## AngouriMath

## MathS

## Description

**Summary**

## Members

### Abs (AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Absolute_value**Parameter "a"**Argument node of which Abs function will be taken**Returns**Abs node### Apply (AngouriMath. Entity, AngouriMath. Entity[])

Method**Summary**Applies the list of arguments to the given expression

### Arccos (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arccosine will be taken**Returns**Arccosine node### Arccosec (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arccosecant will be taken**Returns**Arcsine node with the reciprocal of the argument### Arccotan (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arccotangent will be taken**Returns**Arccotangent node### Arcsec (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arcsecant will be taken**Returns**Arccosine node with the reciprocal of the argument### Arcsin (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arcsine will be taken**Returns**Arcsine node### Arctan (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which arctangent will be taken**Returns**Arctangent node### Cbrt (AngouriMath. Entity)

Method**Summary**Special case of https://en.wikipedia.org/wiki/Power_function**Parameter "a"**The argument of which cube root will be taken**Returns**Power node with (1/3) as the power### Conjunction (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Logical_conjunction**Parameter "a"**Left argument node of which Conjunction function will be taken**Parameter "b"**Right argument node of which Conjunction disjunction function will be taken**Returns**And node### Cos (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of cosine**Returns**Cosine node### Cosec (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of cosecant**Returns**Cosine node### Cotan (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which cotangent will be taken**Returns**Cotangent node### Derivative

Method and its overloads### Derivative (AngouriMath. Entity, AngouriMath. Entity, System. Int32)

**Summary**Hangs your Entity to a derivative node

(to evaluate instead use Derivative(AngouriMath.Entity,AngouriMath.Entity.Variable))

**Parameter "expr"**Expression to be hung**Parameter "var"**Variable over which derivative is taken**Parameter "power"**Number of times derivative is taken. Only integers will be simplified or evaluated.### Derivative (AngouriMath. Entity, AngouriMath. Entity)

**Summary**Hangs your Entity to a derivative node

(to evaluate instead use Derivative(AngouriMath.Entity,AngouriMath.Entity.Variable))

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

### Det (AngouriMath. Entity. Matrix)

Method**Summary**Finds the determinant of the given matrix. If

the matrix is non-square, returns null

### Disjunction (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Logical_disjunction**Parameter "a"**The left argument node of which Disjunction function will be taken**Parameter "b"**The right argument node of which Disjunction function will be taken**Returns**Or node### e

Field**Summary**The e constant

https://en.wikipedia.org/wiki/E_(mathematical_constant)### Equality (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**Do NOT confuse it with Equation

**Parameter "a"**Left argument node of which Equality function will be taken**Parameter "b"**Right argument node of which Equality disjunction function will be taken**Returns**An Equals node### Equations

Method and its overloads### Equations (AngouriMath. Entity[])

**Summary**Use it to solve equations**Parameter "equations"****Returns**An EquationSystem which can then be solved### Equations (System. Collections. Generic. IEnumerable{AngouriMath. Entity})

**Summary**Use it to solve equations**Parameter "equations"****Returns**An EquationSystem which can then be solved

### ExclusiveDisjunction (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Exclusive_or**Parameter "a"**Left argument node of which Exclusive disjunction function will be taken**Parameter "b"**Right argument node of which Exclusive disjunction function will be taken**Returns**Xor node### Factorial (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which factorial will be taken**Returns**Factorial node### FromBaseN (System. String, System. Int32)

Method**Summary**Translates a number in baseN into base 10**Parameter "num"**A Real in baseN to be translated into base 10**Parameter "N"**The base to translate the number from**Returns**The Real in base 10### FromString

Method and its overloads### FromString (System. String, System. Boolean)

**Summary**Converts a String to an expression**Parameter "expr"**String expression, for example,`"2 * x + 3 + sqrt(x)"`

**Parameter "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### FromString (System. String)

**Summary**Converts a String to an expression**Parameter "expr"**String expression, for example,`"2 * x + 3 + sqrt(x)"`

**Returns**The parsed expression

### Gamma (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which gamma function will be taken**Returns**Factorial node with one added to the argument### GreaterOrEqualThan (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the greter than or equal node will be taken**Parameter "b"**Right argument node of which the greater than or equal node function will be taken**Returns**A node### GreaterThan (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the greater than node will be taken**Parameter "b"**Right argument node of which the greater than node function will be taken**Returns**A node### i

Field**Summary**The imaginary one

https://en.wikipedia.org/wiki/Imaginary_unit### I_1

Field**Summary**The square identity matrix of size 1

### I_2

Field**Summary**The square identity matrix of size 2

### I_3

Field**Summary**The square identity matrix of size 3

### I_4

Field**Summary**The square identity matrix of size 4

### IdentityMatrix

Method and its overloads### IdentityMatrix (System. Int32, System. Int32)

