All Packages Class Hierarchy
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Index of all Fields and Methods
- actionPerformed(ActionEvent).
Method in class math.topol.Braid.braidCanvas
- Takes care of ActionEvents in this braidCanvas.
- addPopup(PopupMenu).
Method in class math.topol.Braid.braidCanvas
- Add a popup menu.
- addTerm(Term).
Method in class math.alg.PowerSeries.NCseries
- Adds a term to this NCseries.
- appendFactor(Factor).
Method in class math.alg.PowerSeries.Term
- Appends a Factor f to the monomial for this term.
- ArtinDecomposition(braid).
Method in class math.topol.Braid.braid
- Returns a Vector of intArrays, which represents the fully combed
form of the given (pure!) braid.
- binomial(int, int).
Static method in class math.topol.Braid.braid
- Get small binomial coefficient ($n$ choose $k$) as an int, for
small values of $k$.
- braid(int).
Constructor for class math.topol.Braid.braid
- Creates an empty braid with the given number of strands.
- braid(int[]).
Constructor for class math.topol.Braid.braid
- Creates a braid from the given word in the standard generators
(elementary braids), given as an int[] array.
- braid(intArray).
Constructor for class math.topol.Braid.braid
- Creates a braid from the given word in the standard
generators (elementary braids), given as an intArray.
- braid(String).
Constructor for class math.topol.Braid.braid
- Creates a braid from the given String in the standard
generators (elementary braids).
- braidCanvas(Applet, ActionListener).
Constructor for class math.topol.Braid.braidCanvas
-
- braidCanvas(Applet, ActionListener, int, int).
Constructor for class math.topol.Braid.braidCanvas
-
- clone().
Method in class math.alg.PowerSeries.Factor
- Returns a clone of this factor.
- ColArray.
Static variable in class math.topol.Braid.braidCanvas
-
- collect().
Method in class math.alg.PowerSeries.NCseries
- Collects like terms in this NCseries.
- comb(braid).
Method in class math.topol.Braid.braid
- Returns a braid, which represent the fully combed form of the
given (pure!) braid.
- compare(NCseries, NCseries).
Static method in class math.alg.PowerSeries.NCseries
- Compares two NCseries: returns $-1$ if the first is $<$ the
second, 0 if they're equal, and 1 if the first is $>$ the second.
- compare(Term, Term).
Static method in class math.alg.PowerSeries.Term
- Compares two terms $t1$, $t2$: returns $-1$ if $t1 < t2$,
0 if they're equal, and 1 if $t1 > t2$.
- compare_to(NCseries).
Method in class math.alg.PowerSeries.NCseries
- Compares this NCseries with the given NCseries: returns $-1$ if this
is < the given NCseries, 0 if they're equal, and 1 if this > the
given NCseries.
- compare_to(Term).
Method in class math.alg.PowerSeries.Term
- Compares this term with term t: returns $-1$ if this $< t$, 0 if
they're equal, and 1 if this $> t$.
- crosslist.
Variable in class math.topol.Braid.braid
- The braid word: a list of elementary generators.
- dbinomial(int, int).
Static method in class math.topol.Braid.braid
- Returns large binomial coefficient $(-1)^{k1} \times k! / k1!
(k-k1)!$
- DefaultTruncDegree.
Static variable in class math.alg.PowerSeries.NCseries
-
- divided_by(NCseries).
Method in class math.alg.PowerSeries.NCseries
- Returns the result of dividing this NCseries by the given
NCseries.
- draw().
Method in class math.topol.Braid.braidCanvas
- Plots the braid.
- drawBraid(braid).
Method in class math.topol.Braid.braidCanvas
- Draws given braid in this braidCanvas.
- drawCrossing(int, RealPoint).
Method in class math.topol.Braid.braidCanvas
- Draws given elementary generator at the given basepoint.
- embed().
Method in class math.topol.Braid.braid
- Returns this braid naturally embedded in a braid with one
more strand.
- Factor(int, int).
Constructor for class math.alg.PowerSeries.Factor
- Constructs a new factor with the given index and degree.
