Class FunctionExpression<T extends Ring<T>>

java.lang.Object

org.episteme.core.mathematics.symbolic.FunctionExpression<T>

All Implemented Interfaces:

Expression<T>

public class FunctionExpression<T extends Ring<T>>
extends Object
implements Expression<T>

Represents a transcendental function as a symbolic expression.

Supports sin, cos, tan, exp, log, sqrt, and power functions. Differentiation is not yet fully implemented (requires division operation).

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	FunctionExpression.FunctionType	Enumeration of supported function types.

Method Summary

Modifier and Type	Method	Description
Expression<T>	add(Expression<T> other)	Adds this expression to another.
Expression<T>	compose(Variable<T> variable, Expression<T> substitution)	Composes this expression by substituting a variable with another expression.
static <T extends Ring<T>> FunctionExpression<T>	cos(Expression<T> arg)	Creates a cosine function expression.
Expression<T>	differentiate(Variable<T> variable)	Differentiates this expression with respect to the given variable.
Expression<T>	divide(Expression<T> other)	Divides this expression by another.
T	evaluate(Map<Variable<T>, T> assignments)	Evaluates this expression with the given variable assignments.
static <T extends Ring<T>> FunctionExpression<T>	exp(Expression<T> arg)	Creates an exponential function expression.
Expression<T>	getArgument()
Expression<T>	getExponent()
Ring<T>	getRing()	Returns the ring this expression belongs to.
FunctionExpression.FunctionType	getType()
Expression<T>	integrate(Variable<T> variable)	Integrates this expression with respect to the given variable.
static <T extends Ring<T>> FunctionExpression<T>	log(Expression<T> arg)	Creates a natural logarithm function expression.
Expression<T>	multiply(Expression<T> other)	Multiplies this expression by another.
Expression<T>	negate()	Negates this expression.
static <T extends Ring<T>> FunctionExpression<T>	pow(Expression<T> base, Expression<T> exp)	Creates a power function expression.
Expression<T>	simplify()	Simplifies this expression using algebraic rules.
static <T extends Ring<T>> FunctionExpression<T>	sin(Expression<T> arg)	Creates a sine function expression.
static <T extends Ring<T>> FunctionExpression<T>	sqrt(Expression<T> arg)	Creates a square root function expression.
Expression<T>	subtract(Expression<T> other)	Subtracts another expression from this.
static <T extends Ring<T>> FunctionExpression<T>	tan(Expression<T> arg)	Creates a tangent function expression.
String	toLatex()	Converts this expression to LaTeX format.
String	toString()

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface Expression

pow

Method Details

sin

public static <T extends Ring<T>>
FunctionExpression<T> sin(Expression<T> arg)

Creates a sine function expression.

cos

public static <T extends Ring<T>>
FunctionExpression<T> cos(Expression<T> arg)

Creates a cosine function expression.

tan

public static <T extends Ring<T>>
FunctionExpression<T> tan(Expression<T> arg)

Creates a tangent function expression.

exp

public static <T extends Ring<T>>
FunctionExpression<T> exp(Expression<T> arg)

Creates an exponential function expression.

log

public static <T extends Ring<T>>
FunctionExpression<T> log(Expression<T> arg)

Creates a natural logarithm function expression.

sqrt

public static <T extends Ring<T>>
FunctionExpression<T> sqrt(Expression<T> arg)

Creates a square root function expression.

pow

public static <T extends Ring<T>>
FunctionExpression<T> pow(Expression<T> base,
 Expression<T> exp)

Creates a power function expression.

add

public Expression<T> add(Expression<T> other)

Description copied from interface: Expression

Adds this expression to another.

Specified by:

add in interface Expression<T extends Ring<T>>

Parameters:

other - the other expression

Returns:

the sum expression

multiply

public Expression<T> multiply(Expression<T> other)

Description copied from interface: Expression

Multiplies this expression by another.

Specified by:

multiply in interface Expression<T extends Ring<T>>

Parameters:

other - the other expression

Returns:

the product expression

subtract

public Expression<T> subtract(Expression<T> other)

Description copied from interface: Expression

Subtracts another expression from this.

Specified by:

subtract in interface Expression<T extends Ring<T>>

Parameters:

other - the subtrahend

Returns:

the difference expression

negate

public Expression<T> negate()

Description copied from interface: Expression

Negates this expression.

Specified by:

negate in interface Expression<T extends Ring<T>>

Returns:

the negated expression

divide

public Expression<T> divide(Expression<T> other)

Description copied from interface: Expression

Divides this expression by another.

Specified by:

divide in interface Expression<T extends Ring<T>>

Parameters:

other - the divisor

Returns:

the quotient expression

getRing

public Ring<T> getRing()

Description copied from interface: Expression

Returns the ring this expression belongs to.

Specified by:

getRing in interface Expression<T extends Ring<T>>

Returns:

the ring

differentiate

public Expression<T> differentiate(Variable<T> variable)

Description copied from interface: Expression

Differentiates this expression with respect to the given variable.

Specified by:

differentiate in interface Expression<T extends Ring<T>>

Parameters:

variable - the variable to differentiate by

Returns:

the derivative expression

integrate

public Expression<T> integrate(Variable<T> variable)

Description copied from interface: Expression

Integrates this expression with respect to the given variable.

Specified by:

integrate in interface Expression<T extends Ring<T>>

Parameters:

variable - the variable to integrate by

Returns:

the integral expression

compose

public Expression<T> compose(Variable<T> variable,
 Expression<T> substitution)

Description copied from interface: Expression

Composes this expression by substituting a variable with another expression.

Specified by:

compose in interface Expression<T extends Ring<T>>

Parameters:

variable - the variable to substitute

substitution - the expression to substitute with

Returns:

the composed expression

simplify

public Expression<T> simplify()

Description copied from interface: Expression

Simplifies this expression using algebraic rules.

Specified by:

simplify in interface Expression<T extends Ring<T>>

Returns:

the simplified expression

toLatex

public String toLatex()

Description copied from interface: Expression

Converts this expression to LaTeX format.

Specified by:

toLatex in interface Expression<T extends Ring<T>>

Returns:

the LaTeX string

evaluate

public T evaluate(Map<Variable<T>, T> assignments)

Description copied from interface: Expression

Evaluates this expression with the given variable assignments.

Specified by:

evaluate in interface Expression<T extends Ring<T>>

Parameters:

assignments - the variable assignments

Returns:

the evaluated value

toString

public String toString()

Overrides:

toString in class Object

getType

public FunctionExpression.FunctionType getType()

getArgument

public Expression<T> getArgument()

getExponent

public Expression<T> getExponent()