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# Class JSci.maths.groups.U1

    java.lang.Object
       |
       +----JSci.maths.groups.LieGroup
               |
               +----JSci.maths.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.

##

U1()
  Constructs a U(1) group.

##

compose(Complex, Complex)
  The group composition law.
getElement(double)
  Returns an element from within the group.
identityAsComplex()
  Returns the identity element.
inverse(Complex)
  Returns the inverse element.
isIdentity(Complex)
  Returns true if the element is the identity element of this group.
isInverse(Complex, Complex)
  Returns true if one element is the inverse of the other.
toString()
  Returns a string representing this group.

##

U1

     public U1()

  Constructs a U(1) group.

##

toString

     public String toString()

  Returns a string representing this group.

  Overrides:
    toString in class Object

getElement

     public Complex getElement(double param)

  Returns an element from within the group.

  Parameters:
    param - parameter to specify the group element

compose

     public Complex compose(Complex a,
                            Complex b)

  The group composition law.

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

identityAsComplex

     public Complex identityAsComplex()

  Returns the identity element.

inverse

     public Complex inverse(Complex a)

  Returns the inverse element.

isIdentity

     public boolean isIdentity(Complex a)

  Returns true if the element is the identity element of this group.

  Parameters:
    a - a group element

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

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