Arithmetic/Complex: Difference between revisions
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Thundergnat (talk | contribs) m (syntax highlighting fixup automation) |
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{{trans|Python}} |
{{trans|Python}} |
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< |
<syntaxhighlight lang=11l>V z1 = 1.5 + 3i |
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V z2 = 1.5 + 1.5i |
V z2 = 1.5 + 1.5i |
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print(z1 + z2) |
print(z1 + z2) |
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print(z1 ^ z2) |
print(z1 ^ z2) |
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print(z1.real) |
print(z1.real) |
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print(z1.imag)</ |
print(z1.imag)</syntaxhighlight> |
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{{out}} |
{{out}} |
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=={{header|Action!}}== |
=={{header|Action!}}== |
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{{libheader|Action! Tool Kit}} |
{{libheader|Action! Tool Kit}} |
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< |
<syntaxhighlight lang=Action!>INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit |
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DEFINE R_="+0" |
DEFINE R_="+0" |
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ComplexConj(y,res) |
ComplexConj(y,res) |
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PrintComplexXY(y,res," conj") |
PrintComplexXY(y,res," conj") |
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RETURN</ |
RETURN</syntaxhighlight> |
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{{out}} |
{{out}} |
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[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Complex.png Screenshot from Atari 8-bit computer] |
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Complex.png Screenshot from Atari 8-bit computer] |
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=={{header|Ada}}== |
=={{header|Ada}}== |
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< |
<syntaxhighlight lang=ada>with Ada.Numerics.Generic_Complex_Types; |
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with Ada.Text_IO.Complex_IO; |
with Ada.Text_IO.Complex_IO; |
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Put("Conjugate(-A) = "); |
Put("Conjugate(-A) = "); |
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C := Conjugate (C); Put(C); |
C := Conjugate (C); Put(C); |
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end Complex_Operations;</ |
end Complex_Operations;</syntaxhighlight> |
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=={{header|ALGOL 68}}== |
=={{header|ALGOL 68}}== |
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Line 259: | Line 259: | ||
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} |
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} |
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{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}} |
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}} |
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< |
<syntaxhighlight lang=algol68>main:( |
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FORMAT compl fmt = $g(-7,5)"⊥"g(-7,5)$; |
FORMAT compl fmt = $g(-7,5)"⊥"g(-7,5)$; |
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); |
); |
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compl operations |
compl operations |
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)</ |
)</syntaxhighlight> |
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{{out}}<pre> |
{{out}}<pre> |
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=={{header|ALGOL W}}== |
=={{header|ALGOL W}}== |
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Complex is a built-in type in Algol W. |
Complex is a built-in type in Algol W. |
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< |
<syntaxhighlight lang=algolw>begin |
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% show some complex arithmetic % |
% show some complex arithmetic % |
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% returns c + d, using the builtin complex + operator % |
% returns c + d, using the builtin complex + operator % |
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write( "1/c : ", cInv( c ) ); |
write( "1/c : ", cInv( c ) ); |
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write( "conj c : ", cConj( c ) ) |
write( "conj c : ", cConj( c ) ) |
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end.</ |
end.</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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-x ⍝negation |
-x ⍝negation |
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¯1J¯1 |
¯1J¯1 |
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</syntaxhighlight> |
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</lang> |
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=={{header|App Inventor}}== |
=={{header|App Inventor}}== |
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=={{header|Arturo}}== |
=={{header|Arturo}}== |
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< |
<syntaxhighlight lang=rebol>a: to :complex [1 1] |
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b: to :complex @[pi 1.2] |
b: to :complex @[pi 1.2] |
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print ["1 / a:" 1 / a] |
print ["1 / a:" 1 / a] |
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print ["neg a:" neg a] |
print ["neg a:" neg a] |
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print ["conj a:" conj a]</ |
print ["conj a:" conj a]</syntaxhighlight> |
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{{out}} |
{{out}} |
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=={{header|AutoHotkey}}== |
=={{header|AutoHotkey}}== |
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contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276431.html#276431 forum] |
contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276431.html#276431 forum] |
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< |
<syntaxhighlight lang=AutoHotkey>Cset(C,1,1) |
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MsgBox % Cstr(C) ; 1 + i*1 |
MsgBox % Cstr(C) ; 1 + i*1 |
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Cneg(C,C) |
Cneg(C,C) |
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NumPut( Cre(A)/d,C,0,"double") |
NumPut( Cre(A)/d,C,0,"double") |
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NumPut(-Cim(A)/d,C,8,"double") |
NumPut(-Cim(A)/d,C,8,"double") |
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}</ |
}</syntaxhighlight> |
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=={{header|AWK}}== |
=={{header|AWK}}== |
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contributed by af |
contributed by af |
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< |
<syntaxhighlight lang=awk># simulate a struct using associative arrays |
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function complex(arr, re, im) { |
function complex(arr, re, im) { |
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arr["re"] = re |
arr["re"] = re |
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mult(i, i, i) |
mult(i, i, i) |
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printComplex(i) |
printComplex(i) |
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}</ |
}</syntaxhighlight> |
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=={{header|BASIC}}== |
=={{header|BASIC}}== |
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{{works with|QuickBasic|4.5}} |
{{works with|QuickBasic|4.5}} |
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< |
<syntaxhighlight lang=qbasic>TYPE complex |
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real AS DOUBLE |
real AS DOUBLE |
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imag AS DOUBLE |
imag AS DOUBLE |
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Line 564: | Line 564: | ||
c.imag = a.imag - b.imag |
c.imag = a.imag - b.imag |
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END SUB |
END SUB |
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</syntaxhighlight> |
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</lang> |
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{{out}} |
{{out}} |
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<pre>Siendo x = 1+ 3i |
<pre>Siendo x = 1+ 3i |
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Line 579: | Line 579: | ||
=={{header|BBC BASIC}}== |
=={{header|BBC BASIC}}== |
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{{works with|BBC BASIC for Windows}} |
{{works with|BBC BASIC for Windows}} |
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< |
<syntaxhighlight lang=bbcbasic> DIM Complex{r, i} |
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DIM a{} = Complex{} : a.r = 1.0 : a.i = 1.0 |
DIM a{} = Complex{} : a.r = 1.0 : a.i = 1.0 |
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DEF FNcomplexshow(src{}) |
DEF FNcomplexshow(src{}) |
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IF src.i >= 0 THEN = STR$(src.r) + " + " +STR$(src.i) + "i" |
IF src.i >= 0 THEN = STR$(src.r) + " + " +STR$(src.i) + "i" |
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= STR$(src.r) + " - " + STR$(-src.i) + "i"</ |
= STR$(src.r) + " - " + STR$(-src.i) + "i"</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>Result of addition is 4.14159265 + 2.2i |
<pre>Result of addition is 4.14159265 + 2.2i |
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=={{header|Bracmat}}== |
=={{header|Bracmat}}== |
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Bracmat recognizes the symbol <code>i</code> as the square root of <code>-1</code>. The results of the functions below are not necessarily of the form <code>a+b*i</code>, but as the last example shows, Bracmat nevertheless can work out that two different representations of the same mathematical object, when subtracted from each other, give zero. You may wonder why in the functions <code>multiply</code> and <code>negate</code> there are terms <code>1</code> and <code>-1</code>. These terms are a trick to force Bracmat to expand the products. As it is more costly to factorize a sum than to expand a product into a sum, Bracmat retains isolated products. However, when in combination with a non-zero term, the product is expanded. |
Bracmat recognizes the symbol <code>i</code> as the square root of <code>-1</code>. The results of the functions below are not necessarily of the form <code>a+b*i</code>, but as the last example shows, Bracmat nevertheless can work out that two different representations of the same mathematical object, when subtracted from each other, give zero. You may wonder why in the functions <code>multiply</code> and <code>negate</code> there are terms <code>1</code> and <code>-1</code>. These terms are a trick to force Bracmat to expand the products. As it is more costly to factorize a sum than to expand a product into a sum, Bracmat retains isolated products. However, when in combination with a non-zero term, the product is expanded. |
