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Graph
interface to minimize the effort to implement this
interface.GenRecoupCoeff
in some format.wrapsize
characters.
YutsisGraph
by implementing the Graph
interface.node
to the end of this Path.
node
to the end of this Path (O(length)).
grf
.
p
to this path where appropriate.
(-1)^(factor*j)
to this
GRCompoundFactor.
(-1)^(factor*j)
to this
GRPreFactor.
(-1)^(factor*j[0]+...+factor*j[j.length-1])
to
this GRPreFactor.
(-1)^(j[0] + ...
- appendExp(String[]) -
Method in class GRPreFactor
- Appends a factor
(-1)^(j[0]+..+j[j.length-1])
to this
GRPreFactor.
- appendFactor(String) -
Method in class GRPreFactor
- Appends a factor
(2*a+1)
to this GRPreFactor.
- appendFactor(String[]) -
Method in class GRPreFactor
- Appends a factor
(2*a[0]+1)* ...
- appendFactor(String[], int) -
Method in class GRCompoundFactor
- Appends a factor
((2*a[0]+1)*...*(2*a[a.length-1]+1))^(exp/2)
to
this GRCompoundFactor.
- appendFactor(String[], int) -
Method in class GRPreFactor
- Appends a factor
((2*a[0]+1)* ...
- appendFactor(String[], int[]) -
Method in class GRPreFactor
- Appends a factor
(2*a[0]+1)^(exp[0]/2)* ...
- appendFactor(String, int) -
Method in class GRCompoundFactor
- Appends a factor
(2*a+1)^(exp/2)
to this
GRCompoundFactor.
- appendFactor(String, int) -
Method in class GRPreFactor
- Appends a factor
(2*a+1)^(exp/2)
to this GRPreFactor.
- args() -
Method in class GR6jSymbol
- Returns the arguments of the GR6jSymbol object.
- args() -
Method in class GRKrDelta
- Returns the arguments of the GRKrDelta object.
Cycle
to reduce and
fills the best edge to interchange out of the cycle (min length
4).
Cycle
to reduce and
fills the best edge to interchange out of the cycle (min length
4).
Cycle
to reduce and fills
the best edge to interchange out of the cycle (min length 4)
together with the best interchange nodes in a canonical way.
Cycle
to reduce and fills
the best edge to interchange out of the cycle (min length 4)
together with the best interchange nodes in a canonical way.
Cycle
to reduce and fills
the best edge to interchange out of the cycle (min length 4)
together with the best interchange nodes in a canonical way.
Cycle
to reduce and fills
the best edge to interchange out of the cycle (min length 4)
together with the best interchange nodes in a canonical way.
Yutsis.bubble()
.
(2*l1+1)^(-1)*delta(l1,l2)
to this
General Recoupling Coefficient as a consequence of the removal of
a bubble between the edges with labels l1, l2
in the
corresponding YutsisGraph.
p
as a new Path object.
i
and j
are connected,
false otherwise.
i
and j
are connected,
false otherwise.
node
is one of the nodes of this Edge.
label
,
false otherwise.
label
, false otherwise.
label
.
Path
s (for even
cycles) or two cyclic canonical shortest Path
s and an edge
(for odd cycles).ry
), a shortest path from r->z
(rz
) and the edge (y,z).
rp
), a shortest path from r->q (rq
)
and the edges (p,y
) and (q,y
).
l
as a ArrayList
of Cycle's.
i
and
j
.
label
going
from tail
to head
.
node
.
node
.
nodes[0]
and
nodes[1]
(max 3) as an array of edges.
node1
and
node2
(max 3) as a Vector or null if
one of the nodes is removed.
(e1,e2)
interchanging the edges
(e1,a)
and (e2,b)
, assuming that
the girth of y
is at least 4.
NodeIterator
over the nodes of this path
following the edges of this path starting at the first node (by
a call to the next() method).
NodeIterator
over the nodeset starting at the node
with lowest label as specified by the
Graph
interface.
root
, left intermediate angular momenta
a[0]...
- getOutputStream() -
Method in class JStreamedTextArea
- Returns the associated OutputStream of this JStreamedTextArea.
- getPrintStream() -
Method in class StreamPanel
- Returns a PrintStream which is connected with the JStreamedTextArea.
- getSaveDir() -
Method in class StreamPanel
- Returns the initial directory of the save to file dialog.
- girth() -
Method in class CycleGenerator
- Returns the girth of the Graph.
