Cos.java :  » Algebra » symja » org » matheclipse » core » reflection » system » Java Open Source

package org.matheclipse.core.reflection.system;

import static org.matheclipse.core.expression.F.*; 

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.ISymbol;
import org.matheclipse.parser.client.SyntaxError;

/**
 * Cosine function
 * 
 * See <a href="http://en.wikipedia.org/wiki/Trigonometric_functions">Trigonometric functions</a>
 */
public class Cos extends AbstractTrigArg1 implements INumeric {
//  final static String[] RULES = {
//   
//      "Cos[Pi/6]=3^(1/2)/2",
//      "Cos[Pi/4]=2^(1/2)/2",
//      "Cos[Pi/3]=1/2",
//      "Cos[Pi/2]=0",
//      "Cos[Pi]=-1",
//      "Cos[I]=Cosh[1]",
//      "Cos[5/12*Pi]=1/4*6^(1/2)*(1-1/3*3^(1/2))",
//      "Cos[1/5*Pi]=1/4*5^(1/2)+1/4",
//      "Cos[1/12*Pi]=1/4*6^(1/2)*(1+1/3*3^(1/2))",
//      "Cos[1/10*Pi]=1/4*2^(1/2)*(5+5^(1/2))^(1/2)",
//      "Cos[2/5*Pi]=1/4*5^(1/2)-1/4",
//      "Cos[3/10*Pi]=1/4*2^(1/2)*(5-5^(1/2))^(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[ArcCos[x_]]:=x",
//      "Cos[ArcSin[x_]]:=(1-x^2)^(1/2)",
//      "Cos[ArcTan[x_]]:=1/(1+x^2)^(1/2)",
//      "Cos[ACot[x_]]:=x /(1+x**2)**1/2",
//      "Cos[x_NumberQ]:= Cos[-x]  /; SignCmp[x]<0",
//      "Cos[x_NumberQ*y_]:= Cos[-x*y]  /; SignCmp[x]<0",
//      "Cos[x_NumberQ*Pi]:=If[x<1,-Cos[(1-x)*Pi],If[x<2,Cos[(2-x)*Pi],Cos[(x-2*Quotient[Trunc[x],2])*Pi]]] /; x>=1/2" };

  /**
   * <pre>
   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[x_NumberQ*y_]:=Cos[(-1)*x*y]/;SignCmp[x]<0,
  Cos[Pi*x_NumberQ]:=If[x<1,(-1)*Cos[(1-x)*Pi],If[x<2,Cos[(2-x)*Pi],Cos[(x-2*Quotient[Trunc[x],2])*Pi]]]/;x>=1/2,
  Cos[ArcCos[x_]]:=x,
  Cos[ArcSin[x_]]:=(1-x^2)^(1/2),
  Cos[x_NumberQ]:=Cos[(-1)*x]/;SignCmp[x]<0,
   </pre>
   */
  final static IAST RULES = List(
      Set(Cos(Times(fraction(1L,10L),Pi)),Times(Times(C1D4,Power(C2,C1D2)),Power(Plus(Power(C5,C1D2),C5),C1D2))),
      Set(Cos(C0),C1),
      Set(Cos(CI),Cosh(C1)),
      Set(Cos(Times(fraction(1L,12L),Pi)),Times(Times(C1D4,Plus(Times(C1D3,Power(C3,C1D2)),C1)),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(Times(CN1,Power(C2,C1D2)),C2),C1D2))),
      Set(Cos(Times(fraction(1L,8L),Pi)),Times(C1D2,Power(Plus(Power(C2,C1D2),C2),C1D2))),
      Set(Cos(Pi),CN1),
      Set(Cos(Times(fraction(5L,12L),Pi)),Times(Times(C1D4,Plus(Times(CN1D3,Power(C3,C1D2)),C1)),Power(integer(6L),C1D2))),
      Set(Cos(Times(fraction(3L,10L),Pi)),Times(Times(C1D4,Power(C2,C1D2)),Power(Plus(Times(CN1,Power(C5,C1D2)),C5),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(Times(C1D4,Power(C5,C1D2)),Times(CN1,C1D4))),
      Set(Cos(Times(fraction(1L,5L),Pi)),Plus(Times(C1D4,Power(C5,C1D2)),C1D4)),
      SetDelayed(Cos(ArcTan($p("x"))),Power(Plus(C1,Power($s("x"),C2)),CN1D2)),
      SetDelayed(Cos(Times($p("x",$s("NumberQ")),$p("y"))),Condition(Cos(Times(Times(CN1,$s("x")),$s("y"))),Less(SignCmp($s("x")),C0))),
      SetDelayed(Cos(Times(Pi,$p("x",$s("NumberQ")))),Condition(If(Less($s("x"),C1),Times(CN1,Cos(Times(Plus(Times(CN1,$s("x")),C1),Pi))),If(Less($s("x"),C2),Cos(Times(Plus(Times(CN1,$s("x")),C2),Pi)),Cos(Times(Plus(Times(integer(-2L),Quotient(Trunc($s("x")),C2)),$s("x")),Pi)))),GreaterEqual($s("x"),C1D2))),
      SetDelayed(Cos(ArcCos($p("x"))),$s("x")),
      SetDelayed(Cos(ArcSin($p("x"))),Power(Plus(Times(CN1,Power($s("x"),C2)),C1),C1D2)),
      SetDelayed(Cos($p("x",$s("NumberQ"))),Condition(Cos(Times(CN1,$s("x"))),Less(SignCmp($s("x")),C0)))
      );

  @Override
  public IAST getRuleAST() {
    return RULES;
  }

  public Cos() {
  }

  @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);
  }
}