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1 package JSci.maths.categories;
2
3 import JSci.maths.*;
4
5
10 public final class Simplicial extends Object  implements Category {
11 public final Bifunctor ADDITION=new Addition();
12
15 public Simplicial() {}
16
19 public Category.Morphism identity(Object a) {
20 Preorder p=(Preorder)a;
21 Integer id[]=new Integer [p.ordinal()];
22 for(int i=0;i<id.length;i++)
23 id[i]=new Integer (i);
24 return new IncreasingMap(p,id);
25 }
26
29 public Object cardinality(Object a) {
30 return new MathInteger(((Preorder)a).ordinal());
31 }
32
35 public Category.HomSet hom(Object a,Object b) {
36 return new FunctionSet((Preorder)a,(Preorder)b);
37 }
38 public Object terminal() {
39 return new Preorder(1);
40 }
41 public class FunctionSet implements Category.HomSet {
42 private final Preorder from,to;
43 public FunctionSet(Preorder a,Preorder b) {
44 from=a;
45 to=b;
46 }
47 public int cardinality() {
48 return (int)ExtraMath.binomial(from.ordinal()+to.ordinal()-1,from.ordinal());
49 }
50 }
51 public class IncreasingMap implements Functor {
52 protected final Preorder from,to;
53 protected final Integer out[];
54 public IncreasingMap(Preorder toObj,Integer toImg[]) {
55 from=new Preorder(toImg.length);
56 to=toObj;
57 out=toImg;
58 }
59 public Object domain() {
60 return from;
61 }
62 public Object codomain() {
63 return to;
64 }
65 public Object map(Object o) {
66 return out[((Integer )o).intValue()];
67 }
68 public Category.Morphism map(Category.Morphism m) {
69 return ((Preorder.RelationSet)to.hom(map(m.domain()),map(m.codomain()))).morphism;
70 }
71 public Category.Morphism compose(Category.Morphism m) {
72 return compose((Functor)m);
73 }
74 public Functor compose(Functor f) {
75 if(f instanceof IncreasingMap) {
76 IncreasingMap im=(IncreasingMap)f;
77 if(to.equals(im.from)) {
78 Integer outImg[]=new Integer [out.length];
79 for(int i=0;i<outImg.length;i++)
80 outImg[i]=(Integer )im.map(out[i]);
81 return new IncreasingMap(im.to,outImg);
82 } else
83 throw new UndefinedCompositionException();
84 } else
85 throw new IllegalArgumentException ("Morphism is not an IncreasingMap.");
86 }
87 }
88 public final class FaceMap extends IncreasingMap {
89 private final int skip;
90 public FaceMap(Preorder toObj,int i) {
91 super(toObj,new Integer [toObj.ordinal()-1]);
92 skip=i;
93 for(i=0;i<skip;i++)
94 out[i]=new Integer (i);
95 for(;i<out.length;i++)
96 out[i]=new Integer (i+1);
97 }
98 }
99 public final class DegeneracyMap extends IncreasingMap {
100 private final int repeat;
101 public DegeneracyMap(Preorder toObj,int i) {
102 super(toObj,new Integer [toObj.ordinal()+1]);
103 repeat=i;
104 for(i=0;i<=repeat;i++)
105 out[i]=new Integer (i);
106 for(;i<out.length;i++)
107 out[i]=new Integer (i-1);
108 }
109 }
110 public final class Addition implements Bifunctor {
111 public Addition() {}
112 public Object map(Object a,Object b) {
113 return new Preorder(((Preorder)a).ordinal()+((Preorder)b).ordinal());
114 }
115 public Category.Morphism map(Category.Morphism m, Category.Morphism n) {
116 IncreasingMap im=(IncreasingMap)m;
117 IncreasingMap in=(IncreasingMap)n;
118 Preorder to=new Preorder(im.to.ordinal()+in.to.ordinal());
119 Integer toObj[]=new Integer [im.out.length+in.out.length];
120 int i;
121 for(i=0;i<im.out.length;i++)
122 toObj[i]=im.out[i];
123 for(;i<toObj.length;i++)
124 toObj[i]=in.out[i];
125 return new IncreasingMap(to,toObj);
126 }
127 }
128 }
129
130 |
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