- girthCycles() -
Method in class CycleGenerator
- Returns all girth cycles as a ArrayList of Cycle's.
- gmlEdgeLabels(int) -
Method in class AbstractGraph
- Returns the edge labels of node i to be used for saving the Graph in
GML-format; this is a default implementation returning null,
indicating that no edge label is used.
- gmlEdgeLabels(int) -
Method in class YutsisGraph
- Returns the edge label to be used for saving the Graph in
GML-format; overloads AbstractGraph.gmlEdgeLabel.
- GR6jSymbol - class GR6jSymbol.
- Class representing a Wigner 6j-symbol {a,b,c;d,e,f}.
- GR6jSymbol(String[], String[]) -
Constructor for class GR6jSymbol
- Constructs a Wigner 6j-symbol with toprow
toprow[0],
toprow[1], toprow[2]
and bottomrow
bottomrow[0], bottomrow[1], bottomrow[2]
.
- Graph - interface Graph.
- Interface of a general graph of which the nodes are labeled with
positive integers in an arbitrary way.
- GRCompoundFactor - class GRCompoundFactor.
- Class represting a product of elementary GRFactor's.
- GRCompoundFactor() -
Constructor for class GRCompoundFactor
- Constructs a new (empty) product of GRFactor's.
- GRCompoundFactor(GRFactor) -
Constructor for class GRCompoundFactor
- Constructs a new product of GRFactor's with initial
GRFactor
f
.
- GRCompoundFactor(int) -
Constructor for class GRCompoundFactor
- Constructs a new (empty) product of GRFactor's with
nroffactors
expected number of factors.
- GRCompoundFactor(int, GRFactor) -
Constructor for class GRCompoundFactor
- Constructs a new product of GRFactor's with initial
GRFactor
f
and nroffactors
expected
number of factors.
- GRFactor - class GRFactor.
- Abstract class representing an elementary factor in the formula
of a General Recoupling Coefficient of angular momenta in terms of
6j-coefficients.
- GRFactor() -
Constructor for class GRFactor
-
- GRKrDelta - class GRKrDelta.
- Class representing a factor KrDelta(l1,l2) in a
General Recoupling Coefficient.
- GRKrDelta(String, String) -
Constructor for class GRKrDelta
- Constructs a new GRKrDelta ChDelta(l1,l2).
- GRPreFactor - class GRPreFactor.
- Class representing a factor
(-1)^exp*(2*f_0+1)^(exp_0/2)+...+(2*f_k+1)^(exp_k/2)
with exp
a lineair combination of labels with
positive, integer coefficients, f_0...f_k labels and exp_0..exp_k
integer powers. - GRPreFactor() -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor.
- GRPreFactor(int) -
Constructor for class GRPreFactor
- Constructs a GRPreFactor with
nroflabels
expected
total number of labels
- GRPreFactor(int, int, String) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(-1)^(factor*j)
with nroflabels
expected number of labels.
- GRPreFactor(int, int, String, String, int) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(-1)^(factor*j)*(2*a+1)^(exp/2)
with
nroflabels
expected number of labels.
- GRPreFactor(int, String) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(-1)^(factor*j)
.
- GRPreFactor(int, String[]) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(-1)^(j[0]+..+j[j.length-1])
with
nroflabels
expected number of labels..
- GRPreFactor(int, String[], int) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
((2*a[0]+1)* ...
- GRPreFactor(int, String[], int[]) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(2*a[0]+1)^exp[0]* ...
- GRPreFactor(int, String, int) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(2*a+1)^(exp/2)
with nroflabels
expected number of labels.
- GRPreFactor(String[]) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(-1)^(j[0]+..+j[j.length-1])
.
- GRPreFactor(String[], int) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
((2*a[0]+1)* ...
- GRPreFactor(String[], int[]) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(2*a[0]+1)^(exp[0]/2)* ...
- GRPreFactor(String, int) -
Constructor for class GRPreFactor
- Constructs a new GRPreFactor representing
(2*a+1)^(exp/2)
.
- GRSummation - class GRSummation.
- Class representing a summation factor
sum(summvar)
*
GRCompoundFactor
appearing in the expression for a
General Recoupling Coefficient for angular momenta. - GRSummation(String, String, String, String, String) -
Constructor for class GRSummation
- Constructs a new GRSummation object with summation variable
summvar
with couplings (a,b,summvar)
and (c,d,summvar)
.
