Data update

Task/Arithmetic-Complex/ArkScript/arithmetic-complex.ark

@@ -0,0 +1,30 @@
+(import std.Math)
+
+(let a (math:complex 1 1))
+(let b (math:complex 3.75 1.25))
+
+(assert
+  (=
+    (math:complex-add a b)
+    (math:complex 4.75 2.25))
+  "complex add")
+(assert
+  (=
+    (math:complex-mul a b)
+    (math:complex 2.5 5))
+  "complex mul")
+(assert
+  (=
+    (math:complex-mul (math:complex -1 0) a)
+    (math:complex -1 -1))
+  "complex negation")
+(assert
+  (=
+    (math:complex-div (math:complex 1 0) a)
+    (math:complex 0.5 -0.5))
+  "complex inversion")
+(assert
+  (=
+    (math:complex-conjugate a)
+    (math:complex 1 -1))
+  "complex conjugate")

Task/Arithmetic-Complex/DuckDB/arithmetic-complex.duckdb

@@ -0,0 +1,86 @@
+CREATE TYPE COMPLEX AS STRUCT(r REAL, i REAL);
+
+CREATE OR REPLACE FUNCTION isreal(a) AS (
+  if (try_cast(a as REAL), true, false)
+);
+
+CREATE OR REPLACE FUNCTION tocomplex(a) AS (
+  coalesce( try_cast(a as COMPLEX),  {r: a, i:0.0 }::COMPLEX )
+);
+
+CREATE OR REPLACE FUNCTION complex_add_(a, b) AS (
+  {r: a.r + b.r, i:a.i + b.i}
+);
+
+CREATE OR REPLACE FUNCTION complex_add(a, b) AS (
+  complex_add_(tocomplex(a), tocomplex(b))
+);
+
+CREATE OR REPLACE FUNCTION complex_mul_(a, b) AS (
+  {r: a.r * b.r - a.i * b.i, i:a.r * b.i + a.i * b.r}
+);
+
+CREATE OR REPLACE FUNCTION complex_mul(a, b) AS (
+  complex_mul_(tocomplex(a), tocomplex(b))
+);
+
+CREATE OR REPLACE FUNCTION complex_mag(a) AS (
+  case when isreal(a)
+       then abs(a::REAL)
+       else sqrt( (a::COMPLEX).r ^ 2 + (a::COMPLEX).i ^2)
+       end
+);
+
+CREATE OR REPLACE FUNCTION complex_conj(a) AS (
+  case when isreal(a)
+       then {r: a::REAL, i: 0.0}
+       else {r: (a::COMPLEX).r, i: - (a::COMPLEX).i}
+       end
+);
+
+CREATE OR REPLACE FUNCTION complex_mag_squared(x) AS (
+  case when isreal(x)
+       then x::REAL*x::REAL
+       else (x::COMPLEX).r ^ 2 + (x::COMPLEX).i ^ 2
+       end
+);
+
+# Oddly, the a.r notation cannot currently be used here
+CREATE OR REPLACE FUNCTION complex_div_(a, b) AS (
+  WITH denom AS (select complex_mag_squared(b) as denom,
+    a['r'] as ar, a['i'] as ai, b['r'] as br, b['i'] as bi
+  )
+  SELECT {r: (ar * br + ai * bi) / denom,
+          i: (ai * br - ar * bi) / denom }
+  FROM denom
+);
+
+CREATE OR REPLACE FUNCTION complex_div(a, b) AS (
+  complex_div_(tocomplex(a), tocomplex(b))
+);
+
+CREATE OR REPLACE FUNCTION complex_exp_(z) AS (
+  complex_mul_( {r: exp(z.r), i: 0.0}, {r: cos(z.i), i:sin(z.i) })
+);
+
+CREATE OR REPLACE FUNCTION complex_exp(z) AS (
+  if( isreal(z),
+      {r:exp(z::REAL), i:0.0},
+      complex_exp_( tocomplex(z) ) )
+);
+
+## Examples
+.mode line
+CREATE OR REPLACE FUNCTION test(x,y) as table (
+  select x as "x",
+         y as "y",
+         complex_add(x,y) as "add",
+         complex_mul(x,y) as "mul",
+         complex_div(1, x) as "1/x",
+         complex_conj(x) as "conj(x)",
+         complex_div(x,y).complex_mul(y) as "(x/y)*y"
+);
+
+from test({r:1,i:1}, {r:0,i:1} );
+
+select complex_exp( {r:0, i:pi()} ) as "e^iπ";

