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1 package JSci.maths.symbolic;
2
3 import JSci.maths.*;
4 import JSci.maths.fields.*;
5 import JSci.maths.groups.*;
6
7 import java.util.*;
8
9
12 public class Function extends Expression {
13
14 public static final String  SIN = "sin";
15 public static final String COS = "cos";
16 public static final String TAN = "tan";
17 public static final String ASIN = "asin";
18 public static final String ACOS = "acos";
19 public static final String ATAN = "atan";
20 public static final String SINH = "sinh";
21 public static final String COSH = "cosh";
22 public static final String TANH = "tanh";
23 public static final String ASINH = "asinh";
24 public static final String ACOSH = "acosh";
25 public static final String ATANH = "atanh";
26 public static final String EXP = "exp";
27 public static final String LOG = "log";
28 public static final String SQRT = "sqrt";
29
30 private final String type;
31 private final Expression arg;
32
33
37 public Function(String n,Expression a) {
38 type=n;
39 arg=a;
40 }
41
42 public String toString() { return type+"("+arg+")"; }
43
44 public int getPriority() {return 15;}
45
46 public Expression differentiate(Variable x) {
47 Expression d=null;
48 if (type.equals(SIN)) d=new Function(COS,arg);
49 if (type.equals(COS)) d=Expression.negative(new Function(SIN,arg));
50 if (type.equals(TAN)) d=Expression.power(new Function(COS,arg),-2);
51 if (type.equals(ASIN)) d=Expression.inverse(new Function(SQRT,Expression.sum( ((Ring)getSet()).one(), Expression.negative(Expression.power(arg,2)) )));
52 if (type.equals(ACOS)) d=Expression.inverse(new Function(SQRT,Expression.sum( ((Ring)getSet()).one(), Expression.negative(Expression.power(arg,2)) ) ));
53 if (type.equals(ATAN)) d=Expression.inverse(Expression.sum( ((Ring)getSet()).one(), Expression.power(arg,2) ));
54 if (type.equals(SINH)) d=new Function(COSH,arg);
55 if (type.equals(COSH)) d=new Function(SINH,arg);
56 if (type.equals(TANH)) d=Expression.power(new Function(COSH,arg),-2);
57 if (type.equals(ASINH)) d=Expression.inverse(new Function(SQRT,Expression.sum(((Ring)getSet()).one(),Expression.power(arg,2))));
58 if (type.equals(ACOSH)) d=Expression.inverse(new Function(SQRT,Expression.sum(((Ring)getSet()).one().negate(),Expression.power(arg,2))));
59 if (type.equals(ATANH)) d=Expression.inverse(new Function(SQRT,Expression.sum(((Ring)getSet()).one(),Expression.power(arg,2).negate())));
60 if (type.equals(EXP)) d=new Function(EXP,arg);
61 if (type.equals(LOG)) d=Expression.inverse(arg);
62 if (type.equals(SQRT)) d=Expression.inverse(Expression.product((Ring.Member)((Ring)getSet()).one().add(((Ring)getSet()).one()),new Function(SQRT,arg)));
63
64 if (d==null)
65 throw new IllegalArgumentException ("Unknown Function type in derivative()");
66 return Expression.product(d,arg.differentiate(x));
67 }
68
69 public boolean equals(Object o) {
70 if (!Function.class.isInstance(o)) return false;
71 Function f = (Function)o;
72 return (type.equals(f.type) && arg.equals(f.arg));
73 }
74
75 public Object getSet() { return arg.getSet(); }
76
77 public Expression evaluate() {
78 Expression sarg = arg.evaluate();
79
80 if (sarg instanceof Constant) {
81 if (((Constant)sarg).getValue() instanceof Complex) {
82 Complex a = (Complex)((Constant)sarg).getValue();
83 if (type.equals(SIN)) return new Constant(Complex.sin(a));