- GRSummation(String, String, String, String, String, GRFactor) -
Constructor for class GRSummation
- Constructs a new GRSummation object with summation variable
summvar
and factor f
.
- GRSummation(String, String, String, String, String, int) -
Constructor for class GRSummation
- Constructs a new GRSummation object with summation variable
summvar
and nroffactors
expected
number of factors.
- GRSummation(String, String, String, String, String, int, GRFactor) -
Constructor for class GRSummation
- Constructs a new GRSummation object with summation variable
summvar
, initial factor f
and
nroffactors
expected number of factors.
- GRVisitor - interface GRVisitor.
- Interface following the Visitor pattern for visiting objects
of the GR-family.
- GRWrappedLaTeXVisitor - class GRWrappedLaTeXVisitor.
- A GRVisitor which constructs a wrapped String representation of an
object from the GR-family in LaTeX format, including
GenRecoupCoeff
. - GRWrappedLaTeXVisitor() -
Constructor for class GRWrappedLaTeXVisitor
- Constructs a new GRWrappedLaTeXVisitor.
- GRWrappedLaTeXVisitor(int) -
Constructor for class GRWrappedLaTeXVisitor
- Constructs a new GRWrappedLaTeXVisitor which wraps at
wrapsize
characters.
- GRWrappedLaTeXVisitor(int, FontMetrics) -
Constructor for class GRWrappedLaTeXVisitor
- Constructs a new GRWrappedLaTeXVisitor, with given wrapsize
in pixels and the FontMetrics class for the used font.
- GRWrappedMapleVisitor - class GRWrappedMapleVisitor.
- A GRVisitor which constructs a wrapped String representation of an
object from the GR-family in Maple format, including
GenRecoupCoeff.
- GRWrappedMapleVisitor() -
Constructor for class GRWrappedMapleVisitor
- Constructs a new GRWrappedMapleVisitor.
- GRWrappedMapleVisitor(int) -
Constructor for class GRWrappedMapleVisitor
- Constructs a new GRWrappedMapleVisitor which wraps at
wrapsize
characters.
- GRWrappedMapleVisitor(int, FontMetrics) -
Constructor for class GRWrappedMapleVisitor
- Constructs a new GRWrappedMapleVisitor, with given wrapsize
in pixels and the FontMetrics class for the used font.
- GRWrappedRacahVisitor - class GRWrappedRacahVisitor.
- A GRVisitor which constructs a wrapped String representation of an
object from the GR-family in Racah format, including
GenRecoupCoeff.
- GRWrappedRacahVisitor() -
Constructor for class GRWrappedRacahVisitor
- Constructs a new GRWrappedRacahVisitor.
- GRWrappedRacahVisitor(int) -
Constructor for class GRWrappedRacahVisitor
- Constructs a new GRRacahMapleVisitor which wraps at
wrapsize
characters.
- GRWrappedRacahVisitor(int, FontMetrics) -
Constructor for class GRWrappedRacahVisitor
- Constructs a new GRWrappedRacahVisitor, with given wrapsize
in pixels and the FontMetrics class for the used font.
- GRWrappedStringVisitor - class GRWrappedStringVisitor.
- A GRVisitor which constructs a wrapped String representation
of an object from the GR-family, including GenRecoupCoeff.
- GRWrappedStringVisitor() -
Constructor for class GRWrappedStringVisitor
- Constructs a new GRWrappedStringVisitor.
- GRWrappedStringVisitor(int) -
Constructor for class GRWrappedStringVisitor
- Constructs a new GRWrappedStringVisitor which wraps at
wrapsize
characters.
- GRWrappedStringVisitor(int, FontMetrics) -
Constructor for class GRWrappedStringVisitor
- Constructs a new GRWrappedStringVisitor, with given wrapsize
in pixels and the FontMetrics class for the used font.
- guessFileFormat(String) -
Static method in class AbstractYutsis
- Guesses the format of the file by looking at the first two lines.
- GYutsis - class GYutsis.
- This class implements a GUI illustrating the algorithm implemented
by
CycleCostAlgorithm
. - GYutsis() -
Constructor for class GYutsis
- Creates the GYutsis window.
- GYutsis(File) -
Constructor for class GYutsis
- Creates the GYutsis window with title
title
and
reads the graph from the File file
.
- GYutsis(YutsisGraph) -
Constructor for class GYutsis
- Creates the GYutsis window with the given YutsisGraph.
