org.jscience.mathematics.algebraic.groups
Class U1

java.lang.Object
  extended by org.jscience.mathematics.algebraic.groups.LieGroup
      extended by org.jscience.mathematics.algebraic.groups.U1

public final class U1
extends LieGroup

The U1 class provides an encapsulation for U(1) groups. Unlike the parent LieGroup class, elements are not limited to being near the identity. The methods in this class assume a complex number representation for convenience. The LieGroup methods still provide a matrix representation.


Method Summary
 Complex getElement(double param)
          Returns an element from within the group.
static U1 getInstance()
          Constructs a U(1) group.
 boolean isIdentity(Complex a)
          Returns true if the element is the identity element of this group.
 boolean isInverse(Complex a, Complex b)
          Returns true if one element is the inverse of the other.
 java.lang.String toString()
          Returns a string representing this group.
 
Methods inherited from class org.jscience.mathematics.algebraic.groups.LieGroup
dimension, getElement, identity, isIdentity, isInverse
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Method Detail

getInstance

public static final U1 getInstance()
Constructs a U(1) group. Singleton.

Returns:
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toString

public java.lang.String toString()
Returns a string representing this group.

Overrides:
toString in class java.lang.Object
Returns:
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getElement

public Complex getElement(double param)
Returns an element from within the group.

Parameters:
param - parameter to specify the group element
Returns:
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isIdentity

public boolean isIdentity(Complex a)
Returns true if the element is the identity element of this group.

Parameters:
a - a group element
Returns:
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isInverse

public boolean isInverse(Complex a,
                         Complex b)
Returns true if one element is the inverse of the other.

Parameters:
a - a group element
b - a group element
Returns:
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