**Summary**Creates a rectangular identity matrix

with the given size

### IdentityMatrix (System. Int32)

**Summary**Creates a square identity matrix

### Implication (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)**Parameter "assumption"**The assumption node**Parameter "conclusion"**The conclusion node**Returns**Implies node### Integral

Method and its overloads### Integral (AngouriMath. Entity, AngouriMath. Entity, System. Int32)

**Summary**Hangs your entity to an integral node

(to evaluate instead use Integral(AngouriMath.Entity,AngouriMath.Entity.Variable))

**Parameter "expr"**Expression to be hung**Parameter "var"**Variable over which integral is taken**Parameter "power"**Number of times integral is taken. Only integers will be simplified or evaluated.### Integral (AngouriMath. Entity, AngouriMath. Entity)

**Summary**Hangs your entity to an integral node

(to evaluate instead use Integral(AngouriMath.Entity,AngouriMath.Entity.Variable))

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

### Intersection (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the intersection set node will be taken**Parameter "b"**Right argument node of which the intersection set node will be taken**Returns**A node### Interval

Method and its overloads### Interval (AngouriMath. Entity, AngouriMath. Entity)

**Summary**Creates a closed interval (segment)

### Interval (AngouriMath. Entity, System. Boolean, AngouriMath. Entity, System. Boolean)

**Summary**Creates an interval with custom endings

### Lambda (AngouriMath. Entity. Variable, AngouriMath. Entity)

Method**Summary**Returns a lambda with the given parameter and body

### Latex (AngouriMath. Core. ILatexiseable)

Method**Returns**The LaTeX representation of the argument

**Parameter "latexiseable"**### LessOrEqualThan (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the less than or equal node will be taken**Parameter "b"**Right argument node of which the less than or equal node function will be taken**Returns**A node### LessThan (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the less than node will be taken**Parameter "b"**Right argument node of which the less than node function will be taken**Returns**A node### Limit (AngouriMath. Entity, AngouriMath. Entity, AngouriMath. Entity, AngouriMath. Core. ApproachFrom)

Method**Summary**Hangs your entity to a limit node

(to evaluate instead use Limit(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity))

**Parameter "expr"**Expression to be hung**Parameter "var"**Variable over which limit is taken**Parameter "dest"**Wherevar approaches (could be finite or infinite)**Parameter "approach"**From where it approaches### Ln (AngouriMath. Entity)

Method**Summary**Is a special case of logarithm where the base equals

e:

https://en.wikipedia.org/wiki/Natural_logarithm**Parameter "a"**Argument node of which natural logarithm will be taken**Returns**Logarithm node with base equal to e### Log

Method and its overloads### Log (AngouriMath. Entity, AngouriMath. Entity)

**Summary****Parameter "base"**Base node of logarithm**Parameter "x"**Argument node of logarithm**Returns**Logarithm node### Log (AngouriMath. Entity)

**Summary****Parameter "x"**Argument node of logarithm**Returns**Logarithm node

### Matrix

Method and its overloads### Matrix (AngouriMath. Entity[0:, 0:])

**Summary**Creates an instance of Matrix.**Parameter "values"**A two-dimensional array of values.

The first dimension is the row count, the second one is for columns.

**Returns**A two-dimensional Matrix which is a matrix### Matrix (System. Int32, System. Int32, System. Func{System. Int32, System. Int32, AngouriMath. Entity})

**Summary**Creates an instance of matrix, where each cell's

index is mapped to a value with the help of the

mapping function.

**Parameter "rowCount"**The number of rows (corresponds to the first index).

**Parameter "colCount"**The number of columns (corresponds to the second index).

**Parameter "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.

### MatrixFromIEnum2x2 (System. Collections. Generic. IEnumerable{System. Collections. Generic. IEnumerable{AngouriMath. Entity}})

Method**Summary**Creates a matrix from given elements

**Parameter "elements"**There should be at least one row.

All rows must have the same number

of columns

### MatrixFromRows (System. Collections. Generic. IEnumerable{AngouriMath. Entity. Matrix})

Method**Summary**Creates a matrix from given rows

**Parameter "vectors"**There should be at least one row.

All rows must have the same number

of columns

### NaN

Field**Summary**That is both undefined and indeterminite

Any operation on NaN returns NaN

### Negation (AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Negation**Parameter "a"**Argument node of which Negation function will be taken**Returns**The Not node### O_1

Field**Summary**The square zero matrix of size 1

### O_2

Field**Summary**The square zero matrix of size 2

### O_3

Field**Summary**The square zero matrix of size 3

### O_4

Field**Summary**The square zero matrix of size 4

### Parse (System. String)

Method**Summary**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.

