Atan.java

package jscl.math.function.trigonometric;

import jscl.math.Generic;
import jscl.math.JsclInteger;
import jscl.math.NumericWrapper;
import jscl.math.Variable;
import jscl.math.function.*;

import javax.annotation.Nonnull;

public class Atan extends ArcTrigonometric {
    public Atan(Generic generic) {
        super("atan", new Generic[]{generic});
    }

    public Generic derivative(int n) {
        return new Inverse(
                JsclInteger.valueOf(1).add(parameters[0].pow(2))
        ).selfExpand();
    }

    public Generic selfExpand() {
        if (parameters[0].signum() < 0) {
            return new Atan(parameters[0].negate()).selfExpand().negate();
        } else if (parameters[0].signum() == 0) {
            return JsclInteger.valueOf(0);
        }
        return expressionValue();
    }

    public Generic selfElementary() {
        return Constants.Generic.I.multiply(
                new Ln(
                        new Root(
                                new Generic[]{
                                        JsclInteger.valueOf(-1).add(Constants.Generic.I.multiply(parameters[0])),
                                        JsclInteger.valueOf(0),
                                        JsclInteger.valueOf(1).add(Constants.Generic.I.multiply(parameters[0]))
                                },
                                0
                        ).selfElementary()
                ).selfElementary()
        );
    }

    public Generic selfNumeric() {
        return ((NumericWrapper) parameters[0]).atan();
    }

    @Nonnull
    public Variable newInstance() {
        return new Atan(null);
    }
}