- factorialExpansion(int, int).
Static method in class math.topol.Braid.braid
- Returns the factorial expansion of $g$ down to the
$(r1 - 1)$-th position.
- freeCanonicalForm(braid).
Method in class math.topol.Braid.braid
- Returns a braid which is equivalent to this braid, but which is
presented as a product of free group generators.
- freeReduce().
Method in class math.topol.Braid.braid
- Reduces this braid, in the free group.
- getCoeff().
Method in class math.alg.PowerSeries.Term
- Gets the coefficient of this term.
- getIndex().
Method in class math.alg.PowerSeries.Factor
- Gets the variable index for this factor
- getLength().
Method in class math.topol.Braid.braid
- Returns the length of this braid.
- getLength().
Method in class math.alg.PowerSeries.NCseries
- Gets the length (number of terms) of this NCseries.
- getMonomial().
Method in class math.alg.PowerSeries.Term
- Returns the monomial of this term.
- getNumStrands().
Method in class math.topol.Braid.braid
- Returns the braid index (number of strands) of this braid.
- getPermutation().
Method in class math.topol.Braid.braid
- Returns the permutation of this braid.
- getPower().
Method in class math.alg.PowerSeries.Factor
- Gets the variable power for this factor
- getTotalDegree().
Method in class math.alg.PowerSeries.Term
- Gets the total degree of this term.
- getTruncDeg().
Method in class math.alg.PowerSeries.NCseries
- Gets the truncation degree of this NCseries.
- getVariableOrder().
Method in class math.alg.PowerSeries.NCseries
- Returns the variable order of this NCseries, as a vector.
- Identity(Vector).
Static method in class math.alg.PowerSeries.NCseries
- Returns an NCseries with the given variable order, representing
the identity series.
- init().
Method in class math.topol.Braid.braid
- Initializes the variables required for the polynomial
computations.
- initGfx().
Method in class math.topol.Braid.braidCanvas
- Initializes the graphics.
- insertFactor(Factor, int).
Method in class math.alg.PowerSeries.Term
- Inserts a Factor f into the monomial for this term at
the given position.
- insertTerm(Term).
Method in class math.alg.PowerSeries.NCseries
- Inserts the given Term into this NCseries in proper order.
- inverse().
Method in class math.topol.Braid.braid
- Returns the inverse of this braid.
- invert(NCseries).
Static method in class math.alg.PowerSeries.NCseries
- Returns the result of inverting the given NCseries.
- isPure(braid).
Static method in class math.topol.Braid.braid
- Returns true if and only if the given braid is a pure braid.
- minus(NCseries).
Method in class math.alg.PowerSeries.NCseries
- Returns the result of subtracting a given series from this NCseries.
- NCseries(Vector).
Constructor for class math.alg.PowerSeries.NCseries
- Creates a new Non-commutative Power Series in the given
variables.
- NoCanvasException(String).
Constructor for class math.topol.Braid.NoCanvasException
-
- numvars.
Variable in class math.alg.PowerSeries.NCseries
- The number of variables involved in this series.
- paint(Graphics).
Method in class math.topol.Braid.braidCanvas
- Calls update to refresh the canvas with the image of the
braid.
- plus(NCseries).
Method in class math.alg.PowerSeries.NCseries
- Returns the result of adding ps to this NCseries.
- processMouseEvent(MouseEvent).
Method in class math.topol.Braid.braidCanvas
- Takes care of MouseEvents in this braidCanvas.
- random(int, int, Random).
Static method in class math.topol.Braid.braid
- Returns a pseudo-random braid of given index, of length less
than or equal to the given length.
- random(int, Random).
Static method in class math.topol.Braid.braid
- Returns a pseudo-random braid of given index.
- reduce(Term).
Method in class math.alg.PowerSeries.Term
- Reduces the given term, so that adjacent similar variables
are coalesced.
- register(braid).
Method in class math.topol.Braid.braidCanvas
- Registers this braid with the canvas so that various operations
can dispense with such operations as threading the braid.
