JSci.maths.categories.FinSet Maven / Gradle / Ivy
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JSci is a set of open source Java packages. The aim is to encapsulate scientific methods/principles in the most natural way possible. As such they should greatly aid the development of scientific based software.
It offers: abstract math interfaces, linear algebra (support for various matrix and vector types), statistics (including probability distributions), wavelets, newtonian mechanics, chart/graph components (AWT and Swing), MathML DOM implementation, ...
Note: some packages, like javax.comm, for the astro and instruments package aren't listed as dependencies (not available).
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package JSci.maths.categories;
import JSci.maths.*;
/**
* The FinSet class encapsulates the category FinSet.
* @version 1.0
* @author Mark Hale
*/
public class FinSet extends Object implements Category {
/**
* Constructs a FinSet category.
*/
public FinSet() {}
/**
* Returns the identity morphism for an object.
*/
public Category.Morphism identity(Object a) {
return new IdentityFunction((MathSet)a);
}
/**
* Returns the cardinality of an object.
*/
public Object cardinality(Object a) {
return new MathInteger(((MathSet)a).cardinality());
}
/**
* Returns a hom-set.
*/
public Category.HomSet hom(Object a,Object b) {
return new FunctionSet((MathSet)a,(MathSet)b);
}
public class FunctionSet implements MathSet, Category.HomSet {
private final MathSet from,to;
private final int size;
public FunctionSet(MathSet a,MathSet b) {
from=a;
to=b;
size=ExtraMath.pow(b.cardinality(),a.cardinality());
}
/**
* Returns an element of this hom-set.
*/
public Function getElement(Object in[],Object out[]) {
return new Function(from,to,in,out);
}
public int cardinality() {
return size;
}
public MathSet union(MathSet set) {
return set.union(this);
}
public MathSet intersect(MathSet set) {
return set.intersect(this);
}
}
public class Function implements Category.Morphism {
private final MathSet from,to;
private final Object in[],out[];
public Function(MathSet a,MathSet b,Object inObjs[],Object outObjs[]) {
from=a;
to=b;
in=inObjs;
out=outObjs;
}
public Object domain() {
return from;
}
public Object codomain() {
return to;
}
public Object map(Object o) {
for(int i=0;i