Task/Arithmetic-Complex/FutureBasic/arithmetic-complex.basic

@@ -0,0 +1,71 @@
+//
+//  Arithmetic/Complex
+//  Using FutureBasic 7.0.34
+//  August 2025, R.W
+
+include "Tlbx complex.incl"
+// through this include file, FB supports the following
+// double complex functions (as of August 2025).
+// Float and long double complex might be
+// available in later versions
+
+//fn creal, cimag, cabs, carg, conj, cproj
+//fn csqrt, cexp,  clog, cpow
+//fn csin,  ccos,  ctan
+//fn casin, cacos, catan
+//fn csinh, ccosh, ctanh
+//fn casinh,cacosh,catanh
+
+// Below is redefining "I" to Cj since I don't want to lose the
+// ability to use "i" as my favorite FOR NEXT / loop variable
+BeginCDeclaration
+#define Cj I
+EndC
+system double Cj
+
+local fn PrintComplexNumber( z as double_complex )
+  double  y
+  print @fn creal( z ) " ";
+  y = fn cimag( z )
+  if ( y >= 0.0 ) then print @"+"; : else print @"-";
+  print @abs( y ) "i"
+end fn
+
+window 1,@"Arithmetic/Complex"
+
+double_complex z1, z2, z3, z4, z5, z6
+double_complex z7, z8, z9, zs, zn
+
+z1 = 1.5 + 3 * Cj        //1.5 + 3i
+z2 = 1.5 + 1.5 * Cj      //1.5 + 1.5i
+
+// Operations using C99 operators
+z3 = z1 + z2        // addition
+z4 = z1 - z2        // subtraction
+z5 = z1 * z2        // multiplication
+z6 = z1 / z2        // division
+//----------------
+z7 = fn conj(z1)    // conjugate
+z8 = fn cpow(z1,z2) // power ^
+z9 = fn cabs(z1)    // norm | magnitude
+zs = fn csqrt(z1)   // square root
+zn = -(z1)          // negate
+
+// Extract real/imag parts using creal/cimag
+print @
+print @" z1 + z2 = "; fn creal(z3); " + "; fn cimag(z3); "i"
+print @" z1 - z2 = "; fn creal(z4); " + "; fn cimag(z4); "i"
+print @" z1 * z2 = "; fn creal(z5); " + "; fn cimag(z5); "i"
+print @" z1 / z2 = "; fn creal(z6); " + "; fn cimag(z6); "i"
+print @" Conj z1 = "; fn creal(z7); "   "; fn cimag(z7); "i"
+print @" Abs  z1 = "; fn creal(z9)
+print @" z1 ^ z2 = ";
+fn PrintComplexNumber(z8)
+print @" cSqrt z1= ";
+fn PrintComplexNumber(zs)
+print @" -(z1)   = ";
+fn PrintComplexNumber(zn)
+print @" z1 real = "; fn creal(z1)
+print @" z1 imag = "; fn cimag(z1)
+
+HandleEvents

Task/Arithmetic-Complex/Pluto/arithmetic-complex.pluto

@@ -0,0 +1,15 @@
+require "complex"
+local fmt = require "fmt"
+
+local x = new complex(1, 3)
+local y = new complex(5, 2)
+
+fmt.print("x     = %s", x)
+fmt.print("y     = %s", y)
+fmt.print("x + y = %s", x + y)
+fmt.print("x - y = %s", x - y)
+fmt.print("x * y = %s", x * y)
+fmt.print("x / y = %s", x / y)
+fmt.print("-x    = %s", -x)
+fmt.print("1 / x = %s", x:inverse())
+fmt.print("x*    = %s", x:conj())

