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public abstract class Shuffle

(source file: Shuffle.java)

java.lang.Object
   |
   +----Printable
           |
           +----Shuffle

The pure class interface.

public abstract class Shuffle
  extends Printable

A shuffle is a morphism built from tensor, composition, identity, symmetry, terminal and diagonal. A shuffle can be represented as a function from integers (the size of the target) to integers (the size of the source). A partial shuffle can be represented by a partial function.

The operations on a partial shuffle are:

identity shuffle.
tensor of two shuffles.
composition of two shuffles.
terminal (an empty shuffle with empty target)
zero (an empty partial shuffle).
mediator of two shuffles (using the product structure of shuffles).
comediator of two partial shuffles (using the coproduct structure of partial shuffles).


Author:: Alan Jeffrey
Version: v1.0 1998/06/02

Shuffle()

source: The size of the source object.
target: The size of the target object.

comediate(Shuffle): The comediation of two partial shuffles.
comp(Shuffle): The composition of two (partial) shuffles.
identity(Obj): An identity shuffle.
initial(Obj): A initial shuffle.
mediate(Shuffle): The mediation of two (partial) shuffles.
morphism(): Build a morphism from a shuffle.
print(Printer): Print the shuffle (useful for debugging).
shuffle(int): The (partial) shuffle viewed as a (partial) function on integers.
tensor(Shuffle): The tensor fo two (partial) shuffles.
terminal(Obj): A terminal shuffle.
zero(Obj, Obj): An empty partial shuffle.

Shuffle

public Shuffle();

source

public Obj source;

The size of the source object.

target

public Obj target;

The size of the target object.

shuffle

public abstract int shuffle(int i);

The (partial) shuffle viewed as a (partial) function on integers.


Parameters:: i - the index ranging 1..target.size.
Returns:: the result ranging 1..source.size (0 if undefined).

identity

public static Shuffle identity(Obj X);

An identity shuffle.


Parameters:: X - the object.
Returns:: the identity morphism.

zero

public static Shuffle zero(Obj X,
                           Obj Y);

An empty partial shuffle.


Parameters:: X - the source object.; Y - the target object.
Returns:: the empty partial shuffle.

terminal

public static Shuffle terminal(Obj X);

A terminal shuffle.


Parameters:: X - the object.
Returns:: the terminal morphism.

initial

public static Shuffle initial(Obj X);

A initial shuffle.


Parameters:: X - the object.
Returns:: the initial morphism.

comediate

public Shuffle comediate(Shuffle f);

The comediation of two partial shuffles.


Parameters:: f - the other partial suffle.
Returns:: the comediation.

mediate

public Shuffle mediate(Shuffle f);

The mediation of two (partial) shuffles.


Parameters:: f - the other (partial) shuffle.
Returns:: the mediation.

comp

public Shuffle comp(Shuffle f);

The composition of two (partial) shuffles.


Parameters:: f - the other (partial) shuffle.
Returns:: the composition.

tensor

public Shuffle tensor(Shuffle f);

The tensor fo two (partial) shuffles.


Parameters:: f - the other (partial) shuffle.
Returns:: the tensor.

morphism

public Mor morphism();

Build a morphism from a shuffle.


Returns:: this shuffle as a morphism.

print

public void print(Printer p);

Print the shuffle (useful for debugging).

Parameters:

p - where to print to.

Overrides:

print in class Printable


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public abstract class Shuffle

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