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< |
<syntaxhighlight lang=bracmat> (add=a b.!arg:(?a,?b)&!a+!b) |
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& ( multiply |
& ( multiply |
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= a b.!arg:(?a,?b)&1+!a*!b+-1 |
= a b.!arg:(?a,?b)&1+!a*!b+-1 |
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& out |
& out |
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$ ("sin$x minus conjugate sin$x =" sin$x+negate$(conjugate$(sin$x))) |
$ ("sin$x minus conjugate sin$x =" sin$x+negate$(conjugate$(sin$x))) |
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& done;</ |
& done;</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>(a+i*b)+(a+i*b) = 2*a+2*i*b |
<pre>(a+i*b)+(a+i*b) = 2*a+2*i*b |
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{{works with|C99}} |
{{works with|C99}} |
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The more recent [[C99]] standard has built-in complex number primitive types, which can be declared with float, double, or long double precision. To use these types and their associated library functions, you must include the <complex.h> header. (Note: this is a ''different'' header than the <complex> templates that are defined by [[C++]].) [http://www.opengroup.org/onlinepubs/009695399/basedefs/complex.h.html] [http://publib.boulder.ibm.com/infocenter/pseries/v5r3/index.jsp?topic=/com.ibm.vacpp7a.doc/language/ref/clrc03complex_types.htm] |
The more recent [[C99]] standard has built-in complex number primitive types, which can be declared with float, double, or long double precision. To use these types and their associated library functions, you must include the <complex.h> header. (Note: this is a ''different'' header than the <complex> templates that are defined by [[C++]].) [http://www.opengroup.org/onlinepubs/009695399/basedefs/complex.h.html] [http://publib.boulder.ibm.com/infocenter/pseries/v5r3/index.jsp?topic=/com.ibm.vacpp7a.doc/language/ref/clrc03complex_types.htm] |
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< |
<syntaxhighlight lang=c>#include <complex.h> |
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#include <stdio.h> |
#include <stdio.h> |
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c = conj(a); |
c = conj(a); |
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printf("\nconj a="); cprint(c); printf("\n"); |
printf("\nconj a="); cprint(c); printf("\n"); |
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}</ |
}</syntaxhighlight> |
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{{works with|C89}} |
{{works with|C89}} |
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User-defined type: |
User-defined type: |
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< |
<syntaxhighlight lang=c>typedef struct{ |
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double real; |
double real; |
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double imag; |
double imag; |
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printf("\n-a="); put(neg(a)); |
printf("\n-a="); put(neg(a)); |
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printf("\nconj a="); put(conj(a)); printf("\n"); |
printf("\nconj a="); put(conj(a)); printf("\n"); |
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}</ |
}</syntaxhighlight> |
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=={{header|C sharp|C#}}== |
=={{header|C sharp|C#}}== |
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{{works with|C sharp|C#|4.0}} |
{{works with|C sharp|C#|4.0}} |
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< |
<syntaxhighlight lang=csharp>namespace RosettaCode.Arithmetic.Complex |
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{ |
{ |
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using System; |
using System; |
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Line 784: | Line 784: | ||
} |
} |
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} |
} |
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}</ |
}</syntaxhighlight> |
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{{works with|C sharp|C#|1.2}} |
{{works with|C sharp|C#|1.2}} |
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< |
<syntaxhighlight lang=csharp>using System; |
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public struct ComplexNumber |
public struct ComplexNumber |
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Console.WriteLine(ComplexMath.Power(j, 0) == 1.0); |
Console.WriteLine(ComplexMath.Power(j, 0) == 1.0); |
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} |
} |
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}</ |
}</syntaxhighlight> |
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=={{header|C++}}== |
=={{header|C++}}== |
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< |
<syntaxhighlight lang=cpp>#include <iostream> |
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#include <complex> |
#include <complex> |
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using std::complex; |
using std::complex; |
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// conjugate |
// conjugate |
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std::cout << std::conj(a) << std::endl; |
std::cout << std::conj(a) << std::endl; |
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}</ |
}</syntaxhighlight> |
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=={{header|Clojure}}== |
=={{header|Clojure}}== |
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Therefore, we use defrecord and the multimethods in |
Therefore, we use defrecord and the multimethods in |
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clojure.algo.generic.arithmetic to make a Complex number type. |
clojure.algo.generic.arithmetic to make a Complex number type. |
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< |
<syntaxhighlight lang=clojure>(ns rosettacode.arithmetic.cmplx |
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(:require [clojure.algo.generic.arithmetic :as ga]) |
(:require [clojure.algo.generic.arithmetic :as ga]) |
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(:import [java.lang Number])) |
(:import [java.lang Number])) |
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(let [m (+ (* r r) (* i i))] |
(let [m (+ (* r r) (* i i))] |
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(->Complex (/ r m) (- (/ i m))))) |
(->Complex (/ r m) (- (/ i m))))) |
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</syntaxhighlight> |
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</lang> |
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=={{header|COBOL}}== |
=={{header|COBOL}}== |
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===.NET Complex class=== |
===.NET Complex class=== |
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{{trans|C#}} |
{{trans|C#}} |
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< |
<syntaxhighlight lang=cobol> $SET SOURCEFORMAT "FREE" |
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$SET ILUSING "System" |
$SET ILUSING "System" |
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$SET ILUSING "System.Numerics" |
$SET ILUSING "System.Numerics" |
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end-perform |
end-perform |
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end method. |
end method. |
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end class.</ |
end class.</syntaxhighlight> |
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===Implementation=== |
===Implementation=== |
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< |
<syntaxhighlight lang=cobol> $SET SOURCEFORMAT "FREE" |
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class-id Prog. |
class-id Prog. |
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method-id. Main static. |
method-id. Main static. |
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end operator. |
end operator. |
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end class.</ |
end class.</syntaxhighlight> |
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=={{header|CoffeeScript}}== |
=={{header|CoffeeScript}}== |
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< |
<syntaxhighlight lang=coffeescript> |
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# create an immutable Complex type |
# create an immutable Complex type |
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class Complex |
class Complex |
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quotient = product.times inverse |
quotient = product.times inverse |
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console.log "(#{product}) / (#{b}) = #{quotient}" |
console.log "(#{product}) / (#{b}) = #{quotient}" |
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</syntaxhighlight> |
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</lang> |
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{{out}} |
{{out}} |
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Complex numbers are a built-in numeric type in Common Lisp. The literal syntax for a complex number is <tt>#C(<var>real</var> <var>imaginary</var>)</tt>. The components of a complex number may be integers, ratios, or floating-point. Arithmetic operations automatically return complex (or real) numbers when appropriate: |
Complex numbers are a built-in numeric type in Common Lisp. The literal syntax for a complex number is <tt>#C(<var>real</var> <var>imaginary</var>)</tt>. The components of a complex number may be integers, ratios, or floating-point. Arithmetic operations automatically return complex (or real) numbers when appropriate: |
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< |
<syntaxhighlight lang=lisp>> (sqrt -1) |
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#C(0.0 1.0) |
#C(0.0 1.0) |
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> (expt #c(0 1) 2) |
> (expt #c(0 1) 2) |
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-1</ |
-1</syntaxhighlight> |
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Here are some arithmetic operations on complex numbers: |
Here are some arithmetic operations on complex numbers: |
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< |
<syntaxhighlight lang=lisp>> (+ #c(0 1) #c(1 0)) |
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#C(1 1) |
#C(1 1) |
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> (conjugate #c(1 1)) |
> (conjugate #c(1 1)) |
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#C(1 -1)</ |
#C(1 -1)</syntaxhighlight> |
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Complex numbers can be constructed from real and imaginary parts using the <tt>complex</tt> function, and taken apart using the <tt>realpart</tt> and <tt>imagpart</tt> functions. |
Complex numbers can be constructed from real and imaginary parts using the <tt>complex</tt> function, and taken apart using the <tt>realpart</tt> and <tt>imagpart</tt> functions. |
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< |
<syntaxhighlight lang=lisp>> (complex 64 (/ 3 4)) |
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#C(64 3/4) |
#C(64 3/4) |
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Line 1,290: | Line 1,290: | ||
> (imagpart (complex 0 pi)) |
> (imagpart (complex 0 pi)) |
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3.141592653589793d0</ |
3.141592653589793d0</syntaxhighlight> |
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=={{header|Component Pascal}}== |
=={{header|Component Pascal}}== |
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BlackBox Component Builder |
BlackBox Component Builder |
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< |
<syntaxhighlight lang=oberon2> |
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MODULE Complex; |
MODULE Complex; |
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IMPORT StdLog; |
IMPORT StdLog; |
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Line 1,381: | Line 1,381: | ||
END Complex. |
END Complex. |
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</syntaxhighlight> |
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</lang> |
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Execute: ^Q Complex.Do<br/> |
Execute: ^Q Complex.Do<br/> |
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{{out}} |
{{out}} |
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=={{header|D}}== |
=={{header|D}}== |
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Built-in complex numbers are now deprecated in D, to simplify the language. |
Built-in complex numbers are now deprecated in D, to simplify the language. |
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< |
<syntaxhighlight lang=d>import std.stdio, std.complex; |
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void main() { |
void main() { |
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writeln(1.0 / x); // inversion |
writeln(1.0 / x); // inversion |
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writeln(-x); // negation |
writeln(-x); // negation |
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}</ |
}</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>4.14159+2.2i |
<pre>4.14159+2.2i |
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=={{header|Dart}}== |
=={{header|Dart}}== |
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< |
<syntaxhighlight lang=dart> |
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class complex { |
class complex { |
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} |
} |
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</syntaxhighlight> |
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</lang> |
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=={{header|Delphi}}== |
=={{header|Delphi}}== |
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{{libheader| System.SysUtils}} |
{{libheader| System.SysUtils}} |
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{{libheader| System.VarCmplx}} |
{{libheader| System.VarCmplx}} |
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< |
<syntaxhighlight lang=Delphi> |
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program Arithmetic_Complex; |
program Arithmetic_Complex; |
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Readln; |
Readln; |
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end.</ |
end.</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>(5 + 3i) + (0,5 + 6i) = 5,5 + 9i |
<pre>(5 + 3i) + (0,5 + 6i) = 5,5 + 9i |
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=={{header|EchoLisp}}== |
=={{header|EchoLisp}}== |
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Complex numbers are part of the language. No special library is needed. |
Complex numbers are part of the language. No special library is needed. |
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< |
<syntaxhighlight lang=lisp> |
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(define a 42+666i) → a |
(define a 42+666i) → a |
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(define b 1+i) → b |
(define b 1+i) → b |
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Line 1,518: | Line 1,518: | ||
(magnitude b) → 1.4142135623730951 ; = sqrt(2) |
(magnitude b) → 1.4142135623730951 ; = sqrt(2) |
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(exp (* I PI)) → -1+0i ; Euler = e^(I*PI) = -1 |
(exp (* I PI)) → -1+0i ; Euler = e^(I*PI) = -1 |
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</syntaxhighlight> |
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</lang> |
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=={{header|Elixir}}== |
=={{header|Elixir}}== |
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< |
<syntaxhighlight lang=elixir>defmodule Complex do |
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import Kernel, except: [abs: 1, div: 2] |
import Kernel, except: [abs: 1, div: 2] |
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Line 1,605: | Line 1,605: | ||
end |
end |
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Complex.task</ |
Complex.task</syntaxhighlight> |
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{{out}} |
{{out}} |
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Line 1,622: | Line 1,622: | ||
=={{header|Erlang}}== |
=={{header|Erlang}}== |
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< |
<syntaxhighlight lang=Erlang>%% Task: Complex Arithmetic |
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%% Author: Abhay Jain |
%% Author: Abhay Jain |
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Line 1,679: | Line 1,679: | ||
true -> |
true -> |
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io:format("Ans = ~p+~pi~n", [A#complex.real, A#complex.img]) |
io:format("Ans = ~p+~pi~n", [A#complex.real, A#complex.img]) |
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end. </ |
end. </syntaxhighlight> |
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{{out}} |
{{out}} |
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< |
<syntaxhighlight lang=Erlang>Ans = 6+5i |
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Ans = -1+17i |
Ans = -1+17i |
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Ans = -1-3i |
Ans = -1-3i |
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Ans = 0.1-0.3i |
Ans = 0.1-0.3i |
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Ans = 1-3i</ |
Ans = 1-3i</syntaxhighlight> |
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=={{header|ERRE}}== |
=={{header|ERRE}}== |
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Line 1,737: | Line 1,737: | ||
PRINT(Z.REAL#;" + ";Z.IMAG#;"i") |
PRINT(Z.REAL#;" + ";Z.IMAG#;"i") |
||
END PROGRAM |
END PROGRAM |
||
</syntaxhighlight> |
|||
</lang> |
|||
Note: Adapted from QuickBasic source code |
Note: Adapted from QuickBasic source code |
||
{{out}} |
{{out}} |
||
Line 1,747: | Line 1,747: | ||
=={{header|Euler Math Toolbox}}== |
=={{header|Euler Math Toolbox}}== |
||
< |
<syntaxhighlight lang=Euler Math Toolbox> |
||
>a=1+4i; b=5-3i; |
>a=1+4i; b=5-3i; |
||
>a+b |
>a+b |
||
Line 1,761: | Line 1,761: | ||
>conj(a) |
>conj(a) |
||
1-4i |
1-4i |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Euphoria}}== |
=={{header|Euphoria}}== |
||
< |
<syntaxhighlight lang=euphoria>constant REAL = 1, IMAG = 2 |
||
type complex(sequence s) |
type complex(sequence s) |
||
return length(s) = 2 and atom(s[REAL]) and atom(s[IMAG]) |
return length(s) = 2 and atom(s[REAL]) and atom(s[IMAG]) |
||
Line 1,821: | Line 1,821: | ||
printf(1,"a*b = %s\n",{scomplex(mult(a,b))}) |
printf(1,"a*b = %s\n",{scomplex(mult(a,b))}) |
||
printf(1,"1/a = %s\n",{scomplex(inv(a))}) |
printf(1,"1/a = %s\n",{scomplex(inv(a))}) |
||
printf(1,"-a = %s\n",{scomplex(neg(a))})</ |
printf(1,"-a = %s\n",{scomplex(neg(a))})</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 1,835: | Line 1,835: | ||
C1: |
C1: |
||
< |
<syntaxhighlight lang=excel> |
||
=IMSUM(A1;B1) |
=IMSUM(A1;B1) |
||
</syntaxhighlight> |
|||
</lang> |
|||
D1: |
D1: |
||
< |
<syntaxhighlight lang=excel> |
||
=IMPRODUCT(A1;B1) |
=IMPRODUCT(A1;B1) |
||
</syntaxhighlight> |
|||
</lang> |
|||
E1: |
E1: |
||
< |
<syntaxhighlight lang=excel> |
||
=IMSUB(0;D1) |
=IMSUB(0;D1) |
||
</syntaxhighlight> |
|||
</lang> |
|||
F1: |
F1: |
||
< |
<syntaxhighlight lang=excel> |
||
=IMDIV(1;E28) |
=IMDIV(1;E28) |
||
</syntaxhighlight> |
|||
</lang> |
|||
G1: |
G1: |
||
< |
<syntaxhighlight lang=excel> |
||
=IMCONJUGATE(C28) |
=IMCONJUGATE(C28) |
||
</syntaxhighlight> |
|||
</lang> |
|||
E1 will have the negation of D1's value |
E1 will have the negation of D1's value |
||
Line 1,863: | Line 1,863: | ||
<lang> |
<lang> |
||
1+2i 3+5i 4+7i -7+11i 7-11i 0,0411764705882353+0,0647058823529412i 4-7i |
1+2i 3+5i 4+7i -7+11i 7-11i 0,0411764705882353+0,0647058823529412i 4-7i |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|F Sharp|F#}}== |
=={{header|F Sharp|F#}}== |
||
Entered into an interactive session to show the results: |
Entered into an interactive session to show the results: |
||
< |
<syntaxhighlight lang=fsharp> |
||
> open Microsoft.FSharp.Math;; |
> open Microsoft.FSharp.Math;; |
||
Line 1,913: | Line 1,913: | ||
i = -1.0; |
i = -1.0; |
||
r = -1.0;} |
r = -1.0;} |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Factor}}== |
=={{header|Factor}}== |
||
< |
<syntaxhighlight lang=factor>USING: combinators kernel math math.functions prettyprint ; |
||
C{ 1 2 } C{ 0.9 -2.78 } { |
C{ 1 2 } C{ 0.9 -2.78 } { |
||
Line 1,933: | Line 1,933: | ||
[ log . ] ! natural logarithm |
[ log . ] ! natural logarithm |
||
[ sqrt . ] ! square root |
[ sqrt . ] ! square root |
||
} cleave</ |
} cleave</syntaxhighlight> |
||
=={{header|Forth}}== |
=={{header|Forth}}== |
||
{{libheader|Forth Scientific Library}} |
{{libheader|Forth Scientific Library}} |
||
Historically, there was no standard syntax or mechanism for complex numbers and several implementations suitable for different uses were provided. However later a wordset ''was'' standardised as "Algorithm #60". |
Historically, there was no standard syntax or mechanism for complex numbers and several implementations suitable for different uses were provided. However later a wordset ''was'' standardised as "Algorithm #60". |
||
< |
<syntaxhighlight lang=forth>S" fsl-util.fs" REQUIRED |
||
S" complex.fs" REQUIRED |
S" complex.fs" REQUIRED |
||
Line 1,950: | Line 1,950: | ||
1e 0e zconstant 1+0i |
1e 0e zconstant 1+0i |
||
1+0i x z@ z/ z. |
1+0i x z@ z/ z. |
||
x z@ znegate z.</ |
x z@ znegate z.</syntaxhighlight> |
||
=={{header|Fortran}}== |
=={{header|Fortran}}== |
||
In ANSI FORTRAN 66 or later, COMPLEX is a built-in data type with full access to intrinsic arithmetic operations. Putting each native operation in a function is horribly inefficient, so I will simply demonstrate the operations. This example shows usage for Fortran 90 or later: |
In ANSI FORTRAN 66 or later, COMPLEX is a built-in data type with full access to intrinsic arithmetic operations. Putting each native operation in a function is horribly inefficient, so I will simply demonstrate the operations. This example shows usage for Fortran 90 or later: |
||
< |
<syntaxhighlight lang=fortran>program cdemo |
||
complex :: a = (5,3), b = (0.5, 6.0) ! complex initializer |
complex :: a = (5,3), b = (0.5, 6.0) ! complex initializer |
||
complex :: absum, abprod, aneg, ainv |
complex :: absum, abprod, aneg, ainv |
||
Line 1,962: | Line 1,962: | ||
aneg = -a |
aneg = -a |
||
ainv = 1.0 / a |
ainv = 1.0 / a |
||