84 if (type.equals(COS)) return new Constant(Complex.cos(a));
85 if (type.equals(TAN)) return new Constant(Complex.tan(a));
86 if (type.equals(ASIN)) return new Constant(Complex.asin(a));
87 if (type.equals(ACOS)) return new Constant(Complex.acos(a));
88 if (type.equals(ATAN)) return new Constant(Complex.atan(a));
89 if (type.equals(SIN)) return new Constant(Complex.sinh(a));
90 if (type.equals(COS)) return new Constant(Complex.cosh(a));
91 if (type.equals(TAN)) return new Constant(Complex.tanh(a));
92 if (type.equals(ASIN)) return new Constant(Complex.asinh(a));
93 if (type.equals(ACOS)) return new Constant(Complex.acosh(a));
94 if (type.equals(ATAN)) return new Constant(Complex.atanh(a));
95 if (type.equals(EXP)) return new Constant(Complex.exp(a));
96 if (type.equals(LOG)) return new Constant(Complex.log(a));
97 if (type.equals(SQRT)) return new Constant(a.sqrt());
98 throw new IllegalArgumentException ("Unknown Function type in evaluate()");
99 }
100 if (((Constant)sarg).getValue() instanceof MathDouble) {
101 MathDouble a = (MathDouble)((Constant)sarg).getValue();
102 if (type.equals(SIN)) return new Constant(MathDouble.sin(a));
103 if (type.equals(COS)) return new Constant(MathDouble.cos(a));
104 if (type.equals(TAN)) return new Constant(MathDouble.tan(a));
105 if (type.equals(ASIN)) return new Constant(MathDouble.asin(a));
106 if (type.equals(ACOS)) return new Constant(MathDouble.acos(a));
107 if (type.equals(ATAN)) return new Constant(MathDouble.atan(a));
108 if (type.equals(SIN)) return new Constant(MathDouble.sinh(a));
109 if (type.equals(COS)) return new Constant(MathDouble.cosh(a));
110 if (type.equals(TAN)) return new Constant(MathDouble.tanh(a));
111 if (type.equals(ASIN)) return new Constant(MathDouble.asinh(a));
112 if (type.equals(ACOS)) return new Constant(MathDouble.acosh(a));
113 if (type.equals(ATAN)) return new Constant(MathDouble.atanh(a));
114 if (type.equals(EXP)) return new Constant(MathDouble.exp(a));
115 if (type.equals(LOG)) return new Constant(MathDouble.log(a));
116 if (type.equals(SQRT)) return new Constant(new MathDouble(Math.sqrt(a.value())));
117 throw new IllegalArgumentException ("Unknown Function type in evaluate()");
118 }
119 throw new IllegalArgumentException ("Function argument is "+sarg.getSet()+" ; must be Complex or MathDouble");
120 }
121
122 if (sarg instanceof Function) {
123 Function f = (Function)sarg;
124 if (type.equals(SIN) && f.type.equals(ASIN)) return f.arg;
125 if (type.equals(COS) && f.type.equals(ACOS)) return f.arg;
126 if (type.equals(TAN) && f.type.equals(ATAN)) return f.arg;
127 if (type.equals(ASIN) && f.type.equals(SIN)) return f.arg;
128 if (type.equals(ACOS) && f.type.equals(COS)) return f.arg;
129 if (type.equals(ATAN) && f.type.equals(TAN)) return f.arg;
130 if (type.equals(SINH) && f.type.equals(ASINH)) return f.arg;
131 if (type.equals(COSH) && f.type.equals(ACOSH)) return f.arg;
132 if (type.equals(TANH) && f.type.equals(ATANH)) return f.arg;
133 if (type.equals(ASINH) && f.type.equals(SINH)) return f.arg;
134 if (type.equals(ACOSH) && f.type.equals(COSH)) return f.arg;
135 if (type.equals(ATANH) && f.type.equals(TANH)) return f.arg;
136 if (type.equals(EXP) && f.type.equals(LOG)) return f.arg;
137 if (type.equals(LOG) && f.type.equals(EXP)) return f.arg;
138 }
139
140 return new Function(type,sarg);
141
142 }
143
144 }
145
146
147
148 |
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