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this, and whose index is that of
this.
this and another CSparse,
returning a CSparse.
this and another DenseMatrixZ,
returning a DenseMatrixZ.
this and y, and whose index is that
of this.
this with its sum with b.
this by adding to it (the value in
factor) times b.
i1 by adding to it
(the value in factor) times (the entry with index
i2).
j1 by adding to it the value in
factor times column j2.
i1 by adding to it the value in
factor times row i2.
SparseElt.bitLength() for all the entries, and
returns the sum in kilobytes (kB).
BigInteger.bitLength(); if the value is stored in a primitive
type, returns the bit length of the type.
SparseVs, first by number of entries
(smallest goes to the left), then by initial entry's index
(largest goes to the left).
SparseVs, putting first that one that's
shorter under SparseV.getNormSq().
CSparse
matrix, this window displays the changing sparsity pattern and
other information. cons, the basic data structure in
Lisp.
cardinal(58) is "fifty-eight", for example.
int.
cols[j] is the j-th column of this
sparse matrix.
SparseEltZs by < on the values.
PPTs lexicographically.
A, B into (A |
B).
this,
and with index indexOfCopy.
this CSparse has entries over Z, returns
a new CSparse whose entries are their reductions mod p.
this mod p, preserving the
index.
this, except that null or zero columns are
omitted.
main(java.lang.String[]) to demonstrate how CSparseWin displays
the reduction of a large sparse matrix (a CSparse)
over Z.BigIntegers, implemented as
m × n arrays in a straightforward
way. this
morphism itself.
this
morphism itself.
int ±1.
this/y and returns a
two-element array with values quotient and remainder.
this/y.
this divides the value of
y; that is, whether there is an x
such that x * this = y.
NumThy).
this and b.
this is a QvspMorphism
V → W with matrix
A, then dual() returns a
QvspMorphism W → V
whose matrix is the transpose of A.
EquCoh.main(java.lang.String[]).f has a kernel morphism and a cokernel morphism, and
furthermore has the following canonical factorization.
v.
SparseElt.isEqualValue(shh.csparse.SparseElt).
QvspMorphism.equals(java.lang.Object).
equal, this tests for equality of the
members.
this and
b have the same size and the entries are equal
term by term.
BigInteger.abs() to the value.
int arrays.
Q.
int.
SparseElt whose value is the i,j value
of the matrix.
ExactCategoryMorphism.
ExactCategoryMorphism.
ExactCategoryMorphism.
ExactCategoryMorphism.
ExactCategoryMorphism.
MPDQ.
g starting at
the indicated vertex.
getObj(deg) to
getObj(deg+1).
i in the sparse
vector, or null if there isn't one.
e.
C that compares by Euclidean
norm.
this object to
itself.
ExactCategoryMorphism.
ExactCategoryMorphism.
ExactCategoryMorphism.
ExactCategoryMorphism.
SparseV.getListIndex(int) for e's
index.
getListIndex(i, 0).
MPDQ holding the Smith normal form for
the underlying matrix.
i is greater than (>) this value,
getObj(i) must be zero.
i is less than (<) this value,
getObj(i) must be zero.
Qvsp.setName(java.lang.String), or null if none has
been set.
QvspMorphism.setName(java.lang.String), or null if none has
been set.
this, with value -1 and unspecified index.
deg.
this, with value 1 and unspecified index.
v is one of the vertices of edge
e, returns the other vertex.
MPDQ.
MPDQ.
[corner, m)
× [corner, n), as a number between 0
and 1.
CSparse.getSparsity(int, boolean) with arguments
(corner, true).
BigInteger.
double.
int and returns it.
BigInteger.intValue() to the value.
this, with value 0 and unspecified index.
source to
this.
this with its upper-triangular Hermite Normal
Form (HNF).
CSparse.HNF().
HopcroftTarjan.Graph, then HopcroftTarjan.getDFS(shh.util.HopcroftTarjan.Graph, java.lang.Object) will perform a depth-first search on it.SparseElt.equals(java.lang.Object).
SparseElt.equals(java.lang.Object).
SparseElt.equals(java.lang.Object).
SparseElt.equals(java.lang.Object).
PPT.equals(java.lang.Object).
Cons.equals(java.lang.Object).
this and f
(see the diagram for Morphism.compose(shh.homolalg.Morphism)) is a zero
morphism.
this is an epimorphism.
this has an inverse morphism.
this is a monomorphism.
this * b0 is zero, without storing
the product.
this * b is zero, without storing the
product.
this is a zero object.
v.
int.
SparseVs, putting to the left the one
whose SparseV.getLastIndex() is smaller.
ints, which
is a member of some matrix group G, and also holds the
int value of a character on G.DenseMatrixZ.doLLL().
CSparse over Z through MPDQ.jac() and prints the results.
CSparse through CSparse.HNF() and prints
the results.
ExactCategoryMorphism.
AB meