package org.matheclipse.core.reflection.system;
import static org.matheclipse.core.expression.F.$p;
import static org.matheclipse.core.expression.F.$s;
import static org.matheclipse.core.expression.F.ArcCos;
import static org.matheclipse.core.expression.F.ArcSin;
import static org.matheclipse.core.expression.F.ArcTan;
import static org.matheclipse.core.expression.F.C0;
import static org.matheclipse.core.expression.F.C1;
import static org.matheclipse.core.expression.F.C1D2;
import static org.matheclipse.core.expression.F.C1D3;
import static org.matheclipse.core.expression.F.C1D4;
import static org.matheclipse.core.expression.F.C2;
import static org.matheclipse.core.expression.F.C3;
import static org.matheclipse.core.expression.F.C5;
import static org.matheclipse.core.expression.F.CI;
import static org.matheclipse.core.expression.F.CN1;
import static org.matheclipse.core.expression.F.CN1D2;
import static org.matheclipse.core.expression.F.CN1D4;
import static org.matheclipse.core.expression.F.Condition;
import static org.matheclipse.core.expression.F.Cos;
import static org.matheclipse.core.expression.F.Cosh;
import static org.matheclipse.core.expression.F.GreaterEqual;
import static org.matheclipse.core.expression.F.If;
import static org.matheclipse.core.expression.F.IntegerPart;
import static org.matheclipse.core.expression.F.Less;
import static org.matheclipse.core.expression.F.List;
import static org.matheclipse.core.expression.F.Pi;
import static org.matheclipse.core.expression.F.Plus;
import static org.matheclipse.core.expression.F.Power;
import static org.matheclipse.core.expression.F.Quotient;
import static org.matheclipse.core.expression.F.Set;
import static org.matheclipse.core.expression.F.SetDelayed;
import static org.matheclipse.core.expression.F.Times;
import static org.matheclipse.core.expression.F.fraction;
import static org.matheclipse.core.expression.F.integer;
import static org.matheclipse.core.expression.F.x;
import org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator;
import org.matheclipse.core.eval.interfaces.AbstractTrigArg1;
import org.matheclipse.core.eval.interfaces.INumeric;
import org.matheclipse.core.expression.ComplexNum;
import org.matheclipse.core.expression.ComplexUtils;
import org.matheclipse.core.expression.F;
import org.matheclipse.core.expression.Num;
import org.matheclipse.core.interfaces.IAST;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.core.interfaces.IFraction;
import org.matheclipse.core.interfaces.IInteger;
import org.matheclipse.core.interfaces.ISymbol;
import org.matheclipse.parser.client.SyntaxError;
/**
* Cosine function
*
* See Trigonometric functions and Wikipedia - Exact trigonometric constants
*/
public class Cos extends AbstractTrigArg1 implements INumeric {
// {
// Cos[1/10*Pi]=1/4*2^(1/2)*(5+5^(1/2))^(1/2),
// Cos[1/12*Pi]=1/4*(1+1/3*3^(1/2))*6^(1/2),
// Cos[1/6*Pi]=1/2*3^(1/2),
// Cos[3/8*Pi]=1/2*(2-2^(1/2))^(1/2),
// Cos[1/8*Pi]=1/2*(2+2^(1/2))^(1/2),
// Cos[Pi]=-1,
// Cos[5/12*Pi]=1/4*(1-1/3*3^(1/2))*6^(1/2),
// Cos[3/10*Pi]=1/4*2^(1/2)*(5-5^(1/2))^(1/2),
// Cos[1/2*Pi]=0,
// Cos[1/3*Pi]=1/2,
// Cos[1/4*Pi]=1/2*2^(1/2),
// Cos[2/5*Pi]=-1/4+1/4*5^(1/2),
// Cos[1/5*Pi]=1/4+1/4*5^(1/2),
// Cos[0]=1,
// Cos[I]=Cosh[1],
// Cos[ArcTan[x_]]:=(1+x^2)^(-1/2),
// Cos[Pi*x_NumberQ]:=If[x<1,(-1)*Cos[(1-x)*Pi],If[x<2,Cos[(2-x)*Pi],Cos[(x-2*Quotient[IntegerPart[x],2])*Pi]]]/;x>=1/2,
