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1 package JSci.maths.categories;
2
3 import JSci.maths.*;
4
5
10 public class FinSet extends Object  implements Category {
11
14 public FinSet() {}
15
18 public Category.Morphism identity(Object a) {
19 return new IdentityFunction((MathSet)a);
20 }
21
24 public Object cardinality(Object a) {
25 return new MathInteger(((MathSet)a).cardinality());
26 }
27
30 public Category.HomSet hom(Object a,Object b) {
31 return new FunctionSet((MathSet)a,(MathSet)b);
32 }
33 public class FunctionSet implements MathSet, Category.HomSet {
34 private final MathSet from,to;
35 private final int size;
36 public FunctionSet(MathSet a,MathSet b) {
37 from=a;
38 to=b;
39 size=ExtraMath.pow(b.cardinality(),a.cardinality());
40 }
41
44 public Function getElement(Object in[],Object out[]) {
45 return new Function(from,to,in,out);
46 }
47 public int cardinality() {
48 return size;
49 }
50 public MathSet union(MathSet set) {
51 return set.union(this);
52 }
53 public MathSet intersect(MathSet set) {
54 return set.intersect(this);
55 }
56 }
57 public class Function implements Category.Morphism {
58 private final MathSet from,to;
59 private final Object in[],out[];
60 public Function(MathSet a,MathSet b,Object inObjs[],Object outObjs[]) {
61 from=a;
62 to=b;
63 in=inObjs;
64 out=outObjs;
65 }
66 public Object domain() {
67 return from;
68 }
69 public Object codomain() {
70 return to;
71 }
72 public Object map(Object o) {
73 for(int i=0;i<in.length;i++) {
74 if(o.equals(in[i]))
75 return out[i];
76 }
77 return null;
78 }
79 public Category.Morphism compose(Category.Morphism m) {
80 if(m instanceof Function) {
81 Function f=(Function)m;
82 if(to.equals(f.from)) {
83 Object outObjs[]=new Object [in.length];
84 for(int i=0;i<outObjs.length;i++)
85 outObjs[i]=f.map(out[i]);
86 return new Function(from,f.to,in,outObjs);
87 } else
88 throw new UndefinedCompositionException();
89 } else
90 throw new IllegalArgumentException ("Morphism is not a Function.");
91 }
92 }
93 private class IdentityFunction extends Function {
94 public IdentityFunction(MathSet s) {
95 super(s,s,null,null);
96 }
97 public Object map(Object o) {
98 return o;
99 }
100 public Category.Morphism compose(Category.Morphism m) {
101 if(m instanceof Function) {
102 return m;
103 } else
104 throw new IllegalArgumentException ("Morphism is not a Function.");
105 }
106 }
107 }
108
109 |
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