AngouriMath.MathS Class Reference

Use functions from this class More...

Collaboration diagram for AngouriMath.MathS:

Classes
class	Boolean
	Some operations on booleans are stored here
class	Compute
	Implements necessary functions for symbolic computation of limits, derivatives and integrals
class	DecimalConst
	Some non-symbolic constants
class	Diagnostic
	This class is used for diagnostic and debug of the library itself.
class	ExperimentalFeatures
	Features that might become stable in the future, but are not guaranteed to do anything useful or correctly at the current moment.
class	Hyperbolic
	Represents a few hyperbolic functions
class	Matrices
	Classes and functions related to matrices are defined here
class	Multithreading
	A few functions convenient to use in industrial projects to keep the system more reliable and distribute computations to other threads
class	Numbers
class	NumberTheory
	Use it in order to explore further number theory
class	Series
	That is a collection of some series, expressed in a symbolic form
class	Sets
	Functions and classes related to sets defined here
class	Settings
	A couple of settings allowing you to set some preferences for AM's algorithms To use these settings the syntax is
class	UnsafeAndInternal
	You may need it to manually manage some issues.
class	Utils
	Some additional functions that would be barely ever used by the user, but kept for "just in case" as public

Static Public Member Functions
static EquationSystem	Equations (params Entity[] equations)
	Use it to solve systems of equations More...
static EquationSystem	Equations (IEnumerable< Entity > equations)
	Use it to solve systems of equations More...
static Set	SolveEquation (Entity equation, Variable var)
	Solves one equation over one variable More...
static Matrix	SolveBooleanTable (Entity expression, params Variable[] variables)
	Solves a boolean expression. More...
static Entity	Sin (Entity a)
	More...
static Entity	Cos (Entity a)
	More...
static Entity	Sec (Entity a)
	More...
static Entity	Cosec (Entity a)
	More...
static Entity	Log (Entity @base, Entity x)
	More...
static Entity	Log (Entity x)
	This is 10-based logarithm. More...
static Entity	Pow (Entity @base, Entity power)
	More...
static Entity	Sqrt (Entity a)
	Special case of More...
static Entity	Cbrt (Entity a)
	Special case of More...
static Entity	Sqr (Entity a)
	Special case of More...
static Entity	Tan (Entity a)
	More...
static Entity	Cotan (Entity a)
	More...
static Entity	Arcsin (Entity a)
	More...
static Entity	Arccos (Entity a)
	More...
static Entity	Arctan (Entity a)
	More...
static Entity	Arccotan (Entity a)
	More...
static Entity	Arcsec (Entity a)
	More...
static Entity	Arccosec (Entity a)
	More...
static Entity	Ln (Entity a)
	Is a special case of logarithm where the base equals e: More...
static Entity	Factorial (Entity a)
	More...
static Entity	Gamma (Entity a)
	More...
static Entity	Signum (Entity a)
	https://en.wikipedia.org/wiki/Sign_function More...
static Entity	Abs (Entity a)
	https://en.wikipedia.org/wiki/Absolute_value More...
static Entity	Negation (Entity a)
	Boolean negation Wikipedia More...
static Entity	Provided (Entity expression, Entity condition)
	This will be turned into expression if the condition is true, into NaN if condition is false, and remain the same otherwise More...
static Entity	Piecewise (IEnumerable< Providedf > cases, Entity? otherwise=null)
	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. More...
static Entity	Piecewise (params(Entity expression, Entity predicate)[] cases)
	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. More...
static Entity	Apply (Entity expr, params Entity[] arguments)
	Applies the list of arguments to the given expression More...
static Entity	Lambda (Variable param, Entity body)
	Returns a lambda with the given parameter and body More...
static Entity	Disjunction (Entity a, Entity b)
	https://en.wikipedia.org/wiki/Logical_disjunction More...
static Entity	Conjunction (Entity a, Entity b)
	https://en.wikipedia.org/wiki/Logical_conjunction More...
static Entity	Implication (Entity assumption, Entity conclusion)
	https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference) More...
static Entity	ExclusiveDisjunction (Entity a, Entity b)
	https://en.wikipedia.org/wiki/Exclusive_or More...
static Entity	Equality (Entity a, Entity b)
	Do NOT confuse it with Equation More...
static Entity	GreaterThan (Entity a, Entity b)
	Parameters a Left argument node of which the greater than node will be taken b Right argument node of which the greater than node function will be taken Returns A node More...
static Entity	LessThan (Entity a, Entity b)
	Parameters a Left argument node of which the less than node will be taken b Right argument node of which the less than node function will be taken Returns A node More...
static Entity	GreaterOrEqualThan (Entity a, Entity b)
	Parameters a Left argument node of which the greter than or equal node will be taken b Right argument node of which the greater than or equal node function will be taken Returns A node More...
static Entity	LessOrEqualThan (Entity a, Entity b)
	Parameters a Left argument node of which the less than or equal node will be taken b Right argument node of which the less than or equal node function will be taken Returns A node More...
static Set	Union (Entity a, Entity b)
	Parameters a Left argument node of which the union set node will be taken b Right argument node of which the union set node will be taken Returns A node More...
static Set	Intersection (Entity a, Entity b)
	Parameters a Left argument node of which the intersection set node will be taken b Right argument node of which the intersection set node will be taken Returns A node More...
static Set	SetSubtraction (Entity a, Entity b)
	Parameters a Left argument node of which the set subtraction node will be taken That is, the resulting set of set subtraction is necessarily superset of this set b Right argument node of which the set subtraction set node will be taken That is, there is no element in the resulting set that belong to this one Returns A node More...
static Variable	Var (string name)
	Creates an instance of Variable. More...
static Entity	FromString (string expr, bool useCache)
	Converts a string to an expression More...
static Entity	FromString (string expr)
	Converts a string to an expression More...
static ParsingResult	Parse (string source)
	Parses an expression silently, that is, without throwing an exception. More...
static string	ToBaseN (Real num, int N)
	Translates a Number in base 10 into base N More...
static Number.Real	FromBaseN (string num, int N)
	Translates a number in base N into base 10 More...
static string	Latex (ILatexiseable latexiseable)
	Returns The LaTeX representation of the argument Parameters latexiseable Any element (Entity, Set, etc.) that can be represented in LaTeX More...
static Entity	Det (Matrix m)
	Finds the determinant of the given matrix. More...
static Matrix	Matrix (Entity[,] values)
	Creates an instance of Entity.Matrix. More...
static Matrix	Matrix (int rowCount, int colCount, Func< int, int, Entity > map)
	Creates an instance of matrix, where each cell's index is mapped to a value with the help of the mapping function. More...
static Matrix	Vector (params Entity[] values)
	Creates an instance of Entity.Matrix that has one column. More...
static Matrix	ZeroMatrix (int size)
	Creates a zero square matrix More...
static Matrix	ZeroMatrix (int rowCount, int columnCount)
	Creates a zero square matrix More...
static Matrix	ZeroVector (int size)
	Creates a zero vector More...
static Matrix	Scalar (Entity value)
	Creates a 1x1 matrix of a given value. More...
static Matrix	MatrixFromRows (IEnumerable< Matrix > vectors)
	Creates a matrix from given rows More...
static Matrix	MatrixFromIEnum2x2 (IEnumerable< IEnumerable< Entity >> elements)
	Creates a matrix from given elements More...
static Interval	Interval (Entity left, Entity right)
	Creates a closed interval (segment) More...
static Interval	Interval (Entity left, bool leftClosed, Entity right, bool rightClosed)
	Creates an interval with custom endings More...
static Matrix	IdentityMatrix (int size)
	Creates a square identity matrix More...
static Matrix	IdentityMatrix (int rowCount, int columnCount)
	Creates a rectangular identity matrix with the given size More...
static bool	TryPolynomial (Entity expr, Variable variable, [NotNullWhen(true)] out Entity? dst)
	Returns an Entity in polynomial order if possible More...
static string	ToSympyCode (Entity expr)
	Returns sympy interpretable format Parameters expr An Entity representing an expression More...
static Entity	Derivative (Entity expr, Entity var)
	Hangs your Entity to a derivative node (to evaluate instead use Compute.Derivative(Entity, Variable)) More...
static Entity	Derivative (Entity expr, Entity var, int power)
	Hangs your Entity to a derivative node (to evaluate instead use Compute.Derivative(Entity, Variable)) More...
static Entity	Integral (Entity expr, Entity var)
	Hangs your entity to an integral node (to evaluate instead use Compute.Integral(Entity, Variable)) More...
static Entity	Integral (Entity expr, Entity var, Entity from, Entity to)
	Hangs your entity to an integral node (to evaluate instead use Compute.Integral(Entity, Variable)) More...
static Entity	Limit (Entity expr, Entity var, Entity dest, ApproachFrom approach=ApproachFrom.BothSides)
	Hangs your entity to a limit node (to evaluate instead use Compute.Limit(Entity, Variable, Entity)) More...

Static Public Attributes
static	Variable
	Creates two instances of Variable. More...
static readonly Real	oo = (Real)(Entity)"+oo"
	Infinity. More...
static readonly Variable	e = Variable.e
	The e constant More...
static readonly Complex	i = Complex.ImaginaryOne
	The imaginary one More...
static readonly Variable	pi = Variable.pi
	The pi constant More...
static readonly Entity	NaN = Real.NaN
	NaN represents both "undefined" and "indeterminate". More...
static readonly Matrix	I_1 = IdentityMatrix(1)
	The square identity matrix of size 1 More...
static readonly Matrix	I_2 = IdentityMatrix(2)
	The square identity matrix of size 2 More...
static readonly Matrix	I_3 = IdentityMatrix(3)
	The square identity matrix of size 3 More...
static readonly Matrix	I_4 = IdentityMatrix(4)
	The square identity matrix of size 4 More...
static readonly Matrix	O_1 = ZeroMatrix(1)
	The square zero matrix of size 1 More...
static readonly Matrix	O_2 = ZeroMatrix(2)
	The square zero matrix of size 2 More...
static readonly Matrix	O_3 = ZeroMatrix(3)
	The square zero matrix of size 3 More...
static readonly Matrix	O_4 = ZeroMatrix(4)
	The square zero matrix of size 4 More...

