AngouriMath

Navigation

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

AngouriMath.Entity.Set

← Back to list of namespaces

Classes within the AngouriMath.Entity.Set namespace

• ConditionalSet

  Summary

  This is the most abstract set. Technically, you can describe
  any set within this one. Formally, you can define set A of
  a condition F(x) in the following way: for each element x in
  the Universal x belongs to A if and only if F(x).
  

  Example

  using AngouriMath;
  using System;
  using static AngouriMath.Entity.Set;
  using static AngouriMath.MathS;
  using static AngouriMath.MathS.Sets;
  
  var set1 = Finite(1, 2, 3);
  var set2 = Finite(2, 3, 4);
  var set3 = MathS.Interval(-6, 2);
  var set4 = new ConditionalSet("x", "100 > x2 > 81");
  Console.WriteLine(Union(set1, set2));
  Console.WriteLine(Union(set1, set2).Simplify());
  Console.WriteLine("----------------------");
  Console.WriteLine(Union(set1, set3));
  Console.WriteLine(Union(set1, set3).Simplify());
  Console.WriteLine("----------------------");
  Console.WriteLine(Union(set1, set4));
  Console.WriteLine(ElementInSet(3, Union(set1, set4)));
  Console.WriteLine(ElementInSet(3, Union(set1, set4)).Simplify());
  Console.WriteLine(ElementInSet(4, Union(set1, set4)));
  Console.WriteLine(ElementInSet(4, Union(set1, set4)).Simplify());
  Console.WriteLine(ElementInSet(9.5, Union(set1, set4)));
  Console.WriteLine(ElementInSet(9.5, Union(set1, set4)).Simplify());
  Console.WriteLine("----------------------");
  Console.WriteLine(Intersection(set1, set2));
  Console.WriteLine(Intersection(set1, set2).Simplify());
  Console.WriteLine("----------------------");
  Console.WriteLine(Intersection(set2, set3));
  Console.WriteLine(Intersection(set2, set3).Simplify());
  Console.WriteLine("----------------------");
  var set5 = MathS.Interval(-3, 11);
  Console.WriteLine(Intersection(set3, set5));
  Console.WriteLine(Intersection(set3, set5).Simplify());
  Console.WriteLine(Union(set3, set5));
  Console.WriteLine(Union(set3, set5).Simplify());
  Console.WriteLine(SetSubtraction(set3, set5));
  Console.WriteLine(SetSubtraction(set3, set5).Simplify());
  Console.WriteLine("----------------------");
  Entity syntax1 = @"{ 1, 2, 3 } /\ { 2, 3, 4 }";
  Console.WriteLine(syntax1);
  Console.WriteLine(syntax1.Simplify());
  Console.WriteLine("----------------------");
  Entity syntax2 = @"5 in ([1; +oo) \/ { x : x < -4 })";
  Console.WriteLine(syntax2);
  Console.WriteLine(syntax2.Simplify());
  Console.WriteLine("----------------------");
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), Q));
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), Q).Simplify());
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), R));
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), R).Simplify());
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), C));
  Console.WriteLine(Intersection(Finite(pi, e, 6, 5.5m, 1 + 3 * i), C).Simplify());

  
  Prints
  

  { 1, 2, 3 } \/ { 2, 3, 4 }
  { 1, 2, 3, 4 }
  ----------------------
  { 1, 2, 3 } \/ [-6; 2]
  { 3 } \/ [-6; 2]
  ----------------------
  { 1, 2, 3 } \/ { x : 100 > x ^ 2 and x ^ 2 > 81 }
  3 in { 1, 2, 3 } \/ { x : 100 > x ^ 2 and x ^ 2 > 81 }
  True
  4 in { 1, 2, 3 } \/ { x : 100 > x ^ 2 and x ^ 2 > 81 }
  False
  19/2 in { 1, 2, 3 } \/ { x : 100 > x ^ 2 and x ^ 2 > 81 }
  True
  ----------------------
  { 1, 2, 3 } /\ { 2, 3, 4 }
  { 2, 3 }
  ----------------------
  { 2, 3, 4 } /\ [-6; 2]
  { 2 }
  ----------------------
  [-6; 2] /\ [-3; 11]
  [-3; 2]
  [-6; 2] \/ [-3; 11]
  [-6; 11]
  [-6; 2] \ [-3; 11]
  [-6; -3)
  ----------------------
  { 1, 2, 3 } /\ { 2, 3, 4 }
  { 2, 3 }
  ----------------------
  5 in [1; +oo) \/ { x : x < -4 }
  True
  ----------------------
  { pi, e, 6, 11/2, 1 + 3i } /\ QQ
  { 6, 11/2 }
  { pi, e, 6, 11/2, 1 + 3i } /\ RR
  { pi, e, 6, 11/2 }
  { pi, e, 6, 11/2, 1 + 3i } /\ CC
  { pi, e, 6, 11/2, 1 + 3i }

• FiniteSet

  Summary

  A finite set is a set whose elements can be counted and enumerated
  

• Inf

  Summary

  This node represents whether the given element is in the set
  

• Intersectionf

  Summary

  Finds the intersection of two sets
  It is true that an entity is in an intersection if it is in both of intersection's operands
  

• Interval

  Summary

  An interval represents all numbres in between two Entities
  LeftClosed stands for whether Left is included
  RightClosed stands for whether Right is included
  

• SetMinusf

  Summary

  Finds A & !B
  It is true that an entity is in SetMinus if it is in Left but not in Right
  

• SpecialSet

  Summary

  Special set is something that cannot be easily expressed in other
  types of sets.
  

• Unionf

  Summary

  Unites two sets
  It is true that an entity is in a union if it is at least in one of union's operands