Task/Arithmetic-Complex/REXX/arithmetic-complex.rexx

@@ -1,4 +1,4 @@
--- 19 May 2025
+-- 7 Aug 2025
 include Settings
 
 say 'COMPLEX ARITHMETIC'
@@ -6,48 +6,45 @@ say version
 say
 a = '1 2'; b = '3 4'; c = '5 6'; d = '7 8'; i = I()
 say 'VALUES'
-say 'a =' crec2form(a)
-say 'b =' crec2form(b)
-say 'c =' crec2form(c)
-say 'd =' crec2form(d)
+say 'a =' Rec2FormC(a)
+say 'b =' Rec2FormC(b)
+say 'c =' Rec2FormC(c)
+say 'd =' Rec2FormC(d)
 say
 say 'BASICS'
-say 'i*i     =' crec2form(Csquare(i()))
-say 'a+b     =' crec2form(Cadd(a,b))
-say 'a-b     =' crec2form(Csub(a,b))
-say 'a*b     =' crec2form(Cmul(a,b))
-say 'a/b     =' crec2form(Cdiv(a,b))
-say 'a^2     =' crec2form(Csquare(a,2))
-say 'a^5     =' crec2form(Cpow(a,5))
-say '-a      =' crec2form(Cneg(a))
-say '1/a     =' crec2form(Cinv(a))
-say 'a+b+c+d =' crec2form(Cadd(a,b,c,d))
-say 'a-b-c-d =' crec2form(Csub(a,b,c,d))
-say 'a*b*c*d =' crec2form(Cmul(a,b,c,d))
-say 'a/b/c/d =' crec2form(Cnormal(Cdiv(a,b,c,d)))
+say 'i*i     =' Rec2FormC(SquareC(i()))
+say 'a+b     =' Rec2FormC(AddC(a,b))
+say 'a-b     =' Rec2FormC(SubC(a,b))
+say 'a*b     =' Rec2FormC(MulC(a,b))
+say 'a/b     =' Rec2FormC(DivC(a,b))
+say 'a^2     =' Rec2FormC(SquareC(a,2))
+say 'a^5     =' Rec2FormC(PowC(a,5))
+say '-a      =' Rec2FormC(NegC(a))
+say '1/a     =' Rec2FormC(InvC(a))
+say 'a+b+c+d =' Rec2FormC(AddC(a,b,c,d))
+say 'a-b-c-d =' Rec2FormC(SubC(a,b,c,d))
+say 'a*b*c*d =' Rec2FormC(MulC(a,b,c,d))
+say 'a/b/c/d =' Rec2FormC(Normal(DivC(a,b,c,d)))
 say
 say 'FORMULA'
 say 'a^2-2ab+3c-4ad^4+5 =' ,
-crec2form(Cadd(Csquare(a),Cmul(-2,a,b),Cmul(3,c),Cmul(-4,a,Cpower(d,4)),5))
+Rec2FormC(AddC(SquareC(a),MulC(-2,a,b),MulC(3,c),MulC(-4,a,PowerC(d,4)),5))
 say
 say 'BONUS'
-say 'Argument(a)  =' Carg(a)+0
-say 'Conjugate(a) =' crec2form(Cconj(a))
-say 'Imag(a)      =' Cim(a)
-say 'Modulus(a)   =' Cmod(a)+0
-say 'Polar(a)     =' Cpol2form(Cnormal(Crec2pol(a)))
-say 'Real(a)      =' Cre(a)
+say 'Argument(a)  =' ArgC(a)+0
+say 'Conjugate(a) =' Rec2FormC(ConjC(a))
+say 'Imag(a)      =' ImC(a)
+say 'Modulus(a)   =' ModC(a)+0
+say 'Polar(a)     =' Pol2FormC(Normal(Rec2PolC(a)))
+say 'Real(a)      =' ReC(a)
 say
 say 'MORE'
-say 'Arcsin(a) =' crec2form(Cnormal(Carcsin(a)))
-say 'Exp(a)    =' crec2form(Cnormal(Cexp(a)))
-say 'Ln(a)     =' crec2form(Cnormal(Cln(a)))
-say 'Sin(a)    =' crec2form(Cnormal(Csin(a)))
-say 'Sqrt(a)   =' crec2form(Cnormal(Csqrt(a)))
-say 'i^i       =' crec2form(Cnormal(Cpower(i,i)))
+say 'Arcsin(a) =' Rec2FormC(Normal(ArcSinC(a)))
+say 'Exp(a)    =' Rec2FormC(Normal(ExpC(a)))
+say 'Ln(a)     =' Rec2FormC(Normal(LnC(a)))
+say 'Sin(a)    =' Rec2FormC(Normal(SinC(a)))
+say 'Sqrt(a)   =' Rec2FormC(Normal(SqRtC(a)))
+say 'i^i       =' Rec2FormC(Normal(PowerC(i,i)))
 exit
 
-include Complex
-include Functions
-include Constants
-include Abend
+include Math