**'org.jscience.mathematics.function.Function'**Java class

org.jscience.mathematics.function

## Class Function<X,Y>

- java.lang.Object
- org.jscience.mathematics.function.Function<X,Y>

- All Implemented Interfaces:
- Serializable, javolution.lang.Realtime

- Direct Known Subclasses:
- DiscreteFunction, Polynomial, RationalFunction

public abstract class Function<X,Y>extends Objectimplements Serializable, javolution.lang.Realtime

This abstract class represents a mapping between two sets such that there is a unique element in the second set assigned to each element in the first set.

Functions can be discrete or continuous and multivariate functions (functions with multiple variables) are also supported as illustrated below:

`// Defines local variables. Variable.Local<Rational> varX =`

**new**Variable.Local<Rational>("x"); Variable.Local<Rational> varY =**new**Variable.Local<Rational>("y"); // f(x, y) = x\xc2\xb2 + x\xc2\xb7y + 1; Polynomial<Rational> x = Polynomial.valueOf(Rational.ONE, varX); Polynomial<Rational> y = Polynomial.valueOf(Rational.ONE, varY); Polynomial<Rational> fx_y = x.pow(2).plus(x.times(y)).plus(Rational.ONE); System.out.println("f(x,y) = " + fx_y); // Evaluates f(1,0) System.out.println("f(1,0) = " + fx_y.evaluate(Rational.ONE, Rational.ZERO)); // Calculates df(x,y)/dx System.out.println("df(x,y)/dx = " + fx_y.differentiate(varX)); > f(x,y) = [1/1]x^2 + [1/1]xy + [1/1] > f(1,0) = 2/1 > df(x,y)/dx = [2/1]x + [1/1]yFunctions are often given by formula (e.g.

`f(x) = x\xc2\xb2-x+1, f(x,y)= x\xc2\xb7y`

) but the general function instance might tabulate the values, solve an equation, etc.

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