end program cdemo</ |
end program cdemo</syntaxhighlight> |
||
And, although you did not ask, here are demonstrations of some other common complex number operations |
And, although you did not ask, here are demonstrations of some other common complex number operations |
||
< |
<syntaxhighlight lang=fortran>program cdemo2 |
||
complex :: a = (5,3), b = (0.5, 6) ! complex initializer |
complex :: a = (5,3), b = (0.5, 6) ! complex initializer |
||
real, parameter :: pi = 3.141592653589793 ! The constant "pi" |
real, parameter :: pi = 3.141592653589793 ! The constant "pi" |
||
Line 1,992: | Line 1,992: | ||
! useful for FFT calculations, among other things |
! useful for FFT calculations, among other things |
||
unit_circle = exp(2*i*pi/n * (/ (j, j=0, n-1) /) ) |
unit_circle = exp(2*i*pi/n * (/ (j, j=0, n-1) /) ) |
||
end program cdemo2</ |
end program cdemo2</syntaxhighlight> |
||
=={{header|FreeBASIC}}== |
=={{header|FreeBASIC}}== |
||
< |
<syntaxhighlight lang=freebasic>' FB 1.05.0 Win64 |
||
Type Complex |
Type Complex |
||
Line 2,059: | Line 2,059: | ||
Print |
Print |
||
Print "Press any key to quit" |
Print "Press any key to quit" |
||
Sleep</ |
Sleep</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 2,076: | Line 2,076: | ||
=={{header|Free Pascal}}== |
=={{header|Free Pascal}}== |
||
FreePascal has a complex units. Example of usage: |
FreePascal has a complex units. Example of usage: |
||
< |
<syntaxhighlight lang=Pascal>Program ComplexDemo; |
||
uses |
uses |
||
Line 2,104: | Line 2,104: | ||
writeln ('conj(5 + i3): ', acong.re:3:1, ' + i', acong.im:3:1); |
writeln ('conj(5 + i3): ', acong.re:3:1, ' + i', acong.im:3:1); |
||
end. |
end. |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Frink}}== |
=={{header|Frink}}== |
||
Frink's operations handle complex numbers naturally. The real and imaginary parts of complex numbers can be arbitrary-sized integers, arbitrary-sized rational numbers, or arbitrary-precision floating-point numbers. |
Frink's operations handle complex numbers naturally. The real and imaginary parts of complex numbers can be arbitrary-sized integers, arbitrary-sized rational numbers, or arbitrary-precision floating-point numbers. |
||
< |
<syntaxhighlight lang=frink> |
||
add[x,y] := x + y |
add[x,y] := x + y |
||
multiply[x,y] := x * y |
multiply[x,y] := x * y |
||
Line 2,122: | Line 2,122: | ||
println["1/$a = " + invert[a]] |
println["1/$a = " + invert[a]] |
||
println["conjugate[$a] = " + conjugate[a]] |
println["conjugate[$a] = " + conjugate[a]] |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
Line 2,135: | Line 2,135: | ||
=={{header|Futhark}}== |
=={{header|Futhark}}== |
||
{{incorrect|Futhark|Futhark's syntax has changed, so "fun" should be "let"}} |
{{incorrect|Futhark|Futhark's syntax has changed, so "fun" should be "let"}} |
||
< |
<syntaxhighlight lang=Futhark> |
||
type complex = (f64,f64) |
type complex = (f64,f64) |
||
Line 2,163: | Line 2,163: | ||
else if o == 3 then complexNeg a |
else if o == 3 then complexNeg a |
||
else complexConj a |
else complexConj a |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|GAP}}== |
=={{header|GAP}}== |
||
< |
<syntaxhighlight lang=gap># GAP knows gaussian integers, gaussian rationals (i.e. Q[i]), and cyclotomic fields. Here are some examples. |
||
# E(n) is an nth primitive root of 1 |
# E(n) is an nth primitive root of 1 |
||
i := Sqrt(-1); |
i := Sqrt(-1); |
||
Line 2,184: | Line 2,184: | ||
# true |
# true |
||
Sqrt(-3) in Cyclotomics; |
Sqrt(-3) in Cyclotomics; |
||
# true</ |
# true</syntaxhighlight> |
||
=={{header|Go}}== |
=={{header|Go}}== |
||
Go has complex numbers built in, with the complex conjugate in the standard library. |
Go has complex numbers built in, with the complex conjugate in the standard library. |
||
< |
<syntaxhighlight lang=go>package main |
||
import ( |
import ( |
||
Line 2,205: | Line 2,205: | ||
fmt.Println("1 / a: ", 1/a) |
fmt.Println("1 / a: ", 1/a) |
||
fmt.Println("a̅: ", cmplx.Conj(a)) |
fmt.Println("a̅: ", cmplx.Conj(a)) |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 2,219: | Line 2,219: | ||
=={{header|Groovy}}== |
=={{header|Groovy}}== |
||
Groovy does not provide any built-in facility for complex arithmetic. However, it does support arithmetic operator overloading. Thus it is not too hard to build a fairly robust, complete, and intuitive complex number class, such as the following: |
Groovy does not provide any built-in facility for complex arithmetic. However, it does support arithmetic operator overloading. Thus it is not too hard to build a fairly robust, complete, and intuitive complex number class, such as the following: |
||
< |
<syntaxhighlight lang=groovy>class Complex { |
||
final Number real, imag |
final Number real, imag |
||
Line 2,319: | Line 2,319: | ||
: realPart + (imag > 0 ? " + " : " - ") + imagPart |
: realPart + (imag > 0 ? " + " : " - ") + imagPart |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
The following ''ComplexCategory'' class allows for modification of regular ''Number'' behavior when interacting with ''Complex''. |
The following ''ComplexCategory'' class allows for modification of regular ''Number'' behavior when interacting with ''Complex''. |
||
< |
<syntaxhighlight lang=groovy>import org.codehaus.groovy.runtime.DefaultGroovyMethods |
||
class ComplexCategory { |
class ComplexCategory { |
||
Line 2,338: | Line 2,338: | ||
: DefaultGroovyMethods.asType(a, type) |
: DefaultGroovyMethods.asType(a, type) |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
Notice also that this solution takes liberal advantage of Groovy's full Unicode support, including support for non-English alphabets used in identifiers. |
Notice also that this solution takes liberal advantage of Groovy's full Unicode support, including support for non-English alphabets used in identifiers. |
||
Test Program (mixes the ComplexCategory methods into the Number class): |
Test Program (mixes the ComplexCategory methods into the Number class): |
||
< |
<syntaxhighlight lang=groovy>import static Complex.* |
||
Number.metaClass.mixin ComplexCategory |
Number.metaClass.mixin ComplexCategory |
||
Line 2,405: | Line 2,405: | ||
println " == 10*0.5 + i*10*√(3/4) == " + fromPolar1 |
println " == 10*0.5 + i*10*√(3/4) == " + fromPolar1 |
||
println "ρ*exp(i*θ) == ${ρ}*exp(i*π/${n}) == " + fromPolar2 |
println "ρ*exp(i*θ) == ${ρ}*exp(i*π/${n}) == " + fromPolar2 |
||
assert (fromPolar1 - fromPolar2).abs < ε</ |
assert (fromPolar1 - fromPolar2).abs < ε</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 2,440: | Line 2,440: | ||
=={{header|Hare}}== |
=={{header|Hare}}== |
||
< |
<syntaxhighlight lang=hare>use fmt; |
||
use math::complex::{c128,addc128,mulc128,divc128,negc128,conjc128}; |
use math::complex::{c128,addc128,mulc128,divc128,negc128,conjc128}; |
||
Line 2,462: | Line 2,462: | ||
let (re, im) = conjc128(x); |
let (re, im) = conjc128(x); |
||
fmt::printfln("{} + {}i", re, im)!; |
fmt::printfln("{} + {}i", re, im)!; |
||
};</ |
};</syntaxhighlight> |
||
=={{header|Haskell}}== |
=={{header|Haskell}}== |
||
Line 2,469: | Line 2,469: | ||
have ''Complex Integer'' for the Gaussian Integers, ''Complex Float'', ''Complex Double'', etc. The operations are just the usual overloaded numeric operations. |
have ''Complex Integer'' for the Gaussian Integers, ''Complex Float'', ''Complex Double'', etc. The operations are just the usual overloaded numeric operations. |
||
< |
<syntaxhighlight lang=haskell>import Data.Complex |
||
main = do |
main = do |
||
Line 2,482: | Line 2,482: | ||
putStrLn $ "Negate: " ++ show (-a) |
putStrLn $ "Negate: " ++ show (-a) |
||
putStrLn $ "Inverse: " ++ show (recip a) |
putStrLn $ "Inverse: " ++ show (recip a) |
||
putStrLn $ "Conjugate:" ++ show (conjugate a)</ |
putStrLn $ "Conjugate:" ++ show (conjugate a)</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 2,497: | Line 2,497: | ||
{{improve|Unicon|This could be better implemented as an object i n Unicon. Note, however, that Unicon doesn't allow for operator overloading at the current time.}} |
{{improve|Unicon|This could be better implemented as an object i n Unicon. Note, however, that Unicon doesn't allow for operator overloading at the current time.}} |
||
Icon doesn't provide native support for complex numbers. Support is included in the IPL. |
Icon doesn't provide native support for complex numbers. Support is included in the IPL. |
||
< |
<syntaxhighlight lang=Icon>procedure main() |
||
SetupComplex() |
SetupComplex() |
||
Line 2,518: | Line 2,518: | ||
write("abs(a) := ", cpxabs(a)) |
write("abs(a) := ", cpxabs(a)) |
||
write("neg(1) := ", cpxstr(cpxneg(1))) |
write("neg(1) := ", cpxstr(cpxneg(1))) |
||
end</ |
end</syntaxhighlight> |
||
Icon doesn't allow for operator overloading but procedures can be overloaded as was done here to allow 'complex' to behave more robustly. |
Icon doesn't allow for operator overloading but procedures can be overloaded as was done here to allow 'complex' to behave more robustly. |
||
{{libheader|Icon Programming Library}} |
{{libheader|Icon Programming Library}} |
||
[http://www.cs.arizona.edu/icon/library/src/procs/complex.icn provides complex number support] supplemented by the code below. |
[http://www.cs.arizona.edu/icon/library/src/procs/complex.icn provides complex number support] supplemented by the code below. |
||
< |
<syntaxhighlight lang=Icon> |
||
link complex # for complex number support |
link complex # for complex number support |
||
Line 2,550: | Line 2,550: | ||
denom := z.rpart ^ 2 + z.ipart ^ 2 |
denom := z.rpart ^ 2 + z.ipart ^ 2 |
||
return complex(z.rpart / denom, z.ipart / denom) |
return complex(z.rpart / denom, z.ipart / denom) |
||
end</ |
end</syntaxhighlight> |
||
To take full advantage of the overloaded 'complex' procedure, |
To take full advantage of the overloaded 'complex' procedure, |
||
the other cpxxxx procedures would need to be rewritten or overloaded. |
the other cpxxxx procedures would need to be rewritten or overloaded. |
||
Line 2,576: | Line 2,576: | ||
<tt>complex</tt> (and <tt>dcomplex</tt> for double-precision) is a built-in data type in IDL: |
<tt>complex</tt> (and <tt>dcomplex</tt> for double-precision) is a built-in data type in IDL: |
||
< |
<syntaxhighlight lang=idl>x=complex(1,1) |
||
y=complex(!pi,1.2) |
y=complex(!pi,1.2) |
||
print,x+y |
print,x+y |
||
Line 2,585: | Line 2,585: | ||
( -1.00000, -1.00000) |
( -1.00000, -1.00000) |
||
print,1/x |
print,1/x |
||
( 0.500000, -0.500000)</ |
( 0.500000, -0.500000)</syntaxhighlight> |
||
=={{header|J}}== |
=={{header|J}}== |
||
Complex numbers are a native numeric data type in J. Although the examples shown here are performed on scalars, all numeric operations naturally apply to arrays of complex numbers. |
Complex numbers are a native numeric data type in J. Although the examples shown here are performed on scalars, all numeric operations naturally apply to arrays of complex numbers. |
||
< |
<syntaxhighlight lang=j> x=: 1j1 |
||
y=: 3.14159j1.2 |
y=: 3.14159j1.2 |
||
x+y NB. addition |
x+y NB. addition |
||
Line 2,601: | Line 2,601: | ||
+x NB. (complex) conjugation |
+x NB. (complex) conjugation |
||
1j_1 |
1j_1 |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Java}}== |
=={{header|Java}}== |
||
< |
<syntaxhighlight lang=java>public class Complex { |
||
public final double real; |
public final double real; |
||
public final double imag; |
public final double imag; |
||
Line 2,655: | Line 2,655: | ||
System.out.println(a.conj()); |
System.out.println(a.conj()); |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
=={{header|JavaScript}}== |
=={{header|JavaScript}}== |
||
< |
<syntaxhighlight lang=javascript>function Complex(r, i) { |
||
this.r = r; |
this.r = r; |
||
this.i = i; |
this.i = i; |
||
Line 2,712: | Line 2,712: | ||
Complex.prototype.getMod = function() { |
Complex.prototype.getMod = function() { |
||
return Math.sqrt( Math.pow(this.r,2) , Math.pow(this.i,2) ) |
return Math.sqrt( Math.pow(this.r,2) , Math.pow(this.i,2) ) |
||
}</ |
}</syntaxhighlight> |
||
=={{header|jq}}== |
=={{header|jq}}== |
||
For speed and for conformance with the complex plane interpretation, x+iy is represented as [x,y]; for flexibility, all the functions defined here will accept both real and complex numbers; and for uniformity, they are implemented as functions that ignore their input. |
For speed and for conformance with the complex plane interpretation, x+iy is represented as [x,y]; for flexibility, all the functions defined here will accept both real and complex numbers; and for uniformity, they are implemented as functions that ignore their input. |
||
Recent versions of jq support modules, so these functions could all be placed in a module to avoid name conflicts, and thus no special prefix is used here.< |
Recent versions of jq support modules, so these functions could all be placed in a module to avoid name conflicts, and thus no special prefix is used here.<syntaxhighlight lang=jq>def real(z): if (z|type) == "number" then z else z[0] end; |
||
def imag(z): if (z|type) == "number" then 0 else z[1] end; |
def imag(z): if (z|type) == "number" then 0 else z[1] end; |
||
Line 2,780: | Line 2,780: | ||
; |
; |
||
test( [1,1]; [0,1] )</ |
test( [1,1]; [0,1] )</syntaxhighlight> |
||
{{Out}} |
{{Out}} |
||
< |
<syntaxhighlight lang=jq>$ jq -n -f complex.jq |
||
"x = [1,1]" |
"x = [1,1]" |
||
"y = [0,1]" |
"y = [0,1]" |
||
Line 2,791: | Line 2,791: | ||
"conj(x): [1,-1]" |
"conj(x): [1,-1]" |
||
"(x/y)*y: [1,1]" |
"(x/y)*y: [1,1]" |
||
"e^iπ: [-1,1.2246467991473532e-16]"</ |
"e^iπ: [-1,1.2246467991473532e-16]"</syntaxhighlight> |
||
=={{header|Julia}}== |
=={{header|Julia}}== |
||
Julia has built-in support for complex arithmetic with arbitrary real types. |
Julia has built-in support for complex arithmetic with arbitrary real types. |
||
< |
<syntaxhighlight lang=julia>julia> z1 = 1.5 + 3im |
||
julia> z2 = 1.5 + 1.5im |
julia> z2 = 1.5 + 1.5im |
||
julia> z1 + z2 |
julia> z1 + z2 |
||
Line 2,816: | Line 2,816: | ||
1.5 |
1.5 |
||
julia> imag(z1) |
julia> imag(z1) |
||
3.0</ |
3.0</syntaxhighlight> |
||
=={{header|Kotlin}}== |
=={{header|Kotlin}}== |
||
< |
<syntaxhighlight lang=scala>class Complex(private val real: Double, private val imag: Double) { |
||
operator fun plus(other: Complex) = Complex(real + other.real, imag + other.imag) |
operator fun plus(other: Complex) = Complex(real + other.real, imag + other.imag) |
||
Line 2,857: | Line 2,857: | ||
println("1 / x = ${x.inv()}") |
println("1 / x = ${x.inv()}") |
||
println("x* = ${x.conj()}") |
println("x* = ${x.conj()}") |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 2,873: | Line 2,873: | ||
=={{header|Lambdatalk}}== |
=={{header|Lambdatalk}}== |
||
< |
<syntaxhighlight lang=scheme> |
||
{require lib_complex} |
{require lib_complex} |
||
Line 2,897: | Line 2,897: | ||
{C.mul {z1} {z2}} -> (0 3) |
{C.mul {z1} {z2}} -> (0 3) |
||
{C.div {z1} {z2}} -> (0.6666666666666667 0) |
{C.div {z1} {z2}} -> (0.6666666666666667 0) |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|LFE}}== |
=={{header|LFE}}== |
||
Line 2,904: | Line 2,904: | ||
A convenient data structure for a complex number is the record: |
A convenient data structure for a complex number is the record: |
||
< |
<syntaxhighlight lang=lisp> |
||
(defrecord complex |
(defrecord complex |
||
real |
real |
||
img) |
img) |
||
</syntaxhighlight> |
|||
</lang> |
|||
Here are the required functions: |
Here are the required functions: |
||
< |
<syntaxhighlight lang=lisp> |
||
(defun add |
(defun add |
||
(((match-complex real r1 img i1) |
(((match-complex real r1 img i1) |
||
Line 2,930: | Line 2,930: | ||
(defun inv (cmplx) |
(defun inv (cmplx) |
||
(div (conj cmplx) (modulus cmplx))) |
(div (conj cmplx) (modulus cmplx))) |
||
</syntaxhighlight> |
|||
</lang> |
|||
Bonus: |
Bonus: |
||
< |
<syntaxhighlight lang=lisp> |
||
(defun conj |
(defun conj |
||
(((match-complex real r img i)) |
(((match-complex real r img i)) |
||
(new r (* -1 i)))) |
(new r (* -1 i)))) |
||
</syntaxhighlight> |
|||
</lang> |
|||
The functions above are built using the following supporting functions: |
The functions above are built using the following supporting functions: |
||
< |
<syntaxhighlight lang=lisp> |
||
(defun new (r i) |
(defun new (r i) |
||
(make-complex real r img i)) |
(make-complex real r img i)) |
||
Line 2,955: | Line 2,955: | ||
(/ (complex-img c3) denom))))) |
(/ (complex-img c3) denom))))) |
||
</syntaxhighlight> |
|||
</lang> |
|||
Finally, we have some functions for use in the conversion and display of our complex number data structure: |
Finally, we have some functions for use in the conversion and display of our complex number data structure: |
||
< |
<syntaxhighlight lang=lisp> |
||
(defun ->str |
(defun ->str |
||
(((match-complex real r img i)) (when (>= i 0)) |
(((match-complex real r img i)) (when (>= i 0)) |
||
Line 2,971: | Line 2,971: | ||
(defun print (cmplx) |
(defun print (cmplx) |
||
(io:format (++ (->str cmplx) "~n"))) |
(io:format (++ (->str cmplx) "~n"))) |
||
</syntaxhighlight> |
|||
</lang> |
|||
Usage is as follows: |
Usage is as follows: |
||
Line 2,998: | Line 2,998: | ||
=={{header|Liberty BASIC}}== |
=={{header|Liberty BASIC}}== |
||
< |
<syntaxhighlight lang=lb>mainwin 50 10 |
||
print " Adding" |
print " Adding" |
||
Line 3,048: | Line 3,048: | ||
D =ar^2 +ai^2 |
D =ar^2 +ai^2 |
||
cinv$ =complex$( ar /D , 0 -ai /D ) |
cinv$ =complex$( ar /D , 0 -ai /D ) |
||
end function</ |
end function</syntaxhighlight> |
||
=={{header|Lua}}== |
=={{header|Lua}}== |
||
< |
<syntaxhighlight lang=lua> |
||
--defines addition, subtraction, negation, multiplication, division, conjugation, norms, and a conversion to strgs. |
--defines addition, subtraction, negation, multiplication, division, conjugation, norms, and a conversion to strgs. |
||
Line 3,084: | Line 3,084: | ||
print("|" .. i .. "| = " .. math.sqrt(i.norm)) |
print("|" .. i .. "| = " .. math.sqrt(i.norm)) |
||
print(i .. "* = " .. i.conj) |
print(i .. "* = " .. i.conj) |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Maple}}== |
=={{header|Maple}}== |
||
Line 3,090: | Line 3,090: | ||
Maple has <code>I</code> (the square root of -1) built-in. Thus: |
Maple has <code>I</code> (the square root of -1) built-in. Thus: |
||
< |
<syntaxhighlight lang=maple>x := 1+I; |
||
y := Pi+I*1.2;</ |
y := Pi+I*1.2;</syntaxhighlight> |
||
By itself, it will perform mathematical operations symbolically, i.e. it will not try to perform computational evaluation unless specifically asked to do so. Thus: |
By itself, it will perform mathematical operations symbolically, i.e. it will not try to perform computational evaluation unless specifically asked to do so. Thus: |
||
< |
<syntaxhighlight lang=maple>x*y; |
||
==> (1 + I) (Pi + 1.2 I) |
==> (1 + I) (Pi + 1.2 I) |
||
simplify(x*y); |
simplify(x*y); |
||
==> 1.941592654 + 4.341592654 I</ |
==> 1.941592654 + 4.341592654 I</syntaxhighlight> |
||
Other than that, the task merely asks for |
Other than that, the task merely asks for |
||
< |
<syntaxhighlight lang=maple>x+y; |
||
x*y; |
x*y; |
||
-x; |
-x; |
||
1/x;</ |
1/x;</syntaxhighlight> |
||
=={{header|Mathematica}} / {{header|Wolfram Language}}== |
=={{header|Mathematica}} / {{header|Wolfram Language}}== |
||
Mathematica has fully implemented support for complex numbers throughout the software. Addition, subtraction, division, multiplications and powering need no further syntax than for real numbers: |
Mathematica has fully implemented support for complex numbers throughout the software. Addition, subtraction, division, multiplications and powering need no further syntax than for real numbers: |
||
< |
<syntaxhighlight lang=Mathematica>x=1+2I |
||
y=3+4I |
y=3+4I |
||
Line 3,119: | Line 3,119: | ||
y^4 => -527 - 336 I |
y^4 => -527 - 336 I |
||
x^y => (1 + 2 I)^(3 + 4 I) |
x^y => (1 + 2 I)^(3 + 4 I) |
||
N[x^y] => 0.12901 + 0.0339241 I</ |
N[x^y] => 0.12901 + 0.0339241 I</syntaxhighlight> |
||
Powering to a complex power can in general not be written shorter, so Mathematica leaves it unevaluated if the numbers are exact. An approximation can be acquired using the function N. |
Powering to a complex power can in general not be written shorter, so Mathematica leaves it unevaluated if the numbers are exact. An approximation can be acquired using the function N. |
||
However Mathematica goes much further, basically all functions can handle complex numbers to arbitrary precision, including (but not limited to!): |
However Mathematica goes much further, basically all functions can handle complex numbers to arbitrary precision, including (but not limited to!): |
||
< |
<syntaxhighlight lang=Mathematica>Exp Log |
||
Sin Cos Tan Csc Sec Cot |
Sin Cos Tan Csc Sec Cot |
||
ArcSin ArcCos ArcTan ArcCsc ArcSec ArcCot |
ArcSin ArcCos ArcTan ArcCsc ArcSec ArcCot |
||
Line 3,130: | Line 3,130: | ||
Haversine InverseHaversine |
Haversine InverseHaversine |
||
Factorial Gamma PolyGamma LogGamma |
Factorial Gamma PolyGamma LogGamma |
||
Erf BarnesG Hyperfactorial Zeta ProductLog RamanujanTauL</ |
Erf BarnesG Hyperfactorial Zeta ProductLog RamanujanTauL</syntaxhighlight> |
||
and many many more. The documentation states: |
and many many more. The documentation states: |
||
Line 3,138: | Line 3,138: | ||
Complex numbers are a primitive data type in MATLAB. All the typical complex operations can be performed. There are two keywords that specify a number as complex: "i" and "j". |
Complex numbers are a primitive data type in MATLAB. All the typical complex operations can be performed. There are two keywords that specify a number as complex: "i" and "j". |
||
< |
<syntaxhighlight lang=MATLAB>>> a = 1+i |
||
a = |
a = |
||
Line 3,196: | Line 3,196: | ||
ans = |
ans = |
||
1.414213562373095</ |
1.414213562373095</syntaxhighlight> |
||
=={{header|Maxima}}== |
=={{header|Maxima}}== |
||
< |
<syntaxhighlight lang=maxima>z1: 5 + 2 * %i; |
||
2*%i+5 |
2*%i+5 |
||
Line 3,242: | Line 3,242: | ||
imagpart(z1); |
imagpart(z1); |
||
2</ |
2</syntaxhighlight> |
||
=={{header|МК-61/52}}== |
=={{header|МК-61/52}}== |
||
Line 3,260: | Line 3,260: | ||
+ П2 ИП1 С/П ИПB ИПD + П2 ИПA ИПC |
+ П2 ИП1 С/П ИПB ИПD + П2 ИПA ИПC |
||
+ ИП1 С/П ИПB ИПD - П2 ИПA ИПC - |
+ ИП1 С/П ИПB ИПD - П2 ИПA ИПC - |
||
П1 С/П</ |
П1 С/П</syntaxhighlight> |
||
=={{header|Modula-2}}== |
=={{header|Modula-2}}== |
||
< |
<syntaxhighlight lang=modula2>MODULE complex; |
||
IMPORT InOut; |
IMPORT InOut; |
||
Line 3,328: | Line 3,328: | ||