Detailed Description

Use functions from this class

Member Function Documentation

Abs()

static Entity AngouriMath.MathS.Abs ( Entity  a )

static

https://en.wikipedia.org/wiki/Absolute_value

Parameters

a	Argument node of which Abs function will be taken

Returns

Abs node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Abs(-5));
Console.WriteLine(Abs(-5).Evaled);
Console.WriteLine(Abs(0));
Console.WriteLine(Abs(0).Evaled);
Console.WriteLine(Abs(5));
Console.WriteLine(Abs(5).Evaled);
Console.WriteLine(Abs(4 + 3 * i));
Console.WriteLine(Abs(4 + 3 * i).Evaled);

Prints

abs(-5)
5
abs(0)
0
abs(5)
5
abs(4 + 3i)
5

Apply()

static Entity AngouriMath.MathS.Apply ( Entity  expr, params Entity []  arguments  )

static

Applies the list of arguments to the given expression

Returns

Entity.Application

Entity expr = "sin";
Console.WriteLine(expr);
var applied = expr.Apply(pi / 3);
Console.WriteLine(applied);
Console.WriteLine(applied.Simplify());
Console.WriteLine(applied.Evaled);
Console.WriteLine("------------------------------");
var lambda = Lambda("x", "x ^ 3 + x");
Console.WriteLine(lambda);
Console.WriteLine(lambda.Apply("3"));
Console.WriteLine(lambda.Apply("3").Evaled);
Console.WriteLine("------------------------------");
var lambda2 = Lambda("y", "y".ToEntity().Apply(pi / 3));
Console.WriteLine(lambda2);
Console.WriteLine(lambda2.Apply("sin").Simplify());
Console.WriteLine(lambda2.Apply("cos").Simplify());
Console.WriteLine(lambda2.Apply("tan").Simplify());
Console.WriteLine("------------------------------");
var lambda3 = Lambda("x", Lambda("y", Lambda("z", "x + y / z")));
Console.WriteLine(lambda3);
Console.WriteLine(lambda3.Apply(5));
Console.WriteLine(lambda3.Apply(5).Simplify());
Console.WriteLine(lambda3.Apply(5).Apply(10));
Console.WriteLine(lambda3.Apply(5).Apply(10).Simplify());
Console.WriteLine(lambda3.Apply(5, 10));
Console.WriteLine(lambda3.Apply(5, 10).Simplify());
Console.WriteLine(lambda3.Apply(5, 10, 7));
Console.WriteLine(lambda3.Apply(5, 10, 7).Simplify());

Prints

sin
sin (pi / 3)
sqrt(3) / 2
<h2>1/2 * sqrt(3)
</h2>
x -> x ^ 3 + x
(x -> x ^ 3 + x) 3
<h2>30
</h2>
y -> y (pi / 3)
sqrt(3) / 2
1/2
<h2>sqrt(3)
</h2>
x -> y -> z -> x + y / z
(x -> y -> z -> x + y / z) 5
y -> z -> 5 + y / z
(x -> y -> z -> x + y / z) 5 10
z -> 5 + 10 / z
(x -> y -> z -> x + y / z) 5 10
z -> 5 + 10 / z
(x -> y -> z -> x + y / z) 5 10 7
45/7

Arccos()

static Entity AngouriMath.MathS.Arccos ( Entity  a )

static

Parameters

a	Argument node of which arccosine will be taken

Returns

Arccosine node

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Arccosec()

static Entity AngouriMath.MathS.Arccosec ( Entity  a )

static

Parameters

a	Argument node of which arccosecant will be taken

Returns

Arcsine node with the reciprocal of the argument

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Arccotan()

static Entity AngouriMath.MathS.Arccotan ( Entity  a )

static

Parameters

a	Argument node of which arccotangent will be taken

Returns

Arccotangent node

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Arcsec()

static Entity AngouriMath.MathS.Arcsec ( Entity  a )

static

Parameters

a	Argument node of which arcsecant will be taken

Returns

Arccosine node with the reciprocal of the argument

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Arcsin()

static Entity AngouriMath.MathS.Arcsin ( Entity  a )

static

Parameters

a	Argument node of which arcsine will be taken

Returns

Arcsine node

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Arctan()

static Entity AngouriMath.MathS.Arctan ( Entity  a )

static

Parameters

a	Argument node of which arctangent will be taken

Returns

Arctangent node

using System;
using static AngouriMath.MathS;
var expr = Arcsin("x") + Arccos("x");
Console.WriteLine(expr);
var expr2 = Arcsin(Sin("x")) + Arccos(Cos("y"));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());
var expr3 = Arctan(Sin("a") / Cos("a"));
Console.WriteLine(expr3);
Console.WriteLine(expr3.Simplify());
var expr4 = Arccotan(Cos("a") / Sin("a"));
Console.WriteLine(expr4);
Console.WriteLine(expr4.Simplify());
var expr5 = Arcsec(Sec("aa")) + Arccosec(Cosec("bb"));
Console.WriteLine(expr5);
Console.WriteLine(expr5.Simplify());

Prints

arcsin(x) + arccos(x)
arcsin(sin(x)) + arccos(cos(y))
x + y
arctan(sin(a) / cos(a))
a
arccotan(cos(a) / sin(a))
a
arcsec(sec(aa)) + arccsc(csc(bb))
aa + bb

Cbrt()

static Entity AngouriMath.MathS.Cbrt ( Entity  a )

static

Special case of

Parameters

a	The argument of which cube root will be taken

Returns

Power node with (1/3) as the power

using System;
using static AngouriMath.MathS;
Console.WriteLine(Pow(2, 5));
Console.WriteLine(Pow(2, 5).Simplify());
Console.WriteLine(Pow(e, 2));
Console.WriteLine(Pow(e, 2).Simplify());
Console.WriteLine(Pow(e, 2).Evaled);
Console.WriteLine(Sqrt(Sqr("x")));
Console.WriteLine(Sqrt(Sqr("x")).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 3));
Console.WriteLine(Pow(Cbrt("a"), 3).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 6));
Console.WriteLine(Pow(Cbrt("a"), 6).Simplify());

Prints

2 ^ 5
32
e ^ 2
e ^ 2
7.389056098930650227230427460575007813180315570551847324087127822522573796079057763384312485079121792
sqrt(x ^ 2)
x
a ^ (1/3) ^ 3
a
a ^ (1/3) ^ 6
a ^ 2

Conjunction()

static Entity AngouriMath.MathS.Conjunction ( Entity  a, Entity  b  )

static

https://en.wikipedia.org/wiki/Logical_conjunction

Parameters

a	Left argument node of which Conjunction function will be taken
b	Right argument node of which Conjunction disjunction function will be taken

Returns

And node

using AngouriMath;
using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var myXor = Disjunction(Conjunction(x, Negation(y)), Conjunction(y, Negation(x)));
Console.WriteLine(myXor);
Console.WriteLine(MathS.Boolean.BuildTruthTable(myXor, x, y).ToString(multilineFormat: true));
Console.WriteLine("------------------");
var expr = ExclusiveDisjunction(Implication(x, y), Implication(y, x));
Console.WriteLine(expr);
Console.WriteLine("------------------");
var expr2 = Conjunction(x, Conjunction(x, y));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());

Prints

x and not y or y and not x
Matrix[4 x 3]
False   False   False   
False   True    True    
True    False   True    
<h2>True    True    False   
</h2>
<h2>(x implies y) xor (y implies x)
</h2>
x and x and y
x and y

Cos()

static Entity AngouriMath.MathS.Cos ( Entity  a )

static

Parameters

a	Argument node of cosine

Returns

Cosine node

using System;
using static AngouriMath.MathS;

var expr = Sin("x").Pow(2) + Cos("x").Pow(2);
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());

Prints

sin(x) ^ 2 + cos(x) ^ 2
1

Cosec()

static Entity AngouriMath.MathS.Cosec ( Entity  a )

static

Parameters

a	Argument node of cosecant

Returns

Cosecant node

using System;
using static AngouriMath.MathS;

var expr = Sec("x") / Cosec("x");
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());

Prints

sec(x) / csc(x)
tan(x)

Cotan()

static Entity AngouriMath.MathS.Cotan ( Entity  a )

static

Parameters

a	Argument node of which cotangent will be taken

Returns

Cotangent node

using System;
using static AngouriMath.MathS;
var expr = Tan("x") * Cotan("x");
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());
var expr2 = Tan("x") * Cos("x");
Console.WriteLine(expr2.Simplify());

Prints

tan(x) * cotan(x)
1
sin(x)

Derivative() [1/2]

static Entity AngouriMath.MathS.Derivative ( Entity  expr, Entity  var  )

static

Hangs your Entity to a derivative node (to evaluate instead use Compute.Derivative(Entity, Variable))

Parameters

expr	Expression to be hung
var	Variable over which derivative is taken

using System;
using static AngouriMath.MathS;

var (x, a) = Var("x", "a");

var e1 = Derivative(Sin(Cos(x)), x);
Console.WriteLine(e1);
Console.WriteLine(e1.InnerSimplified);
Console.WriteLine("-----------------------");
var e2 = Derivative(Sin(Cos(x)), x, 2);
Console.WriteLine(e2);
Console.WriteLine(e2.InnerSimplified);
Console.WriteLine("-----------------------");
var e3 = Integral(Sin(a * x), x);
Console.WriteLine(e3);
Console.WriteLine(e3.InnerSimplified);
Console.WriteLine("-----------------------");
var e4 = Integral(Sin(a * x), x, 2);
Console.WriteLine(e4);
Console.WriteLine(e4.InnerSimplified);
Console.WriteLine("-----------------------");
var e5 = Limit(Sin(a * x) / x, x, 0);
Console.WriteLine(e5);
Console.WriteLine(e5.InnerSimplified);

Prints

derivative(sin(cos(x)), x)
<h2>cos(cos(x)) * -sin(x)
</h2>
derivative(sin(cos(x)), x, 2)
<h2>-sin(cos(x)) * -sin(x) * -sin(x) + cos(x) * (-1) * cos(cos(x))
</h2>
integral(sin(a * x), x)
<h2>-cos(a * x) / a
</h2>
integral(sin(a * x), x, 2)
<h2>-sin(a * x) / a / a
</h2>
limit(sin(a * x) / x, x, 0)
a

Derivative() [2/2]

static Entity AngouriMath.MathS.Derivative ( Entity  expr, Entity  var, int  power  )

static

Hangs your Entity to a derivative node (to evaluate instead use Compute.Derivative(Entity, Variable))

Parameters

expr	Expression to be hung
var	Variable over which derivative is taken
power	Number of times derivative is taken. Only integers will be simplified or evaluated.

using System;
using static AngouriMath.MathS;

var (x, a) = Var("x", "a");

var e1 = Derivative(Sin(Cos(x)), x);
Console.WriteLine(e1);
Console.WriteLine(e1.InnerSimplified);
Console.WriteLine("-----------------------");
var e2 = Derivative(Sin(Cos(x)), x, 2);
Console.WriteLine(e2);
Console.WriteLine(e2.InnerSimplified);
Console.WriteLine("-----------------------");
var e3 = Integral(Sin(a * x), x);
Console.WriteLine(e3);
Console.WriteLine(e3.InnerSimplified);
Console.WriteLine("-----------------------");
var e4 = Integral(Sin(a * x), x, 2);
Console.WriteLine(e4);
Console.WriteLine(e4.InnerSimplified);
Console.WriteLine("-----------------------");
var e5 = Limit(Sin(a * x) / x, x, 0);
Console.WriteLine(e5);
Console.WriteLine(e5.InnerSimplified);

Prints

derivative(sin(cos(x)), x)
<h2>cos(cos(x)) * -sin(x)
</h2>
derivative(sin(cos(x)), x, 2)
<h2>-sin(cos(x)) * -sin(x) * -sin(x) + cos(x) * (-1) * cos(cos(x))
</h2>
integral(sin(a * x), x)
<h2>-cos(a * x) / a
</h2>
integral(sin(a * x), x, 2)
<h2>-sin(a * x) / a / a
</h2>
limit(sin(a * x) / x, x, 0)
a

Det()

static Entity AngouriMath.MathS.Det ( Matrix  m )

static

Finds the determinant of the given matrix.

