  MathS

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Description

Summary

Use functions from this class

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

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 (AngouriMath. Entity, AngouriMath. Entity, System. Int32)

Summary

Hangs your Entity to a derivative node

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

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

Field

Summary

• 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 (AngouriMath. Entity[])

Summary

Use it to solve equations

Parameter "equations"

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

Returns

An EquationSystem which can then be solved

• Equations (System. Collections. Generic. IEnumerable{AngouriMath. Entity})

Summary

Use it to solve equations

Parameter "equations"

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

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 base N into base 10

Parameter "num"

A Real in base N to be translated into base 10

Parameter "N"

The base to translate the number from

Returns

The Real in base 10

• 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

Field

Summary

• 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 (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 (AngouriMath. Entity, AngouriMath. Entity, System. Int32)

Summary

Hangs your entity to an integral node

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

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 (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"

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

• 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

Parameter "expr"

Expression to be hung

Parameter "var"

Variable over which limit is taken

Parameter "dest"

Where var 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

• 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,
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.

Field

Summary

• 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 into expression if the condition is true,
into NaN if condition 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

Parameter "a"

Argument to be squared

Returns

Power node with 2 as the power

• Sqrt (AngouriMath. Entity)

Method

Summary

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 base N

Parameter "num"

A Real in base 10 to be translated into base N

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 be null)

• 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 (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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