NegComplex (z[0], z[2]); ShowComplex (" - z1", z[2]); |
NegComplex (z[0], z[2]); ShowComplex (" - z1", z[2]); |
||
InOut.WriteLn |
InOut.WriteLn |
||
END complex.</ |
END complex.</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>Enter two complex numbers : 5 3 0.5 6 |
<pre>Enter two complex numbers : 5 3 0.5 6 |
||
Line 3,343: | Line 3,343: | ||
{{trans|Java}} |
{{trans|Java}} |
||
This is a translation of the Java version, but it uses operator redefinition where possible. |
This is a translation of the Java version, but it uses operator redefinition where possible. |
||
< |
<syntaxhighlight lang=nanoquery>import math |
||
class Complex |
class Complex |
||
Line 3,398: | Line 3,398: | ||
println a.inv() |
println a.inv() |
||
println a * b |
println a * b |
||
println a.conj()</ |
println a.conj()</syntaxhighlight> |
||
=={{header|Nemerle}}== |
=={{header|Nemerle}}== |
||
< |
<syntaxhighlight lang=Nemerle>using System; |
||
using System.Console; |
using System.Console; |
||
using System.Numerics; |
using System.Numerics; |
||
Line 3,426: | Line 3,426: | ||
WriteLine(Conjugate(complex2).PrettyPrint()); |
WriteLine(Conjugate(complex2).PrettyPrint()); |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>4.14159 + 2.2i |
<pre>4.14159 + 2.2i |
||
Line 3,435: | Line 3,435: | ||
=={{header|Nim}}== |
=={{header|Nim}}== |
||
< |
<syntaxhighlight lang=nim> |
||
import complex |
import complex |
||
var a: Complex = (1.0,1.0) |
var a: Complex = (1.0,1.0) |
||
Line 3,447: | Line 3,447: | ||
echo("-a : " & $(-a)) |
echo("-a : " & $(-a)) |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 3,460: | Line 3,460: | ||
=={{header|Oberon-2}}== |
=={{header|Oberon-2}}== |
||
Oxford Oberon Compiler |
Oxford Oberon Compiler |
||
< |
<syntaxhighlight lang=oberon2> |
||
MODULE Complex; |
MODULE Complex; |
||
IMPORT Files,Out; |
IMPORT Files,Out; |
||
Line 3,546: | Line 3,546: | ||
END Complex. |
END Complex. |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 3,561: | Line 3,561: | ||
=={{header|OCaml}}== |
=={{header|OCaml}}== |
||
The [http://caml.inria.fr/pub/docs/manual-ocaml/libref/Complex.html Complex] module from the standard library provides the functionality of complex numbers: |
The [http://caml.inria.fr/pub/docs/manual-ocaml/libref/Complex.html Complex] module from the standard library provides the functionality of complex numbers: |
||
< |
<syntaxhighlight lang=ocaml>open Complex |
||
let print_complex z = |
let print_complex z = |
||
Line 3,573: | Line 3,573: | ||
print_complex (inv a); |
print_complex (inv a); |
||
print_complex (neg a); |
print_complex (neg a); |
||
print_complex (conj a)</ |
print_complex (conj a)</syntaxhighlight> |
||
Using [http://forge.ocamlcore.org/projects/pa-do/ Delimited Overloading], the syntax can be made closer to the usual one: |
Using [http://forge.ocamlcore.org/projects/pa-do/ Delimited Overloading], the syntax can be made closer to the usual one: |
||
< |
<syntaxhighlight lang=ocaml>let () = |
||
Complex.( |
Complex.( |
||
let print txt z = Printf.printf "%s = %s\n" txt (to_string z) in |
let print txt z = Printf.printf "%s = %s\n" txt (to_string z) in |
||
Line 3,589: | Line 3,589: | ||
print "a^b" (a**b); |
print "a^b" (a**b); |
||
Printf.printf "norm a = %g\n" (float(abs a)); |
Printf.printf "norm a = %g\n" (float(abs a)); |
||
)</ |
)</syntaxhighlight> |
||
=={{header|Octave}}== |
=={{header|Octave}}== |
||
GNU Octave handles naturally complex numbers: |
GNU Octave handles naturally complex numbers: |
||
< |
<syntaxhighlight lang=octave>z1 = 1.5 + 3i; |
||
z2 = 1.5 + 1.5i; |
z2 = 1.5 + 1.5i; |
||
disp(z1 + z2); % 3.0 + 4.5i |
disp(z1 + z2); % 3.0 + 4.5i |
||
Line 3,606: | Line 3,606: | ||
disp( imag(z1) ); % 3 |
disp( imag(z1) ); % 3 |
||
disp( real(z2) ); % 1.5 |
disp( real(z2) ); % 1.5 |
||
%...</ |
%...</syntaxhighlight> |
||
=={{header|Oforth}}== |
=={{header|Oforth}}== |
||
< |
<syntaxhighlight lang=Oforth>Object Class new: Complex(re, im) |
||
Complex method: re @re ; |
Complex method: re @re ; |
||
Line 3,648: | Line 3,648: | ||
Integer method: >complex self 0 Complex new ; |
Integer method: >complex self 0 Complex new ; |
||
Float method: >complex self 0 Complex new ;</ |
Float method: >complex self 0 Complex new ;</syntaxhighlight> |
||
Usage : |
Usage : |
||
< |
<syntaxhighlight lang=Oforth>3.2 >complex I * 2 >complex + .cr |
||
2 3 Complex new 1.2 >complex + .cr |
2 3 Complex new 1.2 >complex + .cr |
||
2 3 Complex new 1.2 >complex * .cr |
2 3 Complex new 1.2 >complex * .cr |
||
2 >complex 2 3 Complex new / .cr</ |
2 >complex 2 3 Complex new / .cr</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 3,668: | Line 3,668: | ||
Ol supports complex numbers by default. Numbers must be entered manually in form A+Bi without spaces between elements, where A and B - numbers (can be rational), i - imaginary unit; or in functional form using function `complex`. |
Ol supports complex numbers by default. Numbers must be entered manually in form A+Bi without spaces between elements, where A and B - numbers (can be rational), i - imaginary unit; or in functional form using function `complex`. |
||
< |
<syntaxhighlight lang=scheme> |
||
(define A 0+1i) ; manually entered numbers |
(define A 0+1i) ; manually entered numbers |
||
(define B 1+0i) |
(define B 1+0i) |
||
Line 3,692: | Line 3,692: | ||
(print "imaginary part of " C " is " (cdr C)) |
(print "imaginary part of " C " is " (cdr C)) |
||
; <== imaginary part of 2/7-3i is -3 |
; <== imaginary part of 2/7-3i is -3 |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|ooRexx}}== |
=={{header|ooRexx}}== |
||
< |
<syntaxhighlight lang=ooRexx>c1 = .complex~new(1, 2) |
||
c2 = .complex~new(3, 4) |
c2 = .complex~new(3, 4) |
||
r = 7 |
r = 7 |
||
Line 3,831: | Line 3,831: | ||
::method hashCode |
::method hashCode |
||
expose r i |
expose r i |
||
return r~hashcode~bitxor(i~hashcode)</ |
return r~hashcode~bitxor(i~hashcode)</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>c1 = 1 + 2i |
<pre>c1 = 1 + 2i |
||
Line 3,852: | Line 3,852: | ||
=={{header|OxygenBasic}}== |
=={{header|OxygenBasic}}== |
||
Implementation of a complex numbers class with arithmetical operations, and powers using DeMoivre's theorem (polar conversion). |
Implementation of a complex numbers class with arithmetical operations, and powers using DeMoivre's theorem (polar conversion). |
||
< |
<syntaxhighlight lang=oxygenbasic> |
||
'COMPLEX OPERATIONS |
'COMPLEX OPERATIONS |
||
'================= |
'================= |
||
Line 3,985: | Line 3,985: | ||
z1 = z1*z4 |
z1 = z1*z4 |
||
print "Z1 = "+z1.show 'RESULT 2.0, 1.0 |
print "Z1 = "+z1.show 'RESULT 2.0, 1.0 |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|PARI/GP}}== |
=={{header|PARI/GP}}== |
||
To use, type, e.g., inv(3 + 7*I). |
To use, type, e.g., inv(3 + 7*I). |
||
< |
<syntaxhighlight lang=parigp>add(a,b)=a+b; |
||
mult(a,b)=a*b; |
mult(a,b)=a*b; |
||
neg(a)=-a; |
neg(a)=-a; |
||
inv(a)=1/a;</ |
inv(a)=1/a;</syntaxhighlight> |
||
=={{header|Pascal}}== |
=={{header|Pascal}}== |
||
{{works with|Extended Pascal}} |
{{works with|Extended Pascal}} |
||
The simple data type <tt>complex</tt> is part of Extended Pascal, ISO standard 10206. |
The simple data type <tt>complex</tt> is part of Extended Pascal, ISO standard 10206. |
||
< |
<syntaxhighlight lang=pascal>program complexDemo(output); |
||
const |
const |
||
Line 4,063: | Line 4,063: | ||
writeLn(' inverse(', asString(z), ') = ', asString(inverse(z))); |
writeLn(' inverse(', asString(z), ') = ', asString(inverse(z))); |
||
writeLn(' conjugation(', asString(y), ') = ', asString(conjugation(y))); |
writeLn(' conjugation(', asString(y), ') = ', asString(conjugation(y))); |
||
end.</ |
end.</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>(-3.00, 2.00) + ( 1.00, 4.00) = (-2.00, 6.00) |
<pre>(-3.00, 2.00) + ( 1.00, 4.00) = (-2.00, 6.00) |
||
Line 4,077: | Line 4,077: | ||
=={{header|Perl}}== |
=={{header|Perl}}== |
||
The <code>Math::Complex</code> module implements complex arithmetic. |
The <code>Math::Complex</code> module implements complex arithmetic. |
||
< |
<syntaxhighlight lang=perl>use Math::Complex; |
||
my $a = 1 + 1*i; |
my $a = 1 + 1*i; |
||
my $b = 3.14159 + 1.25*i; |
my $b = 3.14159 + 1.25*i; |
||
Line 4,086: | Line 4,086: | ||
-$a, # negation |
-$a, # negation |
||
1 / $a, # multiplicative inverse |
1 / $a, # multiplicative inverse |
||
~$a; # complex conjugate</ |
~$a; # complex conjugate</syntaxhighlight> |
||
=={{header|Phix}}== |
=={{header|Phix}}== |
||
<!--< |
<!--<syntaxhighlight lang=Phix>(phixonline)--> |
||
<span style="color: #000080;font-style:italic;">-- demo\rosetta\ArithComplex.exw</span> |
<span style="color: #000080;font-style:italic;">-- demo\rosetta\ArithComplex.exw</span> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
||
Line 4,109: | Line 4,109: | ||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-a = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))})</span> |
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-a = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))})</span> |
||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"conj a = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_conjugate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))})</span> |
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"conj a = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">complex_conjugate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))})</span> |
||
<!--</ |
<!--</syntaxhighlight>--> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 4,127: | Line 4,127: | ||
=={{header|PicoLisp}}== |
=={{header|PicoLisp}}== |
||
< |
<syntaxhighlight lang=PicoLisp>(load "@lib/math.l") |
||
(de addComplex (A B) |
(de addComplex (A B) |
||
Line 4,168: | Line 4,168: | ||
(prinl "A*B = " (fmtComplex (mulComplex A B))) |
(prinl "A*B = " (fmtComplex (mulComplex A B))) |
||
(prinl "1/A = " (fmtComplex (invComplex A))) |
(prinl "1/A = " (fmtComplex (invComplex A))) |
||
(prinl "-A = " (fmtComplex (negComplex A))) )</ |
(prinl "-A = " (fmtComplex (negComplex A))) )</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>A = 1.00000+1.00000i |
<pre>A = 1.00000+1.00000i |
||
Line 4,178: | Line 4,178: | ||
=={{header|PL/I}}== |
=={{header|PL/I}}== |
||
< |
<syntaxhighlight lang=pli>/* PL/I complex numbers may be integer or floating-point. */ |
||
/* In this example, the variables are floating-pint. */ |
/* In this example, the variables are floating-pint. */ |
||
/* For integer variables, change 'float' to 'fixed binary' */ |
/* For integer variables, change 'float' to 'fixed binary' */ |
||
Line 4,198: | Line 4,198: | ||
/* As well, trigonometric functions may be used with complex */ |
/* As well, trigonometric functions may be used with complex */ |
||
/* numbers, such as SIN, COS, TAN, ATAN, and so on. */</ |
/* numbers, such as SIN, COS, TAN, ATAN, and so on. */</syntaxhighlight> |
||
=={{header|Pop11}}== |
=={{header|Pop11}}== |
||
Line 4,211: | Line 4,211: | ||
'1 -: 3' is '1 - 3i' in mathematical notation. |
'1 -: 3' is '1 - 3i' in mathematical notation. |
||
< |
<syntaxhighlight lang=pop11>lvars a = 1.0 +: 1.0, b = 2.0 +: 5.0 ; |
||
a+b => |
a+b => |
||
a*b => |
a*b => |
||
Line 4,229: | Line 4,229: | ||
a-a => |
a-a => |
||
a/b => |
a/b => |
||