If the matrix is non-square, returns null

using System;
using static AngouriMath.Entity;
using static AngouriMath.MathS;

Matrix A = @"
[[1, 2],
 [3, 4]]
";
Console.WriteLine(Det(A));

Matrix B = @"
[[1, 2],
 [3, 6]]
";
Console.WriteLine(Det(B));

Matrix C = @"
[[1, 2],
 [3, 6],
 [7, 8]]
";
Console.WriteLine(Det(C) is null);

Prints

-2
0
True

Disjunction()

static Entity AngouriMath.MathS.Disjunction ( Entity  a, Entity  b  )

static

https://en.wikipedia.org/wiki/Logical_disjunction

Parameters

a	The left argument node of which Disjunction function will be taken
b	The right argument node of which Disjunction function will be taken

Returns

Or node

using AngouriMath;
using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var myXor = Disjunction(Conjunction(x, Negation(y)), Conjunction(y, Negation(x)));
Console.WriteLine(myXor);
Console.WriteLine(MathS.Boolean.BuildTruthTable(myXor, x, y).ToString(multilineFormat: true));
Console.WriteLine("------------------");
var expr = ExclusiveDisjunction(Implication(x, y), Implication(y, x));
Console.WriteLine(expr);
Console.WriteLine("------------------");
var expr2 = Conjunction(x, Conjunction(x, y));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());

Prints

x and not y or y and not x
Matrix[4 x 3]
False   False   False   
False   True    True    
True    False   True    
<h2>True    True    False   
</h2>
<h2>(x implies y) xor (y implies x)
</h2>
x and x and y
x and y

Equality()

static Entity AngouriMath.MathS.Equality ( Entity  a, Entity  b  )

static

Do NOT confuse it with Equation

Parameters

a	Left argument node of which Equality function will be taken
b	Right argument node of which Equality disjunction function will be taken

Returns

An Equals node

using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var equation = Equality(Sqrt(x), 4 * x - 3);
Console.WriteLine(equation);
Console.WriteLine(equation.Solve(x));
Console.WriteLine("----------------------");
var statement1 = Equality(5, 10);
Console.WriteLine(statement1);
Console.WriteLine((bool)statement1.EvalBoolean());
Console.WriteLine("----------------------");
var statement2 = Equality(5, 5);
Console.WriteLine(statement2);
Console.WriteLine((bool)statement2.EvalBoolean());
Console.WriteLine("----------------------");
var statement3 = Equality(x, y);
Console.WriteLine(statement3);
Console.WriteLine(statement3.Simplify());
// throws here!
Console.WriteLine((bool)statement3.EvalBoolean());

Prints

sqrt(x) = 4 * x - 3
<h2>{ 9/16, 1 }
</h2>
5 = 10
<h2>False
</h2>
5 = 5
<h2>True
</h2>
x = y
x = y
Unhandled exception. AngouriMath.Core.Exceptions.CannotEvalException

Equations() [1/2]

static EquationSystem AngouriMath.MathS.Equations ( params Entity []  equations )

static

Use it to solve systems of equations

Parameters

equations

An array of Entity (or strings) the system consists of

var system = MathS.Equations(
    "a + b",
    "a^2 - b + c"
);
var solutions = system.Solve("a", "b");
Console.WriteLine(solutions.ToString(multilineFormat: true));
<br/>
Console.WriteLine();
<br/>
for (int i = 0; i < solutions.RowCount; i++)
{
    var (a, b) = (solutions[i, 0], solutions[i, 1]);
    Console.WriteLine($"Solution #{i}: a = {a}, b = {b}");
}

Prints

Matrix[2 x 2]
(-1 - sqrt(1 - 4 * c)) / 2    -(-1 - sqrt(1 - 4 * c)) / 2   
(-1 + sqrt(1 - 4 * c)) / 2    -(-1 + sqrt(1 - 4 * c)) / 2   
<br/>
Solution #0: a = (-1 - sqrt(1 - 4 * c)) / 2, b = -(-1 - sqrt(1 - 4 * c)) / 2
Solution #1: a = (-1 + sqrt(1 - 4 * c)) / 2, b = -(-1 + sqrt(1 - 4 * c)) / 2

Returns

An EquationSystem which can then be solved

Equations() [2/2]

static EquationSystem AngouriMath.MathS.Equations ( IEnumerable< Entity >  equations )

static

Use it to solve systems of equations

Parameters

equations

A sequence of Entity the system consists of

var equations = LList.Of<Entity>(
    "a + b",
    "a^2 - b + c"
);
var system = MathS.Equations(equations);
var solutions = system.Solve("a", "b");
Console.WriteLine(solutions.ToString(multilineFormat: true));
<br/>
Console.WriteLine();
<br/>
for (int i = 0; i < solutions.RowCount; i++)
{
    var (a, b) = (solutions[i, 0], solutions[i, 1]);
    Console.WriteLine($"Solution #{i}: a = {a}, b = {b}");
}

Prints

Matrix[2 x 2]
(-1 - sqrt(1 - 4 * c)) / 2    -(-1 - sqrt(1 - 4 * c)) / 2   
(-1 + sqrt(1 - 4 * c)) / 2    -(-1 + sqrt(1 - 4 * c)) / 2   
<br/>
Solution #0: a = (-1 - sqrt(1 - 4 * c)) / 2, b = -(-1 - sqrt(1 - 4 * c)) / 2
Solution #1: a = (-1 + sqrt(1 - 4 * c)) / 2, b = -(-1 + sqrt(1 - 4 * c)) / 2

Returns

An EquationSystem which can then be solved

ExclusiveDisjunction()

static Entity AngouriMath.MathS.ExclusiveDisjunction ( Entity  a, Entity  b  )

static

https://en.wikipedia.org/wiki/Exclusive_or

Parameters

a	Left argument node of which Exclusive disjunction function will be taken
b	Right argument node of which Exclusive disjunction function will be taken

Returns

Xor node

using AngouriMath;
using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var myXor = Disjunction(Conjunction(x, Negation(y)), Conjunction(y, Negation(x)));
Console.WriteLine(myXor);
Console.WriteLine(MathS.Boolean.BuildTruthTable(myXor, x, y).ToString(multilineFormat: true));
Console.WriteLine("------------------");
var expr = ExclusiveDisjunction(Implication(x, y), Implication(y, x));
Console.WriteLine(expr);
Console.WriteLine("------------------");
var expr2 = Conjunction(x, Conjunction(x, y));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());

Prints

x and not y or y and not x
Matrix[4 x 3]
False   False   False   
False   True    True    
True    False   True    
<h2>True    True    False   
</h2>
<h2>(x implies y) xor (y implies x)
</h2>
x and x and y
x and y

Factorial()

static Entity AngouriMath.MathS.Factorial ( Entity  a )

static

Parameters

a	Argument node of which factorial will be taken

Returns

Factorial node

using System;
using static AngouriMath.MathS;
var expr = Factorial(5);
Console.WriteLine(expr);
Console.WriteLine(expr.Evaled);
var expr2 = Gamma(4);
Console.WriteLine(expr2);
Console.WriteLine(expr2.Evaled);

Prints

5!
120
(4 + 1)!
120

FromBaseN()

static Number.Real AngouriMath.MathS.FromBaseN ( string  num, int  N  )

static

Translates a number in base N into base 10

Parameters

num	A Real in base N to be translated into base 10
N	The base to translate the number from

Returns

The Real in base 10

using System;
using static AngouriMath.MathS;

using var _ = Settings.DowncastingEnabled.Set(false);

Console.WriteLine(ToBaseN(1.5m, 2));
Console.WriteLine(ToBaseN(3.75m, 2));
Console.WriteLine(ToBaseN(13.125m, 2));
Console.WriteLine(ToBaseN(13.125m, 10));

// uncomment when https://github.com/asc-community/AngouriMath/issues/584
// is fixed
// Console.WriteLine(ToBaseN(13.125m, 5));

Console.WriteLine(ToBaseN(13.125m, 8));
Console.WriteLine("-----------------------");
Console.WriteLine(FromBaseN("FF", 16));
Console.WriteLine(FromBaseN("77", 8));
Console.WriteLine(FromBaseN("1.1", 2));
Console.WriteLine(FromBaseN("1.01", 2));
Console.WriteLine(FromBaseN("1.05", 6));        

Prints

1.1
11.11
1101.001
13.125
<h2>15.1
</h2>
255
63
1.500000000
1.250000000
1.138888888

FromString() [1/2]

static Entity AngouriMath.MathS.FromString ( string  expr, bool  useCache  )

static

Converts a string to an expression

Parameters

expr	string expression, for example, "2 * x + 3 + sqrt(x)"
useCache	By default is true, it boosts performance if you have multiple uses of the same string, for example, Entity expr = (Entity)"+oo" + "x".Limit("x", "+oo") * "+oo"; First occurance will be parsed, others will be replaced with the cached entity

Returns

The parsed expression

Multiple ways to parse an expression.

Entity expr1 = "a + b";
var expr2 = FromString("a + b");
var expr3 = FromString("a + b", useCache: false);
var expr4 = (Entity)"a + b";
var expr5 = Parse("a + b").Switch(
    res => res,
    failure => failure.Reason.Switch<object>(
        unknown => throw new("Unknown reason"),
        missingOp => throw new("Missing operator"),
        internalError => throw new("Internal error") 
    )
);

FromString() [2/2]

static Entity AngouriMath.MathS.FromString ( string  expr )

static

Converts a string to an expression

Parameters

expr	string expression, for example, "2 * x + 3 + sqrt(x)"

Returns

The parsed expression

Multiple ways to parse an expression.

Entity expr1 = "a + b";
var expr2 = FromString("a + b");
var expr3 = FromString("a + b", useCache: false);
var expr4 = (Entity)"a + b";
var expr5 = Parse("a + b").Switch(
    res => res,
    failure => failure.Reason.Switch<object>(
        unknown => throw new("Unknown reason"),
        missingOp => throw new("Missing operator"),
        internalError => throw new("Internal error") 
    )
);

Gamma()

static Entity AngouriMath.MathS.Gamma ( Entity  a )

static

Parameters

a	Argument node of which gamma function will be taken

Returns

Factorial node with one subtracted from the argument

using System;
using static AngouriMath.MathS;
var expr = Factorial(5);
Console.WriteLine(expr);
Console.WriteLine(expr.Evaled);
var expr2 = Gamma(6);
Console.WriteLine(expr2);
Console.WriteLine(expr2.Evaled);

Prints

5!
120
(6 - 1)!
120

GreaterOrEqualThan()

static Entity AngouriMath.MathS.GreaterOrEqualThan ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the greter than or equal node will be taken
b	Right argument node of which the greater than or equal node function will be taken

Returns

A node

using System; using static AngouriMath.MathS;

var (x, y) = Var("x", "y");

Console.WriteLine(GreaterThan(x, y)); Console.WriteLine(GreaterThan(6, 5)); Console.WriteLine(GreaterThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessThan(x, y)); Console.WriteLine(LessThan(6, 5)); Console.WriteLine(LessThan(6, 5).EvalBoolean()); Console.WriteLine(LessThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(GreaterOrEqualThan(x, y)); Console.WriteLine(GreaterOrEqualThan(6, 5)); Console.WriteLine(GreaterOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessOrEqualThan(x, y)); Console.WriteLine(LessOrEqualThan(6, 5)); Console.WriteLine(LessOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(LessOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); var statement1 = GreaterThan(Sqr(x), 5); Console.WriteLine(statement1); Console.WriteLine(statement1.Solve("x")); Console.WriteLine("----------------------------------"); var statement2 = GreaterThan(Sqr(x), 16) & LessThan(x, y); Console.WriteLine(statement2); Console.WriteLine(statement2.Solve("x")); Console.WriteLine("----------------------------------"); var statement3 = LessThan(Sqr(x), 16) & GreaterThan(x, 2); Console.WriteLine(statement3); Console.WriteLine(statement3.Solve("x")); Prints x > y 6 > 5 True

