AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Donate Contacts

← Back to list of members

Piecewise

 Method with 2 overloads

• Piecewise​(System.​Collections.​Generic.​IEnumerable{AngouriMath.​Entity.​Providedf},​AngouriMath.​Entity)

  Summary

  This is a piecewisely defined function, which turns into a particular definition
  once there exists a case number N such that case[N].Predicate is turned into true and
  for all i less than N : case[i].Predicate is turned into false.
  
  For example, Piecewise(new Providedf(a, b), new Providedf(d, false), new Providedf(f, true))
  will remain unchanged, because the first case is uncertain.
  
  Piecewise(new Providedf(a, false), new Providedf(d, false), new Providedf(f, true))
  will turn into f
  
  Piecewise(new Providedf(a, false), new Providedf(d, false), new Providedf(f, false))
  will turn into NaN
  

  Parameter "cases"

  Cases, each of type Provided.
  

  Parameter "otherwise"

  An otherwise case. Will be intepreted as otherwise.Provided(true). Optional.
  

  Example

  using System;
  using static AngouriMath.MathS;
  
  var expr = Piecewise(
      ("-1", "x < 0"),
      ("0", "x = 0"),
      ("1", true)
  );
  Console.WriteLine(expr);
  Console.WriteLine(expr.Substitute("x", 10).Evaled);
  Console.WriteLine(expr.Substitute("x", 0).Evaled);
  Console.WriteLine(expr.Substitute("x", -14).Evaled);
  
  Console.WriteLine();
  
  var weirdSqrt = Piecewise(
      ("sqrt(x)", "x >= 0"),
      ("-sqrt(-x)", true)
  );
  Console.WriteLine(weirdSqrt);
  Console.WriteLine(weirdSqrt.Substitute("x", 16).Evaled);
  Console.WriteLine(weirdSqrt.Substitute("x", -16).Evaled);
  
  Console.WriteLine();
  
  var thousandVisualizer = Piecewise(
      ("a / 1000000 million", "a > 1000000"),
      ("a / 1000 thousand", "a > 1000"),
      ("a", "a >= 0")
  );
  
  Console.WriteLine(thousandVisualizer.Substitute("a", 19301).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", 19301123).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", 32).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", -24).Evaled);

  
  Prints
  

  (-1 if x < 0, 0 if x = 0, 1 if True)
  1
  0
  -1
  
  (sqrt(x) if x >= 0, -sqrt(-x) if True)
  4
  -4
  
  19301/1000 * thousand
  19301123/1000000 * million
  32
  NaN

• Piecewise​(System.​ValueTuple{AngouriMath.​Entity,​AngouriMath.​Entity}[])

  Summary

  This is a piecewisely defined function, which turns into a particular definition
  once there exists a case number N such that case[N].Predicate is turned into true and
  for all i less than N : case[i].Predicate is turned into false.
  
  For example, Piecewise((a, b), (d, false), (f, true))
  will remain unchanged, because the first case is uncertain.
  
  Piecewise((a, false), (d, false), (f, true))
  will turn into f
  
  Piecewise((a, false), (d, false), (f, false))
  will turn into NaN
  

  Parameter "cases"

  Tuples of two expressions: an expression and a predicate
  

  Example

  using System;
  using static AngouriMath.MathS;
  
  var expr = Piecewise(
      ("-1", "x < 0"),
      ("0", "x = 0"),
      ("1", true)
  );
  Console.WriteLine(expr);
  Console.WriteLine(expr.Substitute("x", 10).Evaled);
  Console.WriteLine(expr.Substitute("x", 0).Evaled);
  Console.WriteLine(expr.Substitute("x", -14).Evaled);
  
  Console.WriteLine();
  
  var weirdSqrt = Piecewise(
      ("sqrt(x)", "x >= 0"),
      ("-sqrt(-x)", true)
  );
  Console.WriteLine(weirdSqrt);
  Console.WriteLine(weirdSqrt.Substitute("x", 16).Evaled);
  Console.WriteLine(weirdSqrt.Substitute("x", -16).Evaled);
  
  Console.WriteLine();
  
  var thousandVisualizer = Piecewise(
      ("a / 1000000 million", "a > 1000000"),
      ("a / 1000 thousand", "a > 1000"),
      ("a", "a >= 0")
  );
  
  Console.WriteLine(thousandVisualizer.Substitute("a", 19301).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", 19301123).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", 32).Evaled);
  Console.WriteLine(thousandVisualizer.Substitute("a", -24).Evaled);

  
  Prints
  

  (-1 if x < 0, 0 if x = 0, 1 if True)
  1
  0
  -1
  
  (sqrt(x) if x >= 0, -sqrt(-x) if True)
  4
  -4
  
  19301/1000 * thousand
  19301123/1000000 * million
  32
  NaN