Yutsis.interchange(int
[], int[] )
method.
(nodes[0], nodes[1])
interchanging the edges (nodes[0], icnodes[0])
and (nodes[1].
- interchange(int, int, int, int) -
Method in class AbstractYutsis
- Interchange on the edge
(node1, node2)
interchanging
the edges (node1, icnode1)
and
(node2, icnode2)
.
- interchange(int, int, int, int) -
Method in interface Yutsis
- Interchange on the edge
(node1, node2)
interchanging
the edges (node1, icnode1)
and
(node2, icnode2)
.
- interchange(String, String, String, String, String, String) -
Method in class GenRecoupCoeff
- Appends the summation factor
sum(f)(2f+1){a, b, f; d, c,
e}
(Wigner 6j-symbol) to this Genereal Recoupling
Coefficient as a consequence of an interchange on the edge
with label e
interchanging the edges
b,c
which (respectively) neighboredges a, d
in the corresponding YutsisGraph.
- interchangeNodes(Cycle, int[]) -
Method in class AbstractCCAHeuristic
- This method returns the nodes to be interchanged from the
bestcycledge
in order to reduce the
bestcycle
one unit in length and makes it
canonical, without applying the interchange itself.
- interchangeNodes(Cycle, int[]) -
Method in interface CCAHeuristic
- This method returns the nodes to be interchanged from the
bestcycledge
in order to reduce the
bestcycle
one unit in length and makes it
canonical, without applying the interchange itself.
- intermediateLabelsPresent(String) -
Method in class AbstractYutsis
- Returns true if the intermediate labels APPEAR to be present,
false otherwise.
- intersection(Path) -
Method in class Path
- Returns the nodes common in both paths.
- invert() -
Method in class Edge
- Reverses the direction of this Edge.
- invertEdge(int, Edge) -
Method in class YutsisGraph
- Generates the phase factor (-1)^(2j), with j the label of the
edge with endpoint
node
and inverts the edge
afterwards.
- invertEdge(String) -
Method in class GenRecoupCoeff
- Appends a factor
(-1)^(2*j)
to this General
Recoupling Coefficient as a consequence of the invertion of
the Edge with label j
in the corresponding
YutsisGraph.
- invertNode(String[]) -
Method in class GenRecoupCoeff
- Appends a factor
(-1)^(j[0] + j[1] + j[2])
to this
General Recoupling Coefficient as a consequence of the invertion
of the node sign in wich j[0],j[1],j[2]
are coupled
in the corresponding YutsisGraph.
- invertSign(int) -
Method in class YutsisGraph
- Reverses the sign of
node
.
- isCanonical() -
Method in class Path
- True if this path is cylic canonical.
- isNewLabel(String) -
Method in class YutsisGraph
- True if this label did not appear in the original graph, if true
this label will yield a summation over its complete domain.
- isRemoved(int) -
Method in interface Graph
- Returns true if the specified node is removed or not apparent
in the graph, false otherwise.
- isRemoved(int) -
Method in class YutsisGraph
- Implementation of the
Graph.isRemoved(int)
method.
- isTree(int[]) -
Method in class AbstractGraph
- Checks of the nodes in the nodeset form a vertex induced tree.
- isTree(int[]) -
Method in interface Graph
- Checks of the nodes in the nodeset form a vertex induced tree.
NodeIterator
over the nodes of this cycle
following the edges of this path ending at the node with lowest
label (by a call to the previous() method).
NodeIterator
over the nodeset starting at the node
with highest label in some ordening as specified by the
Graph
interface.
useMacros(boolean) is set to true
.
- macros() -
Static method in class GRWrappedMapleVisitor
- Returns some Maple procedures to be used with the generated formula.
- main(String[]) -
Static method in class CycleCostAlgorithm
- This program reduces a Yutsis Graph to a so called triangular
delta in as few operations possible, while constructing the
general recoupling coefficient associated with it, which is
written to the screen.
- main(String[]) -
Static method in class CycleGenerator
- Program which prints all relevant cycles to the screen of the
YutsisGraph
specified by the first argument.
- main(String[]) -
Static method in class GYutsis
- Main method which creates a GYutsis window.
- main(String[]) -
Static method in class PathGenerator
- Program which prints all shortest paths (not cyclic canonical)
to the screen of the YutsisGraph specified by the first
argument.