False

x < y 6 < 5 False

False

x >= y 6 >= 5 True

True

x <= y 6 <= 5 False

True

x ^ 2 > 5

(-oo; -sqrt(20) / 2) \/ (sqrt(20) / 2; +oo)

x ^ 2 > 16 and x < y

((-oo; -4) \/ (4; +oo)) /\ (-oo; -y / (-1))

x ^ 2 < 16 and x > 2 (2; 4)

GreaterThan()

static Entity AngouriMath.MathS.GreaterThan ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the greater than node will be taken
b	Right argument node of which the greater than node function will be taken

Returns

A node

using System; using static AngouriMath.MathS;

var (x, y) = Var("x", "y");

Console.WriteLine(GreaterThan(x, y)); Console.WriteLine(GreaterThan(6, 5)); Console.WriteLine(GreaterThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessThan(x, y)); Console.WriteLine(LessThan(6, 5)); Console.WriteLine(LessThan(6, 5).EvalBoolean()); Console.WriteLine(LessThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(GreaterOrEqualThan(x, y)); Console.WriteLine(GreaterOrEqualThan(6, 5)); Console.WriteLine(GreaterOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessOrEqualThan(x, y)); Console.WriteLine(LessOrEqualThan(6, 5)); Console.WriteLine(LessOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(LessOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); var statement1 = GreaterThan(Sqr(x), 5); Console.WriteLine(statement1); Console.WriteLine(statement1.Solve("x")); Console.WriteLine("----------------------------------"); var statement2 = GreaterThan(Sqr(x), 16) & LessThan(x, y); Console.WriteLine(statement2); Console.WriteLine(statement2.Solve("x")); Console.WriteLine("----------------------------------"); var statement3 = LessThan(Sqr(x), 16) & GreaterThan(x, 2); Console.WriteLine(statement3); Console.WriteLine(statement3.Solve("x")); Prints x > y 6 > 5 True

False

x < y 6 < 5 False

False

x >= y 6 >= 5 True

True

x <= y 6 <= 5 False

True

x ^ 2 > 5

(-oo; -sqrt(20) / 2) \/ (sqrt(20) / 2; +oo)

x ^ 2 > 16 and x < y

((-oo; -4) \/ (4; +oo)) /\ (-oo; -y / (-1))

x ^ 2 < 16 and x > 2 (2; 4)

IdentityMatrix() [1/2]

static Matrix AngouriMath.MathS.IdentityMatrix ( int  size )

static

Creates a square identity matrix

using System;
using static AngouriMath.MathS;

Console.WriteLine(IdentityMatrix(4).ToString(multilineFormat: true));
Console.WriteLine(IdentityMatrix(4, 3).ToString(multilineFormat: true));

Prints

Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1   
Matrix[4 x 3]
1   0   0   
0   1   0   
0   0   1   
0   0   0   

IdentityMatrix() [2/2]

static Matrix AngouriMath.MathS.IdentityMatrix ( int  rowCount, int  columnCount  )

static

Creates a rectangular identity matrix with the given size

using System;
using static AngouriMath.MathS;

Console.WriteLine(IdentityMatrix(4).ToString(multilineFormat: true));
Console.WriteLine(IdentityMatrix(4, 3).ToString(multilineFormat: true));

Prints

Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1   
Matrix[4 x 3]
1   0   0   
0   1   0   
0   0   1   
0   0   0   

Implication()

static Entity AngouriMath.MathS.Implication ( Entity  assumption, Entity  conclusion  )

static

https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)

Parameters

assumption	The assumption node
conclusion	The conclusion node

Returns

Implies node

using AngouriMath;
using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var myXor = Disjunction(Conjunction(x, Negation(y)), Conjunction(y, Negation(x)));
Console.WriteLine(myXor);
Console.WriteLine(MathS.Boolean.BuildTruthTable(myXor, x, y).ToString(multilineFormat: true));
Console.WriteLine("------------------");
var expr = ExclusiveDisjunction(Implication(x, y), Implication(y, x));
Console.WriteLine(expr);
Console.WriteLine("------------------");
var expr2 = Conjunction(x, Conjunction(x, y));
Console.WriteLine(expr2);
Console.WriteLine(expr2.Simplify());

Prints

x and not y or y and not x
Matrix[4 x 3]
False   False   False   
False   True    True    
True    False   True    
<h2>True    True    False   
</h2>
<h2>(x implies y) xor (y implies x)
</h2>
x and x and y
x and y

Integral() [1/2]

static Entity AngouriMath.MathS.Integral ( Entity  expr, Entity  var  )

static

Hangs your entity to an integral node (to evaluate instead use Compute.Integral(Entity, Variable))

Parameters

expr	Expression to be hung
var	Variable over which integral is taken

using System;
using static AngouriMath.MathS;

var (x, a) = Var("x", "a");

var e1 = Derivative(Sin(Cos(x)), x);
Console.WriteLine(e1);
Console.WriteLine(e1.InnerSimplified);
Console.WriteLine("-----------------------");
var e2 = Derivative(Sin(Cos(x)), x, 2);
Console.WriteLine(e2);
Console.WriteLine(e2.InnerSimplified);
Console.WriteLine("-----------------------");
var e3 = Integral(Sin(a * x), x);
Console.WriteLine(e3);
Console.WriteLine(e3.InnerSimplified);
Console.WriteLine("-----------------------");
var e4 = Integral(Sin(a * x), x, 2);
Console.WriteLine(e4);
Console.WriteLine(e4.InnerSimplified);
Console.WriteLine("-----------------------");
var e5 = Limit(Sin(a * x) / x, x, 0);
Console.WriteLine(e5);
Console.WriteLine(e5.InnerSimplified);

Prints

derivative(sin(cos(x)), x)
<h2>cos(cos(x)) * -sin(x)
</h2>
derivative(sin(cos(x)), x, 2)
<h2>-sin(cos(x)) * -sin(x) * -sin(x) + cos(x) * (-1) * cos(cos(x))
</h2>
integral(sin(a * x), x)
<h2>-cos(a * x) / a
</h2>
integral(sin(a * x), x, 2)
<h2>-sin(a * x) / a / a
</h2>
limit(sin(a * x) / x, x, 0)
a

Integral() [2/2]

static Entity AngouriMath.MathS.Integral ( Entity  expr, Entity  var, Entity  from, Entity  to  )

static

Hangs your entity to an integral node (to evaluate instead use Compute.Integral(Entity, Variable))

Parameters

expr	Expression to be hung
var	Variable over which integral is taken
from	The lower bound for integrating
to	The upper bound for integrating

using System;
using static AngouriMath.MathS;

var (x, a) = Var("x", "a");

var e1 = Derivative(Sin(Cos(x)), x);
Console.WriteLine(e1);
Console.WriteLine(e1.InnerSimplified);
Console.WriteLine("-----------------------");
var e2 = Derivative(Sin(Cos(x)), x, 2);
Console.WriteLine(e2);
Console.WriteLine(e2.InnerSimplified);
Console.WriteLine("-----------------------");
var e3 = Integral(Sin(a * x), x);
Console.WriteLine(e3);
Console.WriteLine(e3.InnerSimplified);
Console.WriteLine("-----------------------");
var e4 = Integral(Sin(a * x), x, 2);
Console.WriteLine(e4);
Console.WriteLine(e4.InnerSimplified);
Console.WriteLine("-----------------------");
var e5 = Limit(Sin(a * x) / x, x, 0);
Console.WriteLine(e5);
Console.WriteLine(e5.InnerSimplified);

Prints

derivative(sin(cos(x)), x)
<h2>cos(cos(x)) * -sin(x)
</h2>
derivative(sin(cos(x)), x, 2)
<h2>-sin(cos(x)) * -sin(x) * -sin(x) + cos(x) * (-1) * cos(cos(x))
</h2>
integral(sin(a * x), x)
<h2>-cos(a * x) / a
</h2>
integral(sin(a * x), x, 2)
<h2>-sin(a * x) / a / a
</h2>
limit(sin(a * x) / x, x, 0)
a

Intersection()

static Set AngouriMath.MathS.Intersection ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the intersection set node will be taken
b	Right argument node of which the intersection set node will be taken

Returns

A node

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 &gt; x2 &gt; 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 }

Interval() [1/2]

static Interval AngouriMath.MathS.Interval ( Entity  left, Entity  right  )

static

Creates a closed interval (segment)

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 }
<h2>{ 1, 2, 3, 4 }
</h2>
{ 1, 2, 3 } \/ [-6; 2]
<h2>{ 3 } \/ [-6; 2]
</h2>
{ 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 }
<h2>True
</h2>
{ 1, 2, 3 } /\ { 2, 3, 4 }
<h2>{ 2, 3 }
</h2>
{ 2, 3, 4 } /\ [-6; 2]
<h2>{ 2 }
</h2>
[-6; 2] /\ [-3; 11]
[-3; 2]
[-6; 2] \/ [-3; 11]
[-6; 11]
[-6; 2] \ [-3; 11]
<h2>[-6; -3)
</h2>
{ 1, 2, 3 } /\ { 2, 3, 4 }
<h2>{ 2, 3 }
</h2>
5 in [1; +oo) \/ { x : x < -4 }
<h2>True
</h2>
{ 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 }

Interval() [2/2]

static Interval AngouriMath.MathS.Interval ( Entity  left, bool  leftClosed, Entity  right, bool  rightClosed  )

static

Creates an interval with custom endings

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 }
<h2>{ 1, 2, 3, 4 }
</h2>
{ 1, 2, 3 } \/ [-6; 2]
<h2>{ 3 } \/ [-6; 2]
</h2>
{ 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 }
<h2>True
</h2>
{ 1, 2, 3 } /\ { 2, 3, 4 }
<h2>{ 2, 3 }
</h2>
{ 2, 3, 4 } /\ [-6; 2]
<h2>{ 2 }
</h2>
[-6; 2] /\ [-3; 11]
[-3; 2]
[-6; 2] \/ [-3; 11]
[-6; 11]
[-6; 2] \ [-3; 11]
<h2>[-6; -3)
</h2>
{ 1, 2, 3 } /\ { 2, 3, 4 }
<h2>{ 2, 3 }
</h2>
5 in [1; +oo) \/ { x : x < -4 }
<h2>True
</h2>
{ 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 }

Lambda()

static Entity AngouriMath.MathS.Lambda ( Variable  param, Entity  body  )

static

Returns a lambda with the given parameter and body

Entity expr = "sin";
Console.WriteLine(expr);
var applied = expr.Apply(pi / 3);
Console.WriteLine(applied);
Console.WriteLine(applied.Simplify());
Console.WriteLine(applied.Evaled);
Console.WriteLine("------------------------------");
var lambda = Lambda("x", "x ^ 3 + x");
Console.WriteLine(lambda);
Console.WriteLine(lambda.Apply("3"));
Console.WriteLine(lambda.Apply("3").Evaled);
Console.WriteLine("------------------------------");
var lambda2 = Lambda("y", "y".ToEntity().Apply(pi / 3));
Console.WriteLine(lambda2);
Console.WriteLine(lambda2.Apply("sin").Simplify());
Console.WriteLine(lambda2.Apply("cos").Simplify());
Console.WriteLine(lambda2.Apply("tan").Simplify());
Console.WriteLine("------------------------------");
var lambda3 = Lambda("x", Lambda("y", Lambda("z", "x + y / z")));
Console.WriteLine(lambda3);
Console.WriteLine(lambda3.Apply(5));
Console.WriteLine(lambda3.Apply(5).Simplify());
Console.WriteLine(lambda3.Apply(5).Apply(10));
Console.WriteLine(lambda3.Apply(5).Apply(10).Simplify());
Console.WriteLine(lambda3.Apply(5, 10));
Console.WriteLine(lambda3.Apply(5, 10).Simplify());
Console.WriteLine(lambda3.Apply(5, 10, 7));
Console.WriteLine(lambda3.Apply(5, 10, 7).Simplify());

