How to resolve the algorithm Set of real numbers step by step in the zkl programming language

Published on 12 May 2024 09:40 PM
#Zkl

How to resolve the algorithm Set of real numbers step by step in the zkl programming language

Table of Contents

Problem Statement

All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary: Note that if a = b, of the four only [a, a] would be non-empty. Task Implementation notes Optional work |sin(π x)| > 1/2 is the same as n + 1/6 < x < n + 5/6 for all integers n; your program does not need to derive this by itself.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Set of real numbers step by step in the zkl programming language

Source code in the zkl programming language

class RealSet{
   fcn init(fx){ var [const] contains=fx; }
   fcn holds(x){ contains(x) }
   fcn __opAdd(rs){ RealSet('wrap(x){ contains(x) or rs.contains(x) }) }
   fcn __opSub(rs){ RealSet('wrap(x){ contains(x) and not rs.contains(x) }) }
   fcn intersection(rs) { RealSet('wrap(x){ contains(x) and rs.contains(x) }) }
}

tester := TheVault.Test.UnitTester.UnitTester();

    // test union
s:=RealSet(fcn(x){ 0.0 <  x <= 1.0 }) + 
   RealSet(fcn(x){ 0.0 <= x <  1.0 });
tester.testRun(s.holds(0.0),Void,True,__LINE__);
tester.testRun(s.holds(1.0),Void,True,__LINE__);
tester.testRun(s.holds(2.0),Void,False,__LINE__);

    // test difference
s1 := RealSet(fcn(x){ 0.0 <= x < 3.0 }) -
      RealSet(fcn(x){ 0.0 <  x < 1.0 });
tester.testRun(s1.holds(0.0),Void,True,__LINE__);
tester.testRun(s1.holds(0.5),Void,False,__LINE__);
tester.testRun(s1.holds(1.0),Void,True,__LINE__);
tester.testRun(s1.holds(2.0),Void,True,__LINE__);

s2 := RealSet(fcn(x){ 0.0 <= x <  3.0 }) -
      RealSet(fcn(x){ 0.0 <= x <= 1.0 });
tester.testRun(s2.holds(0.0),Void,False,__LINE__);
tester.testRun(s2.holds(1.0),Void,False,__LINE__);
tester.testRun(s2.holds(2.0),Void,True,__LINE__);

    // test intersection
s := RealSet(fcn(x){ 0.0 <= x <  2.0 }).intersection(
     RealSet(fcn(x){ 1.0 <  x <= 2.0 }));
tester.testRun(s.holds(0.0),Void,False,__LINE__);
tester.testRun(s.holds(1.0),Void,False,__LINE__);
tester.testRun(s.holds(2.0),Void,False,__LINE__);

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