- main(String[]) -
Static method in class YutsisGraph
- This program constructs the YutsisGraph specified by the first
argument and presents an interactive interface allowing the
user to get information about the YutsisGraph and the
reductionprocess.
- makeCanonical() -
Method in class PathGenerator
- Only the Path's wich passes nodes bigger than the start
node will remain.
- MAPLE_OUTPUT -
Static variable in class GYutsis
- Generate LaTeX output.
- MORE_SMALLER_LESS_BIGGER_HEURISTIC -
Static variable in class GYutsis
- Use an instance of CycleCountHeuristic.MORE_SMALLER_LESS_BIGGER as
heuristic (default).
node
.
node
or null
if the node is removed from the graph as specified by the
Graph
interface.
index
if the cycle
was iterated by a NodeIterator
.
d
from the startnode
of this Path.
NodeIterator
over the nodes of this cycle
following the edges of this cycle starting at the specified node
(by a call to the next() method).
node
by a NodeIterator#next() call.
NodeIterator
which will return node
by a NodeIterator.next()
call as specified by the
Graph
interface.
{tail,head}
.
Graph.nrOfEdges()
as
specified by the Graph
interface.
Graph
interface.
nrOfNodes()
nodes with labels between
Order()
, the latter not
included.
Graph
interface.
node
or -1
if the given node is no endpoint of this Edge.
apath[0]->..->apath[apath.length-1]
.
i
,j
).
g
.
i
and
j
(e1,e2)
interchanging the edges
(e1,a)
and (e2,b)
, assuming that
the girth of y
is at least 4 to System.out.
(e1,e2)
interchanging the edges
(e1,a)
and (e2,b)
, assuming that
the girth of y
is at least 4 to the given PrinStream.
Yutsis.removeBubble(int
[])
method.
triangle[0],
triangle[1], triangle[2]
, as specified by the Yutsis
interface.
triangle[0], triangle[1],
triangle[2]
.
node1, node2, node3
.
node1, node2, node3
.
newhead
.
newlabel
.
newnodes[0]
and the head to newnodes[1]
.
newtail
and the head to newhead
.
newtail
.
node
.
savebutton
is true
a save-to-file-button and a title.
label = (tail,head)
.
Yutsis.triangle()
method.
{j[0], j[1], j[2];l[0], l[1], l[2]}
(Wigner 6j-symbol) to this Genereal Recoupling Coefficient as
a consequence of the removal of a the triangle l[0], l[1],
l[2]
with neighboredges j[0], j[1], j[2]
such
that j[i] is not coupled with l[i]
in
the corresponding YutsisGraph.
- triangles() -
Method in class YutsisGraph
- Implementation of the abstract
Yutsis.triangles()
method.
- triangles() -
Method in interface Yutsis
- Returns all triangles as an array of int [3] objects.
- triangularDelta() -
Method in class AbstractYutsis
- True if the graph represents a triangular delta, false
otherwise.
- triangularDelta() -
Method in class YutsisGraph
- Overrides the
Yutsis.triangularDelta()
method, taking in
account node signs and edge directions.
- triangularDelta() -
Method in interface Yutsis
- True if the graph represents a triangular delta, false
otherwise.
- triangularDelta(int[]) -
Method in class AbstractYutsis
- True if the graph represents a triangular delta between node
td[0]
and td[1]
, false otherwise.
- triangularDelta(int[]) -
Method in class YutsisGraph
- Overrides the
Yutsis.triangularDelta(int [])
method,
taking in account node signs and edge directions.
- triangularDelta(int[]) -
Method in interface Yutsis
- True if the graph represents a triangular delta between node
td[0]
and td[1]
, false otherwise.
- triangularDelta(int, int) -
Method in class AbstractYutsis
- True if the graph represents a triangular delta between node
node1
and node2
, false otherwise.
- triangularDelta(int, int) -
Method in class YutsisGraph
- Overrides the
Yutsis.triangularDelta(int, int)
method,
taking in account node signs and edge directions.
- triangularDelta(int, int) -
Method in interface Yutsis
- True if the graph represents a triangular delta between node
node1
and node2
, false otherwise.
true
if macros will be used in the generated
formula.
true
LaTeX macros will be used to simplify
the generated formula.
AbstractYutsis
class
representing a Yutsis graph in order to generate the summation
formula in terms of 6j-coefficients for the general angular
momentum recoupling coefficient (or 3nj-coefficents)
represented by the couplings in this Yutsis graph.
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