Prints

sin
sin (pi / 3)
sqrt(3) / 2
<h2>1/2 * sqrt(3)
</h2>
x -> x ^ 3 + x
(x -> x ^ 3 + x) 3
<h2>30
</h2>
y -> y (pi / 3)
sqrt(3) / 2
1/2
<h2>sqrt(3)
</h2>
x -> y -> z -> x + y / z
(x -> y -> z -> x + y / z) 5
y -> z -> 5 + y / z
(x -> y -> z -> x + y / z) 5 10
z -> 5 + 10 / z
(x -> y -> z -> x + y / z) 5 10
z -> 5 + 10 / z
(x -> y -> z -> x + y / z) 5 10 7
45/7

Latex()

static string AngouriMath.MathS.Latex ( ILatexiseable  latexiseable )

static

Returns

The LaTeX representation of the argument

Parameters

latexiseable

Any element (Entity, Set, etc.) that can be represented in LaTeX

using System; using AngouriMath; using static AngouriMath.MathS;

Entity expr = "sqrt(a) + integral(sin(x), x)"; Console.WriteLine(expr); Console.WriteLine(Latex(expr)); Entity expr2 = "a / b ^ limit(sin(x) - cosh(y), x, +oo)"; Console.WriteLine(expr2); Console.WriteLine(Latex(expr2)); Prints sqrt(a) + integral(sin(x), x) {a}+ [(x)] dx a / b ^ limit(sin(x) - (e ^ y + e ^ (-y)) / 2, x, +oo) {a}{{b}^{{x } [(x)-{{e}^{y}+{e}^{-y}}{2}]}}

LessOrEqualThan()

static Entity AngouriMath.MathS.LessOrEqualThan ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the less than or equal node will be taken
b	Right argument node of which the less than or equal node function will be taken

Returns

A node

using System; using static AngouriMath.MathS;

var (x, y) = Var("x", "y");

Console.WriteLine(GreaterThan(x, y)); Console.WriteLine(GreaterThan(6, 5)); Console.WriteLine(GreaterThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessThan(x, y)); Console.WriteLine(LessThan(6, 5)); Console.WriteLine(LessThan(6, 5).EvalBoolean()); Console.WriteLine(LessThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(GreaterOrEqualThan(x, y)); Console.WriteLine(GreaterOrEqualThan(6, 5)); Console.WriteLine(GreaterOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessOrEqualThan(x, y)); Console.WriteLine(LessOrEqualThan(6, 5)); Console.WriteLine(LessOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(LessOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); var statement1 = GreaterThan(Sqr(x), 5); Console.WriteLine(statement1); Console.WriteLine(statement1.Solve("x")); Console.WriteLine("----------------------------------"); var statement2 = GreaterThan(Sqr(x), 16) & LessThan(x, y); Console.WriteLine(statement2); Console.WriteLine(statement2.Solve("x")); Console.WriteLine("----------------------------------"); var statement3 = LessThan(Sqr(x), 16) & GreaterThan(x, 2); Console.WriteLine(statement3); Console.WriteLine(statement3.Solve("x")); Prints x > y 6 > 5 True

False

x < y 6 < 5 False

False

x >= y 6 >= 5 True

True

x <= y 6 <= 5 False

True

x ^ 2 > 5

(-oo; -sqrt(20) / 2) \/ (sqrt(20) / 2; +oo)

x ^ 2 > 16 and x < y

((-oo; -4) \/ (4; +oo)) /\ (-oo; -y / (-1))

x ^ 2 < 16 and x > 2 (2; 4)

LessThan()

static Entity AngouriMath.MathS.LessThan ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the less than node will be taken
b	Right argument node of which the less than node function will be taken

Returns

A node

using System; using static AngouriMath.MathS;

var (x, y) = Var("x", "y");

Console.WriteLine(GreaterThan(x, y)); Console.WriteLine(GreaterThan(6, 5)); Console.WriteLine(GreaterThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessThan(x, y)); Console.WriteLine(LessThan(6, 5)); Console.WriteLine(LessThan(6, 5).EvalBoolean()); Console.WriteLine(LessThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(GreaterOrEqualThan(x, y)); Console.WriteLine(GreaterOrEqualThan(6, 5)); Console.WriteLine(GreaterOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(GreaterOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); Console.WriteLine(LessOrEqualThan(x, y)); Console.WriteLine(LessOrEqualThan(6, 5)); Console.WriteLine(LessOrEqualThan(6, 5).EvalBoolean()); Console.WriteLine(LessOrEqualThan(6, 6).EvalBoolean()); Console.WriteLine("----------------------------------"); var statement1 = GreaterThan(Sqr(x), 5); Console.WriteLine(statement1); Console.WriteLine(statement1.Solve("x")); Console.WriteLine("----------------------------------"); var statement2 = GreaterThan(Sqr(x), 16) & LessThan(x, y); Console.WriteLine(statement2); Console.WriteLine(statement2.Solve("x")); Console.WriteLine("----------------------------------"); var statement3 = LessThan(Sqr(x), 16) & GreaterThan(x, 2); Console.WriteLine(statement3); Console.WriteLine(statement3.Solve("x")); Prints x > y 6 > 5 True

False

x < y 6 < 5 False

False

x >= y 6 >= 5 True

True

x <= y 6 <= 5 False

True

x ^ 2 > 5

(-oo; -sqrt(20) / 2) \/ (sqrt(20) / 2; +oo)

x ^ 2 > 16 and x < y

((-oo; -4) \/ (4; +oo)) /\ (-oo; -y / (-1))

x ^ 2 < 16 and x > 2 (2; 4)

Limit()

static Entity AngouriMath.MathS.Limit ( Entity  expr, Entity  var, Entity  dest, ApproachFrom  approach = ApproachFrom.BothSides  )

static

Hangs your entity to a limit node (to evaluate instead use Compute.Limit(Entity, Variable, Entity))

Parameters

expr	Expression to be hung
var	Variable over which limit is taken
dest	Where var approaches (could be finite or infinite)
approach	From where it approaches

using System;
using static AngouriMath.MathS;

var (x, a) = Var("x", "a");

var e1 = Derivative(Sin(Cos(x)), x);
Console.WriteLine(e1);
Console.WriteLine(e1.InnerSimplified);
Console.WriteLine("-----------------------");
var e2 = Derivative(Sin(Cos(x)), x, 2);
Console.WriteLine(e2);
Console.WriteLine(e2.InnerSimplified);
Console.WriteLine("-----------------------");
var e3 = Integral(Sin(a * x), x);
Console.WriteLine(e3);
Console.WriteLine(e3.InnerSimplified);
Console.WriteLine("-----------------------");
var e4 = Integral(Sin(a * x), x, 2);
Console.WriteLine(e4);
Console.WriteLine(e4.InnerSimplified);
Console.WriteLine("-----------------------");
var e5 = Limit(Sin(a * x) / x, x, 0);
Console.WriteLine(e5);
Console.WriteLine(e5.InnerSimplified);

Prints

derivative(sin(cos(x)), x)
<h2>cos(cos(x)) * -sin(x)
</h2>
derivative(sin(cos(x)), x, 2)
<h2>-sin(cos(x)) * -sin(x) * -sin(x) + cos(x) * (-1) * cos(cos(x))
</h2>
integral(sin(a * x), x)
<h2>-cos(a * x) / a
</h2>
integral(sin(a * x), x, 2)
<h2>-sin(a * x) / a / a
</h2>
limit(sin(a * x) / x, x, 0)
a

Ln()

static Entity AngouriMath.MathS.Ln ( Entity  a )

static

Is a special case of logarithm where the base equals e:

Parameters

a	Argument node of which natural logarithm will be taken

Returns

Logarithm node with base equal to e

using System;
using static AngouriMath.MathS;
Console.WriteLine(Log(2, 16));
Console.WriteLine(Log(2, 16).Evaled);
Console.WriteLine(Log(3, 81));
Console.WriteLine(Log(3, 81).Evaled);
Console.WriteLine(Log(10, 1000));
Console.WriteLine(Log(10, 1000).Evaled);
Console.WriteLine(Log(1000));
Console.WriteLine(Log(1000).Evaled);
Console.WriteLine(Ln(e.Pow(16)));
Console.WriteLine(Ln(e.Pow(16)).Evaled);

Prints

log(2, 16)
4
log(3, 81)
4
log(10, 1000)
3
log(10, 1000)
3
ln(e ^ 16)
16

Log() [1/2]

static Entity AngouriMath.MathS.Log ( Entity @  base, Entity  x  )

static

Parameters

base	Base node of logarithm
x	Argument node of logarithm

Returns

Logarithm node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Log(2, 16));
Console.WriteLine(Log(2, 16).Evaled);
Console.WriteLine(Log(3, 81));
Console.WriteLine(Log(3, 81).Evaled);
Console.WriteLine(Log(10, 1000));
Console.WriteLine(Log(10, 1000).Evaled);
Console.WriteLine(Log(1000));
Console.WriteLine(Log(1000).Evaled);
Console.WriteLine(Ln(e.Pow(16)));
Console.WriteLine(Ln(e.Pow(16)).Evaled);

Prints

log(2, 16)
4
log(3, 81)
4
log(10, 1000)
3
log(10, 1000)
3
ln(e ^ 16)
16

Log() [2/2]

static Entity AngouriMath.MathS.Log ( Entity  x )

static

This is 10-based logarithm.

Argument node of logarithm Logarithm node using System; using static AngouriMath.MathS; Console.WriteLine(Log(2, 16)); Console.WriteLine(Log(2, 16).Evaled); Console.WriteLine(Log(3, 81)); Console.WriteLine(Log(3, 81).Evaled); Console.WriteLine(Log(10, 1000)); Console.WriteLine(Log(10, 1000).Evaled); Console.WriteLine(Log(1000)); Console.WriteLine(Log(1000).Evaled); Console.WriteLine(Ln(e.Pow(16))); Console.WriteLine(Ln(e.Pow(16)).Evaled); Prints log(2, 16) 4 log(3, 81) 4 log(10, 1000) 3 log(10, 1000) 3 ln(e ^ 16) 16

Matrix() [1/2]

static Matrix AngouriMath.MathS.Matrix ( Entity  values[,] )

static

Creates an instance of Entity.Matrix.

Parameters

values

A two-dimensional array of values. The first dimension is the row count, the second one is for columns.

Returns

A two-dimensional Entity.Matrix which is a matrix

using System;
using AngouriMath;
using static AngouriMath.Entity;
using static AngouriMath.MathS;

var A = Matrix(new Entity[,]
    {
        { 1, 2, 3 },
        { 4, 5, 6 }
    }
);
Console.WriteLine(A.ToString(multilineFormat: true));

var B = Vector(1, 2, 3, 4);
Console.WriteLine(B.ToString(multilineFormat: true));

Matrix C = @"
[[1, 2],
 [3, 4],
 [5, 6]]
 ";
Console.WriteLine(C.ToString(multilineFormat: true));

Matrix D = "[1, 2, 3, 4]";
Console.WriteLine(D.ToString(multilineFormat: true));

Prints

Matrix[2 x 3]
1   2   3   
4   5   6   
Matrix[4 x 1]
1   
2   
3   
4   
Matrix[3 x 2]
1   2   
3   4   
5   6   
Matrix[4 x 1]
1   
2   
3   
4

Matrix() [2/2]

static Matrix AngouriMath.MathS.Matrix ( int  rowCount, int  colCount, Func< int, int, Entity >  map  )

static

Creates an instance of matrix, where each cell's index is mapped to a value with the help of the mapping function.