// Cos[ArcCos[x_]]:=x,
// Cos[ArcSin[x_]]:=(1-x^2)^(1/2)
// }
final static IAST RULES = List(
Set(Cos(Times(fraction(1L, 10L), Pi)), Times(Times(C1D4, Power(C2, C1D2)), Power(Plus(C5, Power(C5, C1D2)), C1D2))),
Set(Cos(Times(fraction(1L, 12L), Pi)),
Times(Times(C1D4, Plus(C1, Times(C1D3, Power(C3, C1D2)))), Power(integer(6L), C1D2))),
Set(Cos(Times(fraction(1L, 6L), Pi)), Times(C1D2, Power(C3, C1D2))),
Set(Cos(Times(fraction(3L, 8L), Pi)), Times(C1D2, Power(Plus(C2, Times(CN1, Power(C2, C1D2))), C1D2))),
Set(Cos(Times(fraction(1L, 8L), Pi)), Times(C1D2, Power(Plus(C2, Power(C2, C1D2)), C1D2))),
Set(Cos(Pi), CN1),
Set(Cos(Times(fraction(5L, 12L), Pi)),
Times(Times(C1D4, Plus(C1, Times(CN1, Times(C1D3, Power(C3, C1D2))))), Power(integer(6L), C1D2))),
Set(Cos(Times(fraction(3L, 10L), Pi)),
Times(Times(C1D4, Power(C2, C1D2)), Power(Plus(C5, Times(CN1, Power(C5, C1D2))), C1D2))),
Set(Cos(Times(C1D2, Pi)), C0),
Set(Cos(Times(C1D3, Pi)), C1D2),
Set(Cos(Times(C1D4, Pi)), Times(C1D2, Power(C2, C1D2))),
Set(Cos(Times(fraction(2L, 5L), Pi)), Plus(CN1D4, Times(C1D4, Power(C5, C1D2)))),
Set(Cos(Times(fraction(1L, 5L), Pi)), Plus(C1D4, Times(C1D4, Power(C5, C1D2)))),
Set(Cos(C0), C1),
Set(Cos(CI), Cosh(C1)),
SetDelayed(Cos(ArcTan($p(x))), Power(Plus(C1, Power(x, C2)), CN1D2)),
SetDelayed(
Cos(Times(Pi, $p(x, $s("NumberQ")))),
Condition(
If(Less(x, C1),
Times(CN1, Cos(Times(Plus(C1, Times(CN1, x)), Pi))),
If(Less(x, C2), Cos(Times(Plus(C2, Times(CN1, x)), Pi)),
Cos(Times(Plus(x, Times(CN1, Times(C2, Quotient(IntegerPart(x), C2)))), Pi)))),
GreaterEqual(x, C1D2))), SetDelayed(Cos(ArcCos($p(x))), x),
SetDelayed(Cos(ArcSin($p(x))), Power(Plus(C1, Times(CN1, Power(x, C2))), C1D2)));
@Override
public IAST getRuleAST() {
return RULES;
}
public Cos() {
}
@Override
public IExpr evaluateArg1(final IExpr arg1) {
if (AbstractFunctionEvaluator.isNegativeExpression(arg1)) {
return Cos(Times(CN1, arg1));
}
IExpr imPart = AbstractFunctionEvaluator.getPureImaginaryPart(arg1);
if (imPart != null) {
return F.Cosh(imPart);
}
IExpr[] parts = AbstractFunctionEvaluator.getPeriodicParts(arg1);
if (parts != null) {
if (parts[1].isInteger()) {
// period 2*Pi
IInteger i = (IInteger) parts[1];
if (i.isEven()) {
return F.Cos(parts[0]);
} else {
return F.Times(F.CN1, F.Cos(parts[0]));
}
} else if (parts[1].isFraction()) {
// period 2*Pi
IFraction f = (IFraction) parts[1];
if (f.equals(F.C1D2)) {// TODO refine this
return F.Times(F.CN1, F.Sin(parts[0]));
}
}
}
return null;
}
@Override
public IExpr numericEvalD1(final Num arg1) {
return F.num(Math.cos(arg1.getRealPart()));
}
@Override
public IExpr numericEvalDC1(final ComplexNum arg1) {
return ComplexUtils.cos(arg1);
}
public double evalReal(final double[] stack, final int top, final int size) {
if (size != 1) {
throw new UnsupportedOperationException();
}
return Math.cos(stack[top]);
}
// public IExpr evalInteger(IInteger i) {
// if (i.equals(F.C0)) {
// return F.C1;
// }
// return null;
// }
// public void setUp(ISymbol symbol) throws SyntaxError {
// super.setUp(symbol);
// createRuleFromMethodName(symbol, "Cos[x_Integer]", "evalInteger");
// }
@Override
public void setUp(final ISymbol symbol) throws SyntaxError {
symbol.setAttributes(ISymbol.LISTABLE | ISymbol.NUMERICFUNCTION);
super.setUp(symbol);
}
}
Ads help maintain this website.