- retract(int).
Method in class math.topol.Braid.braid
- Returns the k-fold retraction of this braid, that is, the braid
resulting from deleting the last k strands.
- seedRandom().
Static method in class math.topol.Braid.braid
- Initializes the pseudo-random braid generator with a "random"
value (given by the system clock).
- seedRandom(long).
Static method in class math.topol.Braid.braid
- Initializes the pseudo-random braid generator with the given
seed value of type long.
- setBraid(intArray).
Method in class math.topol.Braid.braid
- Sets this braid to the given braidword, expressed as an
intArray.
- setCoeff(int).
Method in class math.alg.PowerSeries.Term
- Sets the coefficient of this term.
- setIndex(int).
Method in class math.alg.PowerSeries.Factor
- Sets the variable index for this factor
- setMonomial(Vector).
Method in class math.alg.PowerSeries.Term
- Sets the monomial of this term to the given monomial.
- setNumStrands(int).
Method in class math.topol.Braid.braid
- Sets the braid index (number of strands) of this braid.
- setPower(int).
Method in class math.alg.PowerSeries.Factor
- Sets the variable power for this factor
- setTruncDeg(int).
Method in class math.alg.PowerSeries.NCseries
- Sets the truncation degree of this NCseries.
- sort().
Method in class math.alg.PowerSeries.NCseries
- Sorts the terms of this NCseries into ascending order, first by
total degree of the terms, then by lexicographic order, based
on the given order of variables.
- Term(NCseries).
Constructor for class math.alg.PowerSeries.Term
- Creates a new term for a NCseries of given type.
- thread().
Method in class math.topol.Braid.braid
- Creates a representation of this braid as a vector of
crossings, with each crossing recording its index,
which strands are involved, and whether it is a positive
or a negative crossing.
- times(braid).
Method in class math.topol.Braid.braid
- Returns the product (this braid)*(b).
- times(NCseries).
Method in class math.alg.PowerSeries.NCseries
- Returns the product of this NCseries times the given NCseries.
- times(Term).
Method in class math.alg.PowerSeries.Term
- Returns the product (non-commutative!) of this term with the
given term.
- toFreeGenList().
Method in class math.topol.Braid.braid
- Returns a list (intArray) representation of this braid, as a
sequence of free generators.
- toFreeGenTeXForm().
Method in class math.topol.Braid.braid
- Returns a String representation of this braid, written as a
string of free generators.
- toMagnus(Vector, intArray).
Static method in class math.alg.PowerSeries.NCseries
- Returns the non-commutative power series (with variable order
given by vars) giving the Magnus representation of word in the
free group.
- toPostScript(braid).
Method in class math.topol.Braid.braidCanvas
- Generates PostScript output which draws this braid.
- toString().
Method in class math.topol.Braid.braid
- Returns a string representation of this braid.
- toString().
Method in class math.alg.PowerSeries.NCseries
- Formats this NCseries as a string and returns the result.
- toString().
Method in class math.alg.PowerSeries.Term
- Formats this term as a string and returns the result.
- toTeXForm().
Method in class math.topol.Braid.braid
- Returns a String representation of this braid,
formatted as TeX input.
- trunc(int).
Method in class math.alg.PowerSeries.NCseries
- Returns the result of truncating this NCseries after terms of
total degree deg.
- two_variable(PrintWriter, StringBuffer).
Method in class math.topol.Braid.braid
- Computes the two-variable polynomial from a braid.
- untwist(braid. disk).
Method in class math.topol.Braid.braid
- Untwists an "innermost" twist of form $\sigma_k^{\mp 1} \cdots$
(other generators involving strand $n$) $\cdots \sigma_{\ell}^{\pm 1}$,
where $\sigma_k$ and $\sigma_{\ell}$ involve strands $i$ and $j$,
and are opposite in sign.
- update(Graphics).
Method in class math.topol.Braid.braidCanvas
- Update this image.
- VariableOrderException(String).
Constructor for class math.alg.PowerSeries.VariableOrderException
-