Reputation: 109
I am trying to define some basic mathematical concepts in java, but keep getting stuck with generics errors. Consider the example below. In this example, I try to define the zero mapping (f(x) = 0 for all x) as both a constant mapping (f(x) = c for all x), and a linear mapping (f(a*x + b*y) = a*f(x) + b*f(y)). The compiler doesn't let me do that because the statement 'the zero mapping is a vector' is ambiguous (in terms of java, but not mathematically).
Can you suggest a clean solution to this problem?
// A vector in a finite-dimensional vector space over the real numbers.
interface Vector<V extends Vector<?>>
{
int dimension();
V plus(V v);
V times(double c);
}
interface Mapping<U extends Vector<?>, V extends Vector<?>>
// Does not inherit from Vector because the set of all mappings is an
// infinite-dimensional vector space.
{
V map(U u);
}
// Linear mappings, on the other hand, from one finite-dimensional vector space
// to another, do form a finite-dimensional vector space.
interface LinearMapping<U extends Vector<?>, V extends Vector<?>>
extends Mapping<U, V>, Vector<LinearMapping<U, V>>
{
}
// All elements of U are mapped to getImage(). If V is finite-dimensional, then
// the set of constant mappings is also a finite-dimensional vector space.
interface ConstMapping<U extends Vector<?>, V extends Vector<?>>
extends Mapping<U, V>, Vector<ConstMapping<U, V>>
{
V getImage();
}
// A zero mapping is both constant and linear, but cannot be defined as such.
interface ZeroMapping<U extends Vector<?>, V extends Vector<?>>
extends LinearMapping<U, V>, ConstMapping<U, V>
// Error: The interface Vector cannot be implemented more than once with
// different arguments: Vector<ConstMapping<U,V>> and Vector<LinearMapping<U,V>>
{
}
Upvotes: 4
Views: 255
Reputation: 1193
The issue seems to be that ZeroMapping is extending both Vector<LinearMapping>
and Vector<ConstMapping>
.
To fix that, we change the generic parameter V of LinearMapping
and ConstMapping
to the lower bounds of their individual classes, so that they can extend the generic Vector<V>
, allowing for more flexibility. Hopefully this captures your intention of making LinearMapping both a Mapping and a Vector (of itself, only).
EDIT: in that case, you may have to go with 3 generic parameters: 2 to capture the "Mapping" and 1 to capture the "Vector" relation with other LinearMappings of the same type.
ZeroMapping then follows the same format.
I've included @LuiggiMendoza 's suggestion in the response below.
interface Vector<V extends Vector<V>>
{
int dimension();
V plus(V v);
V times(double c);
}
interface Mapping<U extends Vector<U>, V extends Vector<V>>
// Does not inherit from Vector because the set of all mappings is an
// infinite-dimensional vector space.
{
V map(U u);
}
// Linear mappings, on the other hand, from one finite-dimensional vector space
// to another, do form a finite-dimenszional vector space.
interface LinearMapping<U extends Vector<U>, V extends Vector<V>, W extends LinearMapping<U, V, W>>
extends Mapping<U, V>, Vector<W>
{
}
// All elements of U are mapped to getImage(). If V is finite-dimensional, then
// the set of constant mappings is also a finite-dimensional vector space.
interface ConstMapping<U extends Vector<U>, V extends Vector<V>, W extends ConstMapping<U, V, W>>
extends Mapping<U, V>, Vector<W>
{
V getImage();
}
// A zero mapping is both constant and linear, but cannot be defined as such.
interface ZeroMapping<U extends Vector<U>, V extends Vector<V>, W extends ZeroMapping<U, V, W>>
extends LinearMapping<U, V, W>, ConstMapping<U, V, W>
{
}
An example of how the class would be implemented could be:
class RealVector implements Vector<RealVector> { // methods here .. // }
class RealLinearMapping implements LinearMapping<RealVector, RealVector, RealLinearMapping>
{
@Override
public RealVector map(RealVector u) { ... }
@Override
public RealLinearMapping plus(RealLinearMapping v) { ... }
}
Upvotes: 3