i + 4j + 5k;
my $q2 = 3 + 4i + 5j + 6k;
my $r = 7;
say "1) q norm = {$q.norm}";
say "2) -q = {-$q}";
say "3) q conj = {$q.conj}";
say "4) q + r = {$q + $r}";
say "5) q1 + q2 = {$q1 + $q2}";
say "6) q * r = {$q * $r}";
say "7) q1 * q2 = {$q1 * $q2}";
say "8) q1q2 { $q1 * $q2 eqv $q2 * $q1 ?? '==' !! '!=' } q2q1";</lang>
{{out}}
<pre>1) q norm = 5.47722557505166
2) -q = -1 + -2i + -3j + -4k
3) q conj = 1 + -2i + -3j + -4k
4) q + r = 8 + 2i + 3j + 4k
5) q1 + q2 = 5 + 7i + 9j + 11k
6) q * r = 7 + 14i + 21j + 28k
7) q1 * q2 = -56 + 16i + 24j + 26k
8) q1q2 != q2q1</pre>
 
=={{header|Phix}}==
Line 5,498 ⟶ 5,436:
task C: q1=q1 --> equal
</pre>
 
 
=={{header|PowerShell}}==
Line 5,946 ⟶ 5,883:
Quaternion(real=0.9999999999999999, i=0.0, j=0.0, k=0.0)
>>> </lang>
 
 
 
=={{header|R}}==
Line 6,094 ⟶ 6,029:
#f
</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
<lang perl6>class Quaternion {
has Real ( $.r, $.i, $.j, $.k );
multi method new ( Real $r, Real $i, Real $j, Real $k ) {
self.bless: :$r, :$i, :$j, :$k;
}
multi qu(*@r) is export { Quaternion.new: |@r }
sub postfix:<j>(Real $x) is export { qu 0, 0, $x, 0 }
sub postfix:<k>(Real $x) is export { qu 0, 0, 0, $x }
method Str () { "$.r + {$.i}i + {$.j}j + {$.k}k" }
method reals () { $.r, $.i, $.j, $.k }
method conj () { qu $.r, -$.i, -$.j, -$.k }
method norm () { sqrt [+] self.reals X** 2 }
multi infix:<eqv> ( Quaternion $a, Quaternion $b ) is export { $a.reals eqv $b.reals }
multi infix:<+> ( Quaternion $a, Real $b ) is export { qu $b+$a.r, $a.i, $a.j, $a.k }
multi infix:<+> ( Real $a, Quaternion $b ) is export { qu $a+$b.r, $b.i, $b.j, $b.k }
multi infix:<+> ( Quaternion $a, Complex $b ) is export { qu $b.re + $a.r, $b.im + $a.i, $a.j, $a.k }
multi infix:<+> ( Complex $a, Quaternion $b ) is export { qu $a.re + $b.r, $a.im + $b.i, $b.j, $b.k }
multi infix:<+> ( Quaternion $a, Quaternion $b ) is export { qu $a.reals Z+ $b.reals }
multi prefix:<-> ( Quaternion $a ) is export { qu $a.reals X* -1 }
multi infix:<*> ( Quaternion $a, Real $b ) is export { qu $a.reals X* $b }
multi infix:<*> ( Real $a, Quaternion $b ) is export { qu $b.reals X* $a }
multi infix:<*> ( Quaternion $a, Complex $b ) is export { $a * qu $b.reals, 0, 0 }
multi infix:<*> ( Complex $a, Quaternion $b ) is export { $b R* qu $a.reals, 0, 0 }
multi infix:<*> ( Quaternion $a, Quaternion $b ) is export {
my @a_rijk = $a.reals;
my ( $r, $i, $j, $k ) = $b.reals;
return qu [+]( @a_rijk Z* $r, -$i, -$j, -$k ), # real
[+]( @a_rijk Z* $i, $r, $k, -$j ), # i
[+]( @a_rijk Z* $j, -$k, $r, $i ), # j
[+]( @a_rijk Z* $k, $j, -$i, $r ); # k
}
}
import Quaternion;
my $q = 1 + 2i + 3j + 4k;
my $q1 = 2 + 3i + 4j + 5k;
my $q2 = 3 + 4i + 5j + 6k;
my $r = 7;
say "1) q norm = {$q.norm}";
say "2) -q = {-$q}";
say "3) q conj = {$q.conj}";
say "4) q + r = {$q + $r}";
say "5) q1 + q2 = {$q1 + $q2}";
say "6) q * r = {$q * $r}";
say "7) q1 * q2 = {$q1 * $q2}";
say "8) q1q2 { $q1 * $q2 eqv $q2 * $q1 ?? '==' !! '!=' } q2q1";</lang>
{{out}}
<pre>1) q norm = 5.47722557505166
2) -q = -1 + -2i + -3j + -4k
3) q conj = 1 + -2i + -3j + -4k
4) q + r = 8 + 2i + 3j + 4k
5) q1 + q2 = 5 + 7i + 9j + 11k
6) q * r = 7 + 14i + 21j + 28k
7) q1 * q2 = -56 + 16i + 24j + 26k
8) q1q2 != q2q1</pre>
 
=={{header|Red}}==
Thundergnat
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