Parameters

rowCount	The number of rows (corresponds to the first index).
colCount	The number of columns (corresponds to the second index).
map	The first argument of the mapping function function is the index of row, the second one for the column index.

Indexing starts from 0.

Returns

A newly created matrix of the given size.

using System;
using AngouriMath.Extensions;
using static AngouriMath.MathS;

var expr = "sin(x) + cos(y)";
var vars = new[] { Var("x"), Var("y") };
var A = Matrix(2, 2, (i1, i2) => expr
    .Differentiate(vars[i1])
    .Differentiate(vars[i2])
    .Simplify());
Console.WriteLine(A.ToString(multilineFormat: true));

Console.WriteLine(ZeroMatrix(3));
Console.WriteLine(ZeroMatrix(3, 4));
Console.WriteLine(ZeroVector(3));

Prints

Matrix[2 x 2]
-sin(x)   0         
0         -cos(y)   
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
[0, 0, 0]

MatrixFromIEnum2x2()

static Matrix AngouriMath.MathS.MatrixFromIEnum2x2 ( IEnumerable< IEnumerable< Entity >>  elements )

inlinestatic

Creates a matrix from given elements

Parameters

elements

There should be at least one row. All rows must have the same number of columns

using System;
using AngouriMath;
using static AngouriMath.MathS;

Console.WriteLine(Scalar(56));
Console.WriteLine(MatrixFromIEnum2x2(new Entity[][]
    {
        new Entity[]{ 1, 2, 3 },
        new Entity[]{ 4, 5, 6 }
    }
));

Prints

[56]
[[1, 2, 3], [4, 5, 6]]

MatrixFromRows()

static Matrix AngouriMath.MathS.MatrixFromRows ( IEnumerable< Matrix >  vectors )

inlinestatic

Creates a matrix from given rows

Parameters

vectors

There should be at least one row. All rows must have the same number of columns

Negation()

static Entity AngouriMath.MathS.Negation ( Entity  a )

static

Boolean negation Wikipedia

Parameters

a	Argument node of which Negation function will be taken

Returns

The Not node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Negation("x"));
Console.WriteLine(Negation(Negation("x")));
Console.WriteLine(Negation(Negation("x")).Simplify());

Prints

not x
not not x
x

Parse()

static ParsingResult AngouriMath.MathS.Parse ( string  source )

static

Parses an expression silently, that is, without throwing an exception.

Instead, it returns a Failure in case of encountered errors during parsing.

Returns

Returns a type union of the successful result and failure, which is a type union of multiple reasons it may have failed.

Multiple ways to parse an expression.

Entity expr1 = "a + b";
var expr2 = FromString("a + b");
var expr3 = FromString("a + b", useCache: false);
var expr4 = (Entity)"a + b";
var expr5 = Parse("a + b").Switch(
    res => res,
    failure => failure.Reason.Switch<object>(
        unknown => throw new("Unknown reason"),
        missingOp => throw new("Missing operator"),
        internalError => throw new("Internal error") 
    )
);

Piecewise() [1/2]

static Entity AngouriMath.MathS.Piecewise ( IEnumerable< Providedf >  cases, Entity?  otherwise = null  )

static

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

Parameters

cases	Cases, each of type Provided.
otherwise	An otherwise case. Will be intepreted as otherwise.Provided(true). Optional.

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() [2/2]

static Entity AngouriMath.MathS.Piecewise ( params(Entity expression, Entity predicate) []  cases )

static

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

Parameters

cases

Tuples of two expressions: an expression and a predicate

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

Pow()

static Entity AngouriMath.MathS.Pow ( Entity @  base, Entity  power  )

static

Parameters

base	Base node of power
power	Argument node of power

Returns

Power node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Pow(2, 5));
Console.WriteLine(Pow(2, 5).Simplify());
Console.WriteLine(Pow(e, 2));
Console.WriteLine(Pow(e, 2).Simplify());
Console.WriteLine(Pow(e, 2).Evaled);
Console.WriteLine(Sqrt(Sqr("x")));
Console.WriteLine(Sqrt(Sqr("x")).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 3));
Console.WriteLine(Pow(Cbrt("a"), 3).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 6));
Console.WriteLine(Pow(Cbrt("a"), 6).Simplify());

Prints

2 ^ 5
32
e ^ 2
e ^ 2
7.389056098930650227230427460575007813180315570551847324087127822522573796079057763384312485079121792
sqrt(x ^ 2)
x
a ^ (1/3) ^ 3
a
a ^ (1/3) ^ 6
a ^ 2

Provided()

static Entity AngouriMath.MathS.Provided ( Entity  expression, Entity  condition  )

static

This will be turned into expression if the condition is true, into NaN if condition is false, and remain the same otherwise

Parameters

expression	The expression is extracted if the predicate is true
condition	Condition when the expression is defined

Returns

The Provided node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Provided("a = b", "pi = 4"));
Console.WriteLine(Provided("a = b", "pi = 4").Simplify());
Console.WriteLine();

var expr = Provided("1000", "a = b")
        .Substitute("a", 5)
        .Substitute("b", 130)
    ;
Console.WriteLine(expr);
Console.WriteLine(expr.Evaled);

Console.WriteLine();

var expr1 = Provided("1000", "a = b")
        .Substitute("a", 5)
        .Substitute("b", 5)
    ;
Console.WriteLine(expr1);
Console.WriteLine(expr1.Evaled);

Prints

a = b provided pi = 4
NaN

1000 provided 5 = 130
NaN

1000 provided 5 = 5
1000

Scalar()

static Matrix AngouriMath.MathS.Scalar ( Entity  value )

static

Creates a 1x1 matrix of a given value.

It will be simplified once InnerSimplified or Evaled are addressed

Returns

A 1x1 matrix, which is also a 1-long vector, or just a scalar.

using System;
using AngouriMath;
using static AngouriMath.MathS;

Console.WriteLine(Scalar(56));
Console.WriteLine(MatrixFromIEnum2x2(new Entity[][]
    {
        new Entity[]{ 1, 2, 3 },
        new Entity[]{ 4, 5, 6 }
    }
));

Prints

[56]
[[1, 2, 3], [4, 5, 6]]

Sec()

static Entity AngouriMath.MathS.Sec ( Entity  a )

static

Parameters

a	Argument node of secant

Returns

Secant node

using System;
using static AngouriMath.MathS;

var expr = Sec("x") / Cosec("x");
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());

Prints

sec(x) / csc(x)
tan(x)

SetSubtraction()

static Set AngouriMath.MathS.SetSubtraction ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the set subtraction node will be taken That is, the resulting set of set subtraction is necessarily superset of this set
b	Right argument node of which the set subtraction set node will be taken That is, there is no element in the resulting set that belong to this one

Returns

A node

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 &gt; x2 &gt; 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 }

Signum()

static Entity AngouriMath.MathS.Signum ( Entity  a )

static

https://en.wikipedia.org/wiki/Sign_function

Parameters

a	Argument node of which Signum function will be taken

Returns

Signum node

using System;
using static AngouriMath.MathS;
Console.WriteLine(Signum(-5));
Console.WriteLine(Signum(-5).Evaled);
Console.WriteLine(Signum(0));
Console.WriteLine(Signum(0).Evaled);
Console.WriteLine(Signum(5));
Console.WriteLine(Signum(5).Evaled);
Console.WriteLine(Signum(4 + 3 * i));
Console.WriteLine(Signum(4 + 3 * i).Evaled);

Prints

sgn(-5)
-1
sgn(0)
0
sgn(5)
1
sgn(4 + 3i)
4/5 + (3/5)i

Sin()

static Entity AngouriMath.MathS.Sin ( Entity  a )

static

Parameters

a	Argument node of sine

Returns

Sine node

using System;
using static AngouriMath.MathS;

var expr = Sin("x").Pow(2) + Cos("x").Pow(2);
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());

Prints

sin(x) ^ 2 + cos(x) ^ 2
1

SolveBooleanTable()

static Matrix AngouriMath.MathS.SolveBooleanTable ( Entity  expression, params Variable []  variables  )

static

Solves a boolean expression.

That is, finds all values for variables such that the expression turns into True when evaluated Uses a simple table of truth Use Entity.SolveBoolean(Variable) for smart solving

Entity expr = "(a xor b or c) implies (a or c)";
var sols = MathS.SolveBooleanTable(expr, "a", "b", "c");

if (sols is null)
    Console.WriteLine("No solution found");
else
{
    Console.WriteLine(sols.ToString(multilineFormat: true));
    Console.WriteLine();
    for (int i = 0; i < sols.RowCount; i++)
    {
        var a = (bool)sols[i, 0].EvalBoolean();
        var b = (bool)sols[i, 1].EvalBoolean();
        var c = (bool)sols[i, 2].EvalBoolean();
        Console.WriteLine($"Solution #{i}: {a}, {b}, {c}");
    }
}

SolveEquation()

static Set AngouriMath.MathS.SolveEquation ( Entity  equation, Variable  var  )

static

Solves one equation over one variable

Parameters

equation	An equation that is assumed to equal 0
var	Variable whose values we are looking for

Returns

A Set of possible values or intervals of values

Entity eq1 = "x^2 - 1";
Console.WriteLine(MathS.SolveEquation(eq1, "x"));

Entity eq2 = "sin(a u) - cos(a u)";
Console.WriteLine(MathS.SolveEquation(eq2, "u"));

Prints { 1, -1 } { ln(-sqrt(-2) / (-1 - i)) / i / a, ln(sqrt(-2) / (-1 - i)) / i / a }

Sqr()

static Entity AngouriMath.MathS.Sqr ( Entity  a )

static

Special case of

Parameters

a	Argument to be squared

Returns

Power node with 2 as the power

using System;
using static AngouriMath.MathS;
Console.WriteLine(Pow(2, 5));
Console.WriteLine(Pow(2, 5).Simplify());
Console.WriteLine(Pow(e, 2));
Console.WriteLine(Pow(e, 2).Simplify());
Console.WriteLine(Pow(e, 2).Evaled);
Console.WriteLine(Sqrt(Sqr("x")));
Console.WriteLine(Sqrt(Sqr("x")).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 3));
Console.WriteLine(Pow(Cbrt("a"), 3).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 6));
Console.WriteLine(Pow(Cbrt("a"), 6).Simplify());

Prints

2 ^ 5
32
e ^ 2
e ^ 2
7.389056098930650227230427460575007813180315570551847324087127822522573796079057763384312485079121792
sqrt(x ^ 2)
x
a ^ (1/3) ^ 3
a
a ^ (1/3) ^ 6
a ^ 2

Sqrt()

static Entity AngouriMath.MathS.Sqrt ( Entity  a )

static

Special case of

Parameters

a	The argument of which square root will be taken

Returns

Power node with (1/2) as the power

using System;
using static AngouriMath.MathS;
Console.WriteLine(Pow(2, 5));
Console.WriteLine(Pow(2, 5).Simplify());
Console.WriteLine(Pow(e, 2));
Console.WriteLine(Pow(e, 2).Simplify());
Console.WriteLine(Pow(e, 2).Evaled);
Console.WriteLine(Sqrt(Sqr("x")));
Console.WriteLine(Sqrt(Sqr("x")).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 3));
Console.WriteLine(Pow(Cbrt("a"), 3).Simplify());
Console.WriteLine(Pow(Cbrt("a"), 6));
Console.WriteLine(Pow(Cbrt("a"), 6).Simplify());

Prints

2 ^ 5
32
e ^ 2
e ^ 2
7.389056098930650227230427460575007813180315570551847324087127822522573796079057763384312485079121792
sqrt(x ^ 2)
x
a ^ (1/3) ^ 3
a
a ^ (1/3) ^ 6
a ^ 2

Tan()

static Entity AngouriMath.MathS.Tan ( Entity  a )

static

Parameters

a	Argument node of which tangent will be taken

Returns

Tangent node

using System;
using static AngouriMath.MathS;
var expr = Tan("x") * Cotan("x");
Console.WriteLine(expr);
Console.WriteLine(expr.Simplify());
var expr2 = Tan("x") * Cos("x");
Console.WriteLine(expr2.Simplify());

Prints

tan(x) * cotan(x)
1
sin(x)

ToBaseN()

static string AngouriMath.MathS.ToBaseN ( Real  num, int  N  )

static

Translates a Number in base 10 into base N

Parameters

num	A Real in base 10 to be translated into base N
N	The base to translate the number into

Returns

A string with the number in the required base

using System;
using static AngouriMath.MathS;

using var _ = Settings.DowncastingEnabled.Set(false);

Console.WriteLine(ToBaseN(1.5m, 2));
Console.WriteLine(ToBaseN(3.75m, 2));
Console.WriteLine(ToBaseN(13.125m, 2));
Console.WriteLine(ToBaseN(13.125m, 10));

// uncomment when https://github.com/asc-community/AngouriMath/issues/584
// is fixed
// Console.WriteLine(ToBaseN(13.125m, 5));

Console.WriteLine(ToBaseN(13.125m, 8));
Console.WriteLine("-----------------------");
Console.WriteLine(FromBaseN("FF", 16));
Console.WriteLine(FromBaseN("77", 8));
Console.WriteLine(FromBaseN("1.1", 2));
Console.WriteLine(FromBaseN("1.01", 2));
Console.WriteLine(FromBaseN("1.05", 6));        

Prints

1.1
11.11
1101.001
13.125
<h2>15.1
</h2>
255
63
1.500000000
1.250000000
1.138888888

ToSympyCode()

static string AngouriMath.MathS.ToSympyCode ( Entity  expr )

inlinestatic

Returns

sympy interpretable format

Parameters

expr	An Entity representing an expression

using System; using static AngouriMath.MathS;

var (x, y, a) = Var("x", "y", "a"); var expr = Limit(Integral(Sin(x) / (Cos(x) + Tan(y)), x) / a, y, +oo); Console.WriteLine(expr); Console.WriteLine("----------------------------"); Console.WriteLine(ToSympyCode(expr)); Prints

limit(integral(sin(x) / (cos(x) + tan(y)), x) / a, y, +oo)

import sympy

x = sympy.Symbol('x') y = sympy.Symbol('y') a = sympy.Symbol('a')

expr = sympy.limit(sympy.integrate(sympy.sin(x) / (sympy.cos(x) + sympy.tan(y)), x, 1) / a, y, +oo)

TryPolynomial()

static bool AngouriMath.MathS.TryPolynomial ( Entity  expr, Variable  variable, [NotNullWhen(true)] out Entity?  dst  )

static

Returns an Entity in polynomial order if possible

Parameters

expr	The unordered Entity
variable	The variable of the polynomial
dst	The ordered result

Returns

if success, otherwise (dst will be )

using System;
using AngouriMath;
using static AngouriMath.MathS;

Entity expr = "a x + b (x + 3) + (x + 2) * (x + 3)";
if (TryPolynomial(expr, "x", out var res))
    Console.WriteLine(res);
else
    Console.WriteLine("Cannot get polynomial :((");

Entity expr2 = "sin(x) + cos(x)";
if (TryPolynomial(expr2, "x", out var res2))
    Console.WriteLine(res2);
else
    Console.WriteLine("Cannot get polynomial :((");

Prints

x ^ 2 + (a + b + 3 + 2) * x + b * 3 + 6
Cannot get polynomial :((

Union()

static Set AngouriMath.MathS.Union ( Entity  a, Entity  b  )

static

Parameters

a	Left argument node of which the union set node will be taken
b	Right argument node of which the union set node will be taken

Returns

A node

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 &gt; x2 &gt; 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 }

Var()

static Variable AngouriMath.MathS.Var ( string  name )

static

Creates an instance of Variable.

Parameters

name	The name of the Variable which equality is based on.

Returns

Variable node

Here are multiple ways to create variables:

Entity.Variable x = "x";
var y = Var("y");
var (a, b) = Var("x", "y");
var (c, d, e) = Var("a", "b", "c");
var f = Var("f_1");
var alpha = Var("alpha");
var alphaPhi = Var("alpha_phi");
var alpha1 = Var("alpha_1");
var inGreek = Var("βγδεζη_кΨеВеТкΩ");
var inCyrillic = Var("Абаваола");

Underscore "_" allows indexing. Greek letter names (e. g. "alpha") will be latexised as Greek letter (but other than that, will appear as "alpha" in other places).

Vector()

static Matrix AngouriMath.MathS.Vector ( params Entity []  values )

static

Creates an instance of Entity.Matrix that has one column.

Parameters

values

The cells of the Entity.Matrix

Returns

A one-dimensional Entity.Matrix which is a vector

using System;
using AngouriMath;
using static AngouriMath.Entity;
using static AngouriMath.MathS;

var A = Matrix(new Entity[,]
    {
        { 1, 2, 3 },
        { 4, 5, 6 }
    }
);
Console.WriteLine(A.ToString(multilineFormat: true));

var B = Vector(1, 2, 3, 4);
Console.WriteLine(B.ToString(multilineFormat: true));

Matrix C = @"
[[1, 2],
 [3, 4],
 [5, 6]]
 ";
Console.WriteLine(C.ToString(multilineFormat: true));

Matrix D = "[1, 2, 3, 4]";
Console.WriteLine(D.ToString(multilineFormat: true));

Prints

Matrix[2 x 3]
1   2   3   
4   5   6   
Matrix[4 x 1]
1   
2   
3   
4   
Matrix[3 x 2]
1   2   
3   4   
5   6   
Matrix[4 x 1]
1   
2   
3   
4

ZeroMatrix() [1/2]

static Matrix AngouriMath.MathS.ZeroMatrix ( int  size )

static

Creates a zero square matrix

using System;
using AngouriMath.Extensions;
using static AngouriMath.MathS;

var expr = "sin(x) + cos(y)";
var vars = new[] { Var("x"), Var("y") };
var A = Matrix(2, 2, (i1, i2) => expr
    .Differentiate(vars[i1])
    .Differentiate(vars[i2])
    .Simplify());
Console.WriteLine(A.ToString(multilineFormat: true));

Console.WriteLine(ZeroMatrix(3));
Console.WriteLine(ZeroMatrix(3, 4));
Console.WriteLine(ZeroVector(3));

Prints

Matrix[2 x 2]
-sin(x)   0         
0         -cos(y)   
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
[0, 0, 0]

ZeroMatrix() [2/2]

static Matrix AngouriMath.MathS.ZeroMatrix ( int  rowCount, int  columnCount  )

static

Creates a zero square matrix

using System;
using AngouriMath.Extensions;
using static AngouriMath.MathS;

var expr = "sin(x) + cos(y)";
var vars = new[] { Var("x"), Var("y") };
var A = Matrix(2, 2, (i1, i2) => expr
    .Differentiate(vars[i1])
    .Differentiate(vars[i2])
    .Simplify());
Console.WriteLine(A.ToString(multilineFormat: true));

Console.WriteLine(ZeroMatrix(3));
Console.WriteLine(ZeroMatrix(3, 4));
Console.WriteLine(ZeroVector(3));

Prints

Matrix[2 x 2]
-sin(x)   0         
0         -cos(y)   
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
[0, 0, 0]

ZeroVector()

static Matrix AngouriMath.MathS.ZeroVector ( int  size )

static

Creates a zero vector

using System;
using AngouriMath.Extensions;
using static AngouriMath.MathS;

var expr = "sin(x) + cos(y)";
var vars = new[] { Var("x"), Var("y") };
var A = Matrix(2, 2, (i1, i2) => expr
    .Differentiate(vars[i1])
    .Differentiate(vars[i2])
    .Simplify());
Console.WriteLine(A.ToString(multilineFormat: true));

Console.WriteLine(ZeroMatrix(3));
Console.WriteLine(ZeroMatrix(3, 4));
Console.WriteLine(ZeroVector(3));

Prints

Matrix[2 x 2]
-sin(x)   0         
0         -cos(y)   
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
[0, 0, 0]

Member Data Documentation

e

readonly Variable AngouriMath.MathS.e = Variable.e

static

The e constant

There are multiple constants available. Examples:

var x = Var("x");
Console.WriteLine(e);
Console.WriteLine(e.Evaled);
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo));
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify());
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify() == e);
Console.WriteLine("-----------------------");
Console.WriteLine(pi);
Console.WriteLine(pi.Evaled);
Console.WriteLine(Sin(pi / 3).Simplify());
Console.WriteLine(Cos(pi / 3).Simplify());
Console.WriteLine("-----------------------");
Console.WriteLine(i);
Console.WriteLine(4 + 3 * i);
Console.WriteLine("-----------------------");
Console.WriteLine(e.Pow(i * pi));
Console.WriteLine(e.Pow(i * pi).Simplify());

Prints

e
2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427
limit((1 + 1 / x) ^ x, x, +oo)
e
<h2>True
</h2>
pi
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
sqrt(3) / 2
<h2>1/2
</h2>
i
<h2>4 + 3i
</h2>
e ^ (i * pi)
-1

i

readonly Complex AngouriMath.MathS.i = Complex.ImaginaryOne

static

The imaginary one

There are multiple constants available. Examples:

var x = Var("x");
Console.WriteLine(e);
Console.WriteLine(e.Evaled);
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo));
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify());
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify() == e);
Console.WriteLine("-----------------------");
Console.WriteLine(pi);
Console.WriteLine(pi.Evaled);
Console.WriteLine(Sin(pi / 3).Simplify());
Console.WriteLine(Cos(pi / 3).Simplify());
Console.WriteLine("-----------------------");
Console.WriteLine(i);
Console.WriteLine(4 + 3 * i);
Console.WriteLine("-----------------------");
Console.WriteLine(e.Pow(i * pi));
Console.WriteLine(e.Pow(i * pi).Simplify());

Prints

e
2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427
limit((1 + 1 / x) ^ x, x, +oo)
e
<h2>True
</h2>
pi
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
sqrt(3) / 2
<h2>1/2
</h2>
i
<h2>4 + 3i
</h2>
e ^ (i * pi)
-1

I_1

readonly Matrix AngouriMath.MathS.I_1 = IdentityMatrix(1)

static

The square identity matrix of size 1

using System;
using static AngouriMath.MathS;

Console.WriteLine(I_1.ToString(multilineFormat: true));
Console.WriteLine(I_2.ToString(multilineFormat: true));
Console.WriteLine(I_3.ToString(multilineFormat: true));
Console.WriteLine(I_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
1   
Matrix[2 x 2]
1   0   
0   1   
Matrix[3 x 3]
1   0   0   
0   1   0   
0   0   1   
Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1

I_2

readonly Matrix AngouriMath.MathS.I_2 = IdentityMatrix(2)

static

The square identity matrix of size 2

using System;
using static AngouriMath.MathS;

Console.WriteLine(I_1.ToString(multilineFormat: true));
Console.WriteLine(I_2.ToString(multilineFormat: true));
Console.WriteLine(I_3.ToString(multilineFormat: true));
Console.WriteLine(I_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
1   
Matrix[2 x 2]
1   0   
0   1   
Matrix[3 x 3]
1   0   0   
0   1   0   
0   0   1   
Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1

I_3

readonly Matrix AngouriMath.MathS.I_3 = IdentityMatrix(3)

static

The square identity matrix of size 3

using System;
using static AngouriMath.MathS;

Console.WriteLine(I_1.ToString(multilineFormat: true));
Console.WriteLine(I_2.ToString(multilineFormat: true));
Console.WriteLine(I_3.ToString(multilineFormat: true));
Console.WriteLine(I_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
1   
Matrix[2 x 2]
1   0   
0   1   
Matrix[3 x 3]
1   0   0   
0   1   0   
0   0   1   
Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1

I_4

readonly Matrix AngouriMath.MathS.I_4 = IdentityMatrix(4)

static

The square identity matrix of size 4

using System;
using static AngouriMath.MathS;

Console.WriteLine(I_1.ToString(multilineFormat: true));
Console.WriteLine(I_2.ToString(multilineFormat: true));
Console.WriteLine(I_3.ToString(multilineFormat: true));
Console.WriteLine(I_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
1   
Matrix[2 x 2]
1   0   
0   1   
Matrix[3 x 3]
1   0   0   
0   1   0   
0   0   1   
Matrix[4 x 4]
1   0   0   0   
0   1   0   0   
0   0   1   0   
0   0   0   1

NaN

readonly Entity AngouriMath.MathS.NaN = Real.NaN

static

NaN represents both "undefined" and "indeterminate".

Any operation on NaN returns NaN

Let's consider MathS.oo and MathS.NaN.

using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var expr1 = Sin(x) / y;
Console.WriteLine(expr1);
Console.WriteLine(expr1.Substitute(y, 0));
Console.WriteLine(expr1.Substitute(y, 0).Evaled);
Console.WriteLine(expr1.Substitute(y, 0).Evaled == NaN);
Console.WriteLine("--------------------------------");
var expr2 = 5 + NaN;
Console.WriteLine(expr2);
Console.WriteLine(expr2.Evaled);
Console.WriteLine("--------------------------------");
var expr3 = Sin(NaN) / Cos(x) + y;
Console.WriteLine(expr3);
Console.WriteLine(expr3.Evaled);
Console.WriteLine("--------------------------------");
var expr4 = 10 * +oo;
Console.WriteLine(expr4);
Console.WriteLine("--------------------------------");
var expr5 = -oo * +oo;
Console.WriteLine(expr5);
Console.WriteLine("--------------------------------");
var expr6 = -oo / +oo;
Console.WriteLine(expr6);
Console.WriteLine("--------------------------------");
var expr7 = 50 / -oo;
Console.WriteLine(expr7);

Prints

sin(x) / y
sin(x) / 0
NaN
<h2>True
</h2>
5 + NaN
<h2>NaN
</h2>
sin(NaN) / cos(x) + y
<h2>NaN
</h2>
<h2>+oo
</h2>
<h2>-oo
</h2>
<h2>NaN
</h2>
0

See Entity.IsFinite for determining if there are NaNs or infinities inside an expression.

O_1

readonly Matrix AngouriMath.MathS.O_1 = ZeroMatrix(1)

static

The square zero matrix of size 1

Console.WriteLine(O_1.ToString(multilineFormat: true));
Console.WriteLine(O_2.ToString(multilineFormat: true));
Console.WriteLine(O_3.ToString(multilineFormat: true));
Console.WriteLine(O_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
0   
Matrix[2 x 2]
0   0   
0   0   
Matrix[3 x 3]
0   0   0   
0   0   0   
0   0   0   
Matrix[4 x 4]
0   0   0   0   
0   0   0   0   
0   0   0   0   
0   0   0   0

O_2

readonly Matrix AngouriMath.MathS.O_2 = ZeroMatrix(2)

static

The square zero matrix of size 2

Console.WriteLine(O_1.ToString(multilineFormat: true));
Console.WriteLine(O_2.ToString(multilineFormat: true));
Console.WriteLine(O_3.ToString(multilineFormat: true));
Console.WriteLine(O_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
0   
Matrix[2 x 2]
0   0   
0   0   
Matrix[3 x 3]
0   0   0   
0   0   0   
0   0   0   
Matrix[4 x 4]
0   0   0   0   
0   0   0   0   
0   0   0   0   
0   0   0   0

O_3

readonly Matrix AngouriMath.MathS.O_3 = ZeroMatrix(3)

static

The square zero matrix of size 3

Console.WriteLine(O_1.ToString(multilineFormat: true));
Console.WriteLine(O_2.ToString(multilineFormat: true));
Console.WriteLine(O_3.ToString(multilineFormat: true));
Console.WriteLine(O_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
0   
Matrix[2 x 2]
0   0   
0   0   
Matrix[3 x 3]
0   0   0   
0   0   0   
0   0   0   
Matrix[4 x 4]
0   0   0   0   
0   0   0   0   
0   0   0   0   
0   0   0   0

O_4

readonly Matrix AngouriMath.MathS.O_4 = ZeroMatrix(4)

static

The square zero matrix of size 4

Console.WriteLine(O_1.ToString(multilineFormat: true));
Console.WriteLine(O_2.ToString(multilineFormat: true));
Console.WriteLine(O_3.ToString(multilineFormat: true));
Console.WriteLine(O_4.ToString(multilineFormat: true));

Prints

Matrix[1 x 1]
0   
Matrix[2 x 2]
0   0   
0   0   
Matrix[3 x 3]
0   0   0   
0   0   0   
0   0   0   
Matrix[4 x 4]
0   0   0   0   
0   0   0   0   
0   0   0   0   
0   0   0   0

oo

readonly Real AngouriMath.MathS.oo = (Real)(Entity)"+oo"

static

Infinity.

Recommended to use with a plus or minus trailing.

Let's consider MathS.oo and MathS.NaN.

using System;
using static AngouriMath.MathS;

var (x, y) = Var("x", "y");
var expr1 = Sin(x) / y;
Console.WriteLine(expr1);
Console.WriteLine(expr1.Substitute(y, 0));
Console.WriteLine(expr1.Substitute(y, 0).Evaled);
Console.WriteLine(expr1.Substitute(y, 0).Evaled == NaN);
Console.WriteLine("--------------------------------");
var expr2 = 5 + NaN;
Console.WriteLine(expr2);
Console.WriteLine(expr2.Evaled);
Console.WriteLine("--------------------------------");
var expr3 = Sin(NaN) / Cos(x) + y;
Console.WriteLine(expr3);
Console.WriteLine(expr3.Evaled);
Console.WriteLine("--------------------------------");
var expr4 = 10 * +oo;
Console.WriteLine(expr4);
Console.WriteLine("--------------------------------");
var expr5 = -oo * +oo;
Console.WriteLine(expr5);
Console.WriteLine("--------------------------------");
var expr6 = -oo / +oo;
Console.WriteLine(expr6);
Console.WriteLine("--------------------------------");
var expr7 = 50 / -oo;
Console.WriteLine(expr7);

Prints

sin(x) / y
sin(x) / 0
NaN
<h2>True
</h2>
5 + NaN
<h2>NaN
</h2>
sin(NaN) / cos(x) + y
<h2>NaN
</h2>
<h2>+oo
</h2>
<h2>-oo
</h2>
<h2>NaN
</h2>
0

See Entity.IsFinite for determining if there are NaNs or infinities inside an expression.

pi

readonly Variable AngouriMath.MathS.pi = Variable.pi

static

The pi constant

There are multiple constants available. Examples:

var x = Var("x");
Console.WriteLine(e);
Console.WriteLine(e.Evaled);
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo));
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify());
Console.WriteLine(Limit((1 + 1 / x).Pow(x), x, +oo).Simplify() == e);
Console.WriteLine("-----------------------");
Console.WriteLine(pi);
Console.WriteLine(pi.Evaled);
Console.WriteLine(Sin(pi / 3).Simplify());
Console.WriteLine(Cos(pi / 3).Simplify());
Console.WriteLine("-----------------------");
Console.WriteLine(i);
Console.WriteLine(4 + 3 * i);
Console.WriteLine("-----------------------");
Console.WriteLine(e.Pow(i * pi));
Console.WriteLine(e.Pow(i * pi).Simplify());

Prints

e
2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427
limit((1 + 1 / x) ^ x, x, +oo)
e
<h2>True
</h2>
pi
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
sqrt(3) / 2
<h2>1/2
</h2>
i
<h2>4 + 3i
</h2>
e ^ (i * pi)
-1

Variable

static AngouriMath.MathS.Variable

static

Creates two instances of Variable.

Creates three instances of Variable.

Returns

A tuple of 2 corresponding variable nodes

Here are multiple ways to create variables:

Entity.Variable x = "x";
var y = Var("y");
var (a, b) = Var("x", "y");
var (c, d, e) = Var("a", "b", "c");
var f = Var("f_1");
var alpha = Var("alpha");
var alphaPhi = Var("alpha_phi");
var alpha1 = Var("alpha_1");
var inGreek = Var("βγδεζη_кΨеВеТкΩ");
var inCyrillic = Var("Абаваола");

Underscore "_" allows indexing. Greek letter names (e. g. "alpha") will be latexised as Greek letter (but other than that, will appear as "alpha" in other places).

Returns

A tuple of 3 corresponding variable nodes

Here are multiple ways to create variables:

Entity.Variable x = "x";
var y = Var("y");
var (a, b) = Var("x", "y");
var (c, d, e) = Var("a", "b", "c");
var f = Var("f_1");
var alpha = Var("alpha");
var alphaPhi = Var("alpha_phi");
var alpha1 = Var("alpha_1");
var inGreek = Var("βγδεζη_кΨеВеТкΩ");
var inCyrillic = Var("Абаваола");

Underscore "_" allows indexing. Greek letter names (e. g. "alpha") will be latexised as Greek letter (but other than that, will appear as "alpha" in other places).

Returns

A tuple of 3 corresponding variable nodes

Here are multiple ways to create variables:

Entity.Variable x = "x";
var y = Var("y");
var (a, b) = Var("x", "y");
var (c, d, e) = Var("a", "b", "c");
var (c1, d1, e1, f1) = Var("c_1", "d_1", "e_1", "f_1");
var (c1, d1, e1, f1, g1) = Var("c_1", "d_1", "e_1", "f_1", "g_1");
var f = Var("f_1");
var alpha = Var("alpha");
var alphaPhi = Var("alpha_phi");
var alpha1 = Var("alpha_1");
var inGreek = Var("βγδεζη_кΨеВеТкΩ");
var inCyrillic = Var("Абаваола");

Underscore "_" allows indexing. Greek letter names (e. g. "alpha") will be latexised as Greek letter (but other than that, will appear as "alpha" in other places).

---

The documentation for this class was generated from the following files:

• Sources/AngouriMath/Convenience/Diagnostic/MathS.Diagnostic.cs
• Sources/AngouriMath/Convenience/MathS.cs