a/a =></ |
a/a =></syntaxhighlight> |
||
=={{header|PostScript}}== |
=={{header|PostScript}}== |
||
Line 4,282: | Line 4,282: | ||
}def |
}def |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|PowerShell}}== |
=={{header|PowerShell}}== |
||
===Implementation=== |
===Implementation=== |
||
< |
<syntaxhighlight lang=PowerShell> |
||
class Complex { |
class Complex { |
||
[Double]$x |
[Double]$x |
||
Line 4,326: | Line 4,326: | ||
"1/`$m: $([complex]::show($m.inverse()))" |
"1/`$m: $([complex]::show($m.inverse()))" |
||
"conjugate `$m: $([complex]::show($m.conjugate()))" |
"conjugate `$m: $([complex]::show($m.conjugate()))" |
||
</syntaxhighlight> |
|||
</lang> |
|||
<b>Output:</b> |
<b>Output:</b> |
||
<pre> |
<pre> |
||
Line 4,338: | Line 4,338: | ||
</pre> |
</pre> |
||
===Library=== |
===Library=== |
||
< |
<syntaxhighlight lang=PowerShell> |
||
function show([System.Numerics.Complex]$c) { |
function show([System.Numerics.Complex]$c) { |
||
if(0 -le $c.Imaginary) { |
if(0 -le $c.Imaginary) { |
||
Line 4,355: | Line 4,355: | ||
"1/`$m: $(show ([System.Numerics.Complex]::Reciprocal($m)))" |
"1/`$m: $(show ([System.Numerics.Complex]::Reciprocal($m)))" |
||
"conjugate `$m: $(show ([System.Numerics.Complex]::Conjugate($m)))" |
"conjugate `$m: $(show ([System.Numerics.Complex]::Conjugate($m)))" |
||
</syntaxhighlight> |
|||
</lang> |
|||
<b>Output:</b> |
<b>Output:</b> |
||
<pre> |
<pre> |
||
Line 4,368: | Line 4,368: | ||
=={{header|PureBasic}}== |
=={{header|PureBasic}}== |
||
< |
<syntaxhighlight lang=PureBasic>Structure Complex |
||
real.d |
real.d |
||
imag.d |
imag.d |
||
Line 4,432: | Line 4,432: | ||
*c=Neg_Complex(a): ShowAndFree("-a", *c) |
*c=Neg_Complex(a): ShowAndFree("-a", *c) |
||
Print(#CRLF$+"Press ENTER to exit"):Input() |
Print(#CRLF$+"Press ENTER to exit"):Input() |
||
EndIf</ |
EndIf</syntaxhighlight> |
||
=={{header|Python}}== |
=={{header|Python}}== |
||
< |
<syntaxhighlight lang=python>>>> z1 = 1.5 + 3j |
||
>>> z2 = 1.5 + 1.5j |
>>> z2 = 1.5 + 1.5j |
||
>>> z1 + z2 |
>>> z1 + z2 |
||
Line 4,458: | Line 4,458: | ||
>>> z1.imag |
>>> z1.imag |
||
3.0 |
3.0 |
||
>>> </ |
>>> </syntaxhighlight> |
||
=={{header|R}}== |
=={{header|R}}== |
||
{{trans|Octave}} |
{{trans|Octave}} |
||
< |
<syntaxhighlight lang=rsplus>z1 <- 1.5 + 3i |
||
z2 <- 1.5 + 1.5i |
z2 <- 1.5 + 1.5i |
||
print(z1 + z2) # 3+4.5i |
print(z1 + z2) # 3+4.5i |
||
Line 4,475: | Line 4,475: | ||
print(exp(z1)) # -4.436839+0.632456i |
print(exp(z1)) # -4.436839+0.632456i |
||
print(Re(z1)) # 1.5 |
print(Re(z1)) # 1.5 |
||
print(Im(z1)) # 3</ |
print(Im(z1)) # 3</syntaxhighlight> |
||
=={{header|Racket}}== |
=={{header|Racket}}== |
||
< |
<syntaxhighlight lang=racket> |
||
#lang racket |
#lang racket |
||
Line 4,492: | Line 4,492: | ||
(/ 1 a) ; reciprocal |
(/ 1 a) ; reciprocal |
||
(conjugate a) ; conjugation |
(conjugate a) ; conjugation |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Raku}}== |
=={{header|Raku}}== |
||
Line 4,498: | Line 4,498: | ||
{{works with|Rakudo|2015.12}} |
{{works with|Rakudo|2015.12}} |
||
< |
<syntaxhighlight lang=perl6>my $a = 1 + i; |
||
my $b = pi + 1.25i; |
my $b = pi + 1.25i; |
||
.say for $a + $b, $a * $b, -$a, 1 / $a, $a.conj; |
.say for $a + $b, $a * $b, -$a, 1 / $a, $a.conj; |
||
.say for $a.abs, $a.sqrt, $a.re, $a.im;</ |
.say for $a.abs, $a.sqrt, $a.re, $a.im;</syntaxhighlight> |
||
{{out}} (precision varies with different implementations): |
{{out}} (precision varies with different implementations): |
||
<pre> |
<pre> |
||
Line 4,518: | Line 4,518: | ||
=={{header|REXX}}== |
=={{header|REXX}}== |
||
The REXX language has no complex type numbers, but most complex arithmetic functions can easily be written. |
The REXX language has no complex type numbers, but most complex arithmetic functions can easily be written. |
||
< |
<syntaxhighlight lang=rexx>/*REXX program demonstrates how to support some math functions for complex numbers. */ |
||
x = '(5,3i)' /*define X ─── can use I i J or j */ |
x = '(5,3i)' /*define X ─── can use I i J or j */ |
||
y = "( .5, 6j)" /*define Y " " " " " " " */ |
y = "( .5, 6j)" /*define Y " " " " " " " */ |
||
Line 4,540: | Line 4,540: | ||
C_: return word(translate(arg(1), , '{[(JjIi)]}') 0, 1) /*get # or 0*/ |
C_: return word(translate(arg(1), , '{[(JjIi)]}') 0, 1) /*get # or 0*/ |
||
C#: a=C_(a); b=C_(b); c=C_(c); d=C_(d); ac=a*c; ad=a*d; bc=b*c; bd=b*d;s=c*c+d*d; return |
C#: a=C_(a); b=C_(b); c=C_(c); d=C_(d); ac=a*c; ad=a*d; bc=b*c; bd=b*d;s=c*c+d*d; return |
||
C$: parse arg r,c; _='['r; if c\=0 then _=_","c'j'; return _"]" /*uses j */</ |
C$: parse arg r,c; _='['r; if c\=0 then _=_","c'j'; return _"]" /*uses j */</syntaxhighlight> |
||
'''output''' |
'''output''' |
||
<pre> |
<pre> |
||
Line 4,554: | Line 4,554: | ||
=={{header|RLaB}}== |
=={{header|RLaB}}== |
||
< |
<syntaxhighlight lang=RLaB> |
||
>> x = sqrt(-1) |
>> x = sqrt(-1) |
||
0 + 1i |
0 + 1i |
||
Line 4,563: | Line 4,563: | ||
>> isreal(z) |
>> isreal(z) |
||
1 |
1 |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Ruby}}== |
=={{header|Ruby}}== |
||
< |
<syntaxhighlight lang=ruby> |
||
# Four ways to write complex numbers: |
# Four ways to write complex numbers: |
||
a = Complex(1, 1) # 1. call Kernel#Complex |
a = Complex(1, 1) # 1. call Kernel#Complex |
||
Line 4,580: | Line 4,580: | ||
puts 1.quo a # multiplicative inverse |
puts 1.quo a # multiplicative inverse |
||
puts a.conjugate # complex conjugate |
puts a.conjugate # complex conjugate |
||
puts a.conj # alias for complex conjugate</ |
puts a.conj # alias for complex conjugate</syntaxhighlight> |
||
''Notes:'' |
''Notes:'' |
||
* All of these operations are safe with other numeric types. For example, <code>42.conjugate</code> returns 42. |
* All of these operations are safe with other numeric types. For example, <code>42.conjugate</code> returns 42. |
||
< |
<syntaxhighlight lang=ruby># Other ways to find the multiplicative inverse: |
||
puts 1.quo a # always works |
puts 1.quo a # always works |
||
puts 1.0 / a # works, but forces floating-point math |
puts 1.0 / a # works, but forces floating-point math |
||
puts 1 / a # might truncate to integer</ |
puts 1 / a # might truncate to integer</syntaxhighlight> |
||
=={{header|Rust}}== |
=={{header|Rust}}== |
||
< |
<syntaxhighlight lang=rust>extern crate num; |
||
use num::complex::Complex; |
use num::complex::Complex; |
||
Line 4,606: | Line 4,606: | ||
println!(" -a = {}", -a); |
println!(" -a = {}", -a); |
||
println!("conj(a) = {}", a.conj()); |
println!("conj(a) = {}", a.conj()); |
||
}</ |
}</syntaxhighlight> |
||
=={{header|Scala}}== |
=={{header|Scala}}== |
||
Line 4,612: | Line 4,612: | ||
Scala doesn't come with a Complex library, but one can be made: |
Scala doesn't come with a Complex library, but one can be made: |
||
< |
<syntaxhighlight lang=scala>package org.rosettacode |
||
package object ArithmeticComplex { |
package object ArithmeticComplex { |
||
Line 4,646: | Line 4,646: | ||
def fromPolar(rho:Double, theta:Double) = Complex(rho*math.cos(theta), rho*math.sin(theta)) |
def fromPolar(rho:Double, theta:Double) = Complex(rho*math.cos(theta), rho*math.sin(theta)) |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
Usage example: |
Usage example: |
||
< |
<syntaxhighlight lang=scala>scala> import org.rosettacode.ArithmeticComplex._ |
||
import org.rosettacode.ArithmeticComplex._ |
import org.rosettacode.ArithmeticComplex._ |
||
Line 4,676: | Line 4,676: | ||
scala> -res6 |
scala> -res6 |
||
res7: org.rosettacode.ArithmeticComplex.Complex = -0.2 + 0.4i |
res7: org.rosettacode.ArithmeticComplex.Complex = -0.2 + 0.4i |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Scheme}}== |
=={{header|Scheme}}== |
||
Line 4,682: | Line 4,682: | ||
* rectangular coordinates: <code>''real''+''imag''i</code> (or <code>''real''-''imag''i</code>), where ''real'' is the real part and ''imag'' is the imaginary part. For a pure-imaginary number, the real part may be omitted but the sign of the imaginary part is mandatory (even if it is "+"): <code>+''imag''i</code> (or <code>-''imag''i</code>). If the imaginary part is 1 or -1, the imaginary part can be omitted, leaving only the <code>+i</code> or <code>-i</code> at the end. |
* rectangular coordinates: <code>''real''+''imag''i</code> (or <code>''real''-''imag''i</code>), where ''real'' is the real part and ''imag'' is the imaginary part. For a pure-imaginary number, the real part may be omitted but the sign of the imaginary part is mandatory (even if it is "+"): <code>+''imag''i</code> (or <code>-''imag''i</code>). If the imaginary part is 1 or -1, the imaginary part can be omitted, leaving only the <code>+i</code> or <code>-i</code> at the end. |
||
* polar coordinates: <code>''r''@''theta''</code>, where ''r'' is the absolute value (magnitude) and ''theta'' is the angle |
* polar coordinates: <code>''r''@''theta''</code>, where ''r'' is the absolute value (magnitude) and ''theta'' is the angle |
||
< |
<syntaxhighlight lang=scheme>(define a 1+i) |
||
(define b 3.14159+1.25i) |
(define b 3.14159+1.25i) |
||
Line 4,688: | Line 4,688: | ||
(define c (* a b)) |
(define c (* a b)) |
||
(define c (/ 1 a)) |
(define c (/ 1 a)) |
||
(define c (- a))</ |
(define c (- a))</syntaxhighlight> |
||
=={{header|Seed7}}== |
=={{header|Seed7}}== |
||
< |
<syntaxhighlight lang=seed7>$ include "seed7_05.s7i"; |
||
include "float.s7i"; |
include "float.s7i"; |
||
include "complex.s7i"; |
include "complex.s7i"; |
||
Line 4,711: | Line 4,711: | ||
# negation |
# negation |
||
writeln("-a=" <& -a digits 5); |
writeln("-a=" <& -a digits 5); |
||
end func;</ |
end func;</syntaxhighlight> |
||
=={{header|Sidef}}== |
=={{header|Sidef}}== |
||
< |
<syntaxhighlight lang=ruby>var a = 1:1 # Complex(1, 1) |
||
var b = 3.14159:1.25 # Complex(3.14159, 1.25) |
var b = 3.14159:1.25 # Complex(3.14159, 1.25) |
||
Line 4,726: | Line 4,726: | ||
b.re, # real |
b.re, # real |
||
b.im, # imaginary |
b.im, # imaginary |
||
].each { |c| say c }</ |
].each { |c| say c }</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>4.14159+2.25i |
<pre>4.14159+2.25i |
||
Line 4,740: | Line 4,740: | ||
=={{header|Slate}}== |
=={{header|Slate}}== |
||
< |
<syntaxhighlight lang=slate>[| a b | |
||
a: 1 + 1 i. |
a: 1 + 1 i. |
||
b: Pi + 1.2 i. |
b: Pi + 1.2 i. |
||
Line 4,750: | Line 4,750: | ||
print: a abs. |
print: a abs. |
||
print: a negated. |
print: a negated. |
||
].</ |
].</syntaxhighlight> |
||
=={{header|Smalltalk}}== |
=={{header|Smalltalk}}== |
||
{{works with|GNU Smalltalk}} |
{{works with|GNU Smalltalk}} |
||
< |
<syntaxhighlight lang=smalltalk>PackageLoader fileInPackage: 'Complex'. |
||
|a b| |
|a b| |
||
a := 1 + 1 i. |
a := 1 + 1 i. |
||
Line 4,766: | Line 4,766: | ||
a real displayNl. |
a real displayNl. |
||
a imaginary displayNl. |
a imaginary displayNl. |
||
a negated displayNl.</ |
a negated displayNl.</syntaxhighlight> |
||
{{works with|Smalltalk/X}} |
{{works with|Smalltalk/X}} |
||
Complex is already in the basic class library. Multiples of imaginary are created by sending an "i" message to a number, which can be added to another number. Thus 5i => (0+5i), 1+(1/3)I => (1+1/3i) and (1.0+2i) => (1.0+2i). Notice that the real and imaginary components can be arbitrary integers, fractions or floating point numbers. And the results will be exact (i.e. have fractions or integer) if possible. |