### pi

Field**Summary**The pi constant

https://en.wikipedia.org/wiki/Pi### Piecewise

Method and its overloads### Piecewise (System. Collections. Generic. IEnumerable{AngouriMath. Entity. Providedf}, AngouriMath. Entity)

**Summary**This is a piecewisely defined function, which turns into a particular definition

once there exists a case number N such that case[N].Predicate is turned into true and

for all i less than N : case[i].Predicate is turned into false.

For example, Piecewise(new Providedf(a, b), new Providedf(d, false), new Providedf(f, true))

will remain unchanged, because the first case is uncertain.

Piecewise(new Providedf(a, false), new Providedf(d, false), new Providedf(f, true))

will turn into f

Piecewise(new Providedf(a, false), new Providedf(d, false), new Providedf(f, false))

will turn into NaN

**Parameter "cases"**Cases, each of type Provided.

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

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

**Summary**This is a piecewisely defined function, which turns into a particular definition

once there exists a case number N such that case[N].Predicate is turned into true and

for all i less than N : case[i].Predicate is turned into false.

For example, Piecewise((a, b), (d, false), (f, true))

will remain unchanged, because the first case is uncertain.

Piecewise((a, false), (d, false), (f, true))

will turn into f

Piecewise((a, false), (d, false), (f, false))

will turn into NaN

**Parameter "cases"**Tuples of two expressions: an expression and a predicate

### Pow (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary****Parameter "base"**Base node of power**Parameter "power"**Argument node of power**Returns**Power node### Provided (AngouriMath. Entity, AngouriMath. Entity)

Method**Summary**This will be turned intoexpression if thecondition is true,

into NaN ifcondition is false, and remain the same otherwise

**Parameter "expression"**The expression is extracted if the predicate is true**Parameter "condition"**Condition when the expression is defined**Returns**The Provided node### Scalar (AngouriMath. Entity)

Method**Summary**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.

### Sec (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of secant**Returns**Cosine node### SetSubtraction (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "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

**Parameter "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### Signum (AngouriMath. Entity)

Method**Summary**https://en.wikipedia.org/wiki/Sign_function**Parameter "a"**Argument node of which Signum function will be taken**Returns**Signum node### Sin (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of sine**Returns**Sine node### SolveBooleanTable (AngouriMath. Entity, AngouriMath. Entity. Variable[])

Method**Summary**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 SolveBoolean(AngouriMath.Entity.Variable) for smart solving

### SolveEquation (AngouriMath. Entity, AngouriMath. Entity. Variable)

Method**Summary**Solves one equation over one variable**Parameter "equation"**An equation that is assumed to equal 0**Parameter "var"**Variable whose values we are looking for**Returns**A Set of possible values or intervals of values### Sqr (AngouriMath. Entity)

Method**Summary**Special case of https://en.wikipedia.org/wiki/Power_function**Parameter "a"**Argument to be squared**Returns**Power node with 2 as the power### Sqrt (AngouriMath. Entity)

Method**Summary**Special case of https://en.wikipedia.org/wiki/Power_function**Parameter "a"**The argument of which square root will be taken**Returns**Power node with (1/2) as the power### Tan (AngouriMath. Entity)

Method**Summary****Parameter "a"**Argument node of which tangent will be taken**Returns**Tangent node### ToBaseN (AngouriMath. Entity. Number. Real, System. Int32)

Method**Summary**Translates a Number in base 10 into baseN **Parameter "num"**A Real in base 10 to be translated into baseN **Parameter "N"**The base to translate the number into**Returns**A String with the number in the required base### ToSympyCode (AngouriMath. Entity)

Method**Returns**sympy interpretable format**Parameter "expr"**An Entity representing an expression### TryPolynomial (AngouriMath. Entity, AngouriMath. Entity. Variable, AngouriMath. Entity@)

Method**Summary**Returns an Entity in polynomial order if possible**Parameter "expr"**The unordered Entity**Parameter "variable"**The variable of the polynomial**Parameter "dst"**The ordered result**Returns**true if success,

false otherwise (dst will benull )

### Union (AngouriMath. Entity, AngouriMath. Entity)

Method**Parameter "a"**Left argument node of which the union set node will be taken**Parameter "b"**Right argument node of which the union set node will be taken**Returns**A node### Var (System. String)

Method**Summary**Creates an instance of Variable.**Parameter "name"**The name of the Variable which equality is based on.**Returns**Variable node### Vector (AngouriMath. Entity[])

Method**Summary**Creates an instance of Matrix that has one column.**Parameter "values"**The cells of the Matrix**Returns**A one-dimensional Matrix which is a vector### ZeroMatrix

Method and its overloads### ZeroMatrix (System. Int32, System. Int32)

**Summary**Creates a zero square matrix

### ZeroMatrix (System. Int32)

**Summary**Creates a zero square matrix

### ZeroVector (System. Int32)

Method**Summary**Creates a zero vector

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