Complex is already in the basic class library. Multiples of imaginary are created by sending an "i" message to a number, which can be added to another number. Thus 5i => (0+5i), 1+(1/3)I => (1+1/3i) and (1.0+2i) => (1.0+2i). Notice that the real and imaginary components can be arbitrary integers, fractions or floating point numbers. And the results will be exact (i.e. have fractions or integer) if possible. |
||
< |
<syntaxhighlight lang=smalltalk> |
||
|a b| |
|a b| |
||
a := 1 + 1i. |
a := 1 + 1i. |
||
Line 4,792: | Line 4,792: | ||
Transcript show:'a2*b2 => '; showCR:(a2 * b2). |
Transcript show:'a2*b2 => '; showCR:(a2 * b2). |
||
Transcript show:'a2/b2 => '; showCR:(a2 / b2). |
Transcript show:'a2/b2 => '; showCR:(a2 / b2). |
||
Transcript show:'a2 reciprocal => '; showCR:a2 reciprocal.</ |
Transcript show:'a2 reciprocal => '; showCR:a2 reciprocal.</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>a => (1+1i) |
<pre>a => (1+1i) |
||
Line 4,817: | Line 4,817: | ||
<b>Original author unknown {:o(</b> |
<b>Original author unknown {:o(</b> |
||
< |
<syntaxhighlight lang=qbasic>' complex numbers are native for "smart BASIC" |
||
A=1+2i |
A=1+2i |
||
B=3-5i |
B=3-5i |
||
Line 4,833: | Line 4,833: | ||
' gives output |
' gives output |
||
-1+2i -1-2i</ |
-1+2i -1-2i</syntaxhighlight> |
||
=={{header|SNOBOL4}}== |
=={{header|SNOBOL4}}== |
||
Line 4,841: | Line 4,841: | ||
{{works with|CSnobol}} |
{{works with|CSnobol}} |
||
< |
<syntaxhighlight lang=SNOBOL4>* # Define complex datatype |
||
data('complex(r,i)') |
data('complex(r,i)') |
||
Line 4,880: | Line 4,880: | ||
output = printx( negx(a) ) ', ' printx( negx(b) ) |
output = printx( negx(a) ) ', ' printx( negx(b) ) |
||
output = printx( invx(a) ) ', ' printx( invx(b) ) |
output = printx( invx(a) ) ', ' printx( invx(b) ) |
||
end</ |
end</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 4,889: | Line 4,889: | ||
=={{header|Standard ML}}== |
=={{header|Standard ML}}== |
||
< |
<syntaxhighlight lang=Standard ML> |
||
(* Signature for complex numbers *) |
(* Signature for complex numbers *) |
||
signature COMPLEX = sig |
signature COMPLEX = sig |
||
Line 4,933: | Line 4,933: | ||
Complex.print_number(Complex.times i1 i2); (* -5 + 10i *) |
Complex.print_number(Complex.times i1 i2); (* -5 + 10i *) |
||
Complex.print_number(Complex.invert i1); (* 1/5 - 2i/5 *) |
Complex.print_number(Complex.invert i1); (* 1/5 - 2i/5 *) |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Stata}}== |
=={{header|Stata}}== |
||
< |
<syntaxhighlight lang=stata>mata |
||
C(2,3) |
C(2,3) |
||
2 + 3i |
2 + 3i |
||
Line 4,978: | Line 4,978: | ||
1.28247468 + .982793723i |
1.28247468 + .982793723i |
||
end</ |
end</syntaxhighlight> |
||
=={{header|Swift}}== |
=={{header|Swift}}== |
||
Line 4,985: | Line 4,985: | ||
Use a struct to create a complex number type in Swift. Math Operations can be added using operator overloading |
Use a struct to create a complex number type in Swift. Math Operations can be added using operator overloading |
||
< |
<syntaxhighlight lang=swift> |
||
public struct Complex { |
public struct Complex { |
||
Line 5,032: | Line 5,032: | ||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
Make the Complex Number struct printable and easier to debug by adding making it conform to CustomStringConvertible |
Make the Complex Number struct printable and easier to debug by adding making it conform to CustomStringConvertible |
||
< |
<syntaxhighlight lang=swift> |
||
extension Complex : CustomStringConvertible { |
extension Complex : CustomStringConvertible { |
||
Line 5,063: | Line 5,063: | ||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
Explicitly support subtraction and division |
Explicitly support subtraction and division |
||
< |
<syntaxhighlight lang=swift> |
||
public func - (left:Complex, right:Complex) -> Complex { |
public func - (left:Complex, right:Complex) -> Complex { |
||
return left + -right |
return left + -right |
||
Line 5,078: | Line 5,078: | ||
return Complex(real: num.real/den.real, imaginary: num.imaginary/den.real) |
return Complex(real: num.real/den.real, imaginary: num.imaginary/den.real) |
||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Tcl}}== |
=={{header|Tcl}}== |
||
{{tcllib|math::complexnumbers}} |
{{tcllib|math::complexnumbers}} |
||
< |
<syntaxhighlight lang=tcl>package require math::complexnumbers |
||
namespace import math::complexnumbers::* |
namespace import math::complexnumbers::* |
||
Line 5,090: | Line 5,090: | ||
puts [tostring [* $a $b]] ;# ==> 1.94159+4.34159i |
puts [tostring [* $a $b]] ;# ==> 1.94159+4.34159i |
||
puts [tostring [pow $a [complex -1 0]]] ;# ==> 0.5-0.4999999999999999i |
puts [tostring [pow $a [complex -1 0]]] ;# ==> 0.5-0.4999999999999999i |
||
puts [tostring [- $a]] ;# ==> -1.0-i</ |
puts [tostring [- $a]] ;# ==> -1.0-i</syntaxhighlight> |
||
=={{header|TI-83 BASIC}}== |
=={{header|TI-83 BASIC}}== |
||
Line 5,128: | Line 5,128: | ||
=={{header|UNIX Shell}}== |
=={{header|UNIX Shell}}== |
||
{{works with|ksh93}} |
{{works with|ksh93}} |
||
< |
<syntaxhighlight lang=bash>typeset -T Complex_t=( |
||
float real=0 |
float real=0 |
||
float imag=0 |
float imag=0 |
||
Line 5,202: | Line 5,202: | ||
Complex_t d=(real=2 imag=1) |
Complex_t d=(real=2 imag=1) |
||
d.inverse |
d.inverse |
||
d.to_s # 0.4 + -0.2 i</ |
d.to_s # 0.4 + -0.2 i</syntaxhighlight> |
||
=={{header|Ursala}}== |
=={{header|Ursala}}== |
||
Line 5,212: | Line 5,212: | ||
c..add or ..csin). Real operands are promoted to complex. |
c..add or ..csin). Real operands are promoted to complex. |
||
< |
<syntaxhighlight lang=Ursala>u = 3.785e+00-1.969e+00i |
||
v = 9.545e-01-3.305e+00j |
v = 9.545e-01-3.305e+00j |
||
Line 5,223: | Line 5,223: | ||
complex..mul (u,v), |
complex..mul (u,v), |
||
complex..sub (0.,u), |
complex..sub (0.,u), |
||
complex..div (1.,v)></ |
complex..div (1.,v)></syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>< |
<pre>< |
||
Line 5,233: | Line 5,233: | ||
=={{header|VBA}}== |
=={{header|VBA}}== |
||
< |
<syntaxhighlight lang=VBA> |
||
Public Type Complex |
Public Type Complex |
||
re As Double |
re As Double |
||
Line 5,322: | Line 5,322: | ||
Debug.Print "Sqrt(a) = " & CPrint(c) |
Debug.Print "Sqrt(a) = " & CPrint(c) |
||
End Sub |
End Sub |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 5,339: | Line 5,339: | ||
=={{header|Vlang}}== |
=={{header|Vlang}}== |
||
< |
<syntaxhighlight lang=vlang>import math.complex |
||
fn main() { |
fn main() { |
||
a := complex.complex(1, 1) |
a := complex.complex(1, 1) |
||
Line 5,350: | Line 5,350: | ||
println("1 / a: ${complex.complex(1,0)/a}") |
println("1 / a: ${complex.complex(1,0)/a}") |
||
println("a̅: ${a.conjugate()}") |
println("a̅: ${a.conjugate()}") |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>a: 1.000000+1.000000i |
<pre>a: 1.000000+1.000000i |
||
Line 5,363: | Line 5,363: | ||
=={{header|Wortel}}== |
=={{header|Wortel}}== |
||
{{trans|CoffeeScript}} |
{{trans|CoffeeScript}} |
||
< |
<syntaxhighlight lang=wortel>@class Complex { |
||
&[r i] @: { |
&[r i] @: { |
||
^r || r 0 |
^r || r 0 |
||
Line 5,392: | Line 5,392: | ||
"1 / ({b}) = {b.inv.}" |
"1 / ({b}) = {b.inv.}" |
||
"({!a.mul b}) / ({b}) = {`!.mul b.inv. !a.mul b}" |
"({!a.mul b}) / ({b}) = {`!.mul b.inv. !a.mul b}" |
||
]</ |
]</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre>(5 + 3i) + (4 - 3i) = 9 |
<pre>(5 + 3i) + (4 - 3i) = 9 |
||
Line 5,403: | Line 5,403: | ||
=={{header|Wren}}== |
=={{header|Wren}}== |
||
{{libheader|Wren-complex}} |
{{libheader|Wren-complex}} |
||
< |
<syntaxhighlight lang=ecmascript>import "/complex" for Complex |
||
var x = Complex.new(1, 3) |
var x = Complex.new(1, 3) |
||
Line 5,415: | Line 5,415: | ||
System.print("-x = %(-x)") |
System.print("-x = %(-x)") |
||
System.print("1 / x = %(x.inverse)") |
System.print("1 / x = %(x.inverse)") |
||
System.print("x* = %(x.conj)")</ |
System.print("x* = %(x.conj)")</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 5,431: | Line 5,431: | ||
=={{header|XPL0}}== |
=={{header|XPL0}}== |
||
< |
<syntaxhighlight lang=XPL0>include c:\cxpl\codes; |
||
func real CAdd(A, B, C); \Return complex sum of two complex numbers |
func real CAdd(A, B, C); \Return complex sum of two complex numbers |
||
Line 5,487: | Line 5,487: | ||
COut(0, CInv(U,W)); CrLf(0); |
COut(0, CInv(U,W)); CrLf(0); |
||
COut(0, Conj(U,W)); CrLf(0); |
COut(0, Conj(U,W)); CrLf(0); |
||
]</ |
]</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 5,499: | Line 5,499: | ||
=={{header|Yabasic}}== |
=={{header|Yabasic}}== |
||
< |
<syntaxhighlight lang=Yabasic>rem ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
||
rem CADDI/CADDR addition of complex numbers Z1 + Z2 with Z1 = a1 + b1 *i Z2 = a2 + b2*i |
rem CADDI/CADDR addition of complex numbers Z1 + Z2 with Z1 = a1 + b1 *i Z2 = a2 + b2*i |
||
rem CADDI returns imaginary part and CADDR the real part |
rem CADDI returns imaginary part and CADDR the real part |
||
Line 5,546: | Line 5,546: | ||
print "Example: Z1 + Z2 with Z1 = 3 +2i , Z2 = 1-3i: Z1 + Z2 = 4 -1i" |
print "Example: Z1 + Z2 with Z1 = 3 +2i , Z2 = 1-3i: Z1 + Z2 = 4 -1i" |
||
print caddr(3,2,1,-2), "/", caddi(3,2,1,-3) // 4/-1 |
print caddr(3,2,1,-2), "/", caddi(3,2,1,-3) // 4/-1 |
||
end if</ |
end if</syntaxhighlight> |
||
=={{header|zkl}}== |
=={{header|zkl}}== |
||
< |
<syntaxhighlight lang=zkl>var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library) |
||
(GSL.Z(3,4) + GSL.Z(1,2)).println(); // (4.00+6.00i) |
(GSL.Z(3,4) + GSL.Z(1,2)).println(); // (4.00+6.00i) |
||
(GSL.Z(3,4) - GSL.Z(1,2)).println(); // (2.00+2.00i) |
(GSL.Z(3,4) - GSL.Z(1,2)).println(); // (2.00+2.00i) |
||
Line 5,556: | Line 5,556: | ||
(GSL.Z(1,0) / GSL.Z(1,1)).println(); // (0.50-0.50i) // inversion |
(GSL.Z(1,0) / GSL.Z(1,1)).println(); // (0.50-0.50i) // inversion |
||
(-GSL.Z(3,4)).println(); // (-3.00-4.00i) |
(-GSL.Z(3,4)).println(); // (-3.00-4.00i) |
||
GSL.Z(3,4).conjugate().println(); // (3.00-4.00i)</ |
GSL.Z(3,4).conjugate().println(); // (3.00-4.00i)</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 5,569: | Line 5,569: | ||
=={{header|zonnon}}== |
=={{header|zonnon}}== |
||
< |
<syntaxhighlight lang=zonnon> |
||
module Numbers; |
module Numbers; |
||
type |
type |
||
Line 5,664: | Line 5,664: | ||
Writeln(~b); |
Writeln(~b); |
||
end Main. |
end Main. |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{Out}} |
{{Out}} |
||
<pre> |
<pre> |
||
Line 5,677: | Line 5,677: | ||
=={{header|ZX Spectrum Basic}}== |
=={{header|ZX Spectrum Basic}}== |
||
{{trans|BBC BASIC}} |
{{trans|BBC BASIC}} |
||
< |
<syntaxhighlight lang=zxbasic>5 LET complex=2: LET r=1: LET i=2 |
||
10 DIM a(complex): LET a(r)=1.0: LET a(i)=1.0 |
10 DIM a(complex): LET a(r)=1.0: LET a(i)=1.0 |
||
20 DIM b(complex): LET b(r)=PI: LET b(i)=1.2 |
20 DIM b(complex): LET b(r)=PI: LET b(i)=1.2 |
||
Line 5,700: | Line 5,700: | ||
1000 IF o(i)>=0 THEN PRINT o(r);" + ";o(i);"i": RETURN |
1000 IF o(i)>=0 THEN PRINT o(r);" + ";o(i);"i": RETURN |
||
1010 PRINT o(r);" - ";-o(i);"i": RETURN |
1010 PRINT o(r);" - ";-o(i);"i": RETURN |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre>Result of addition is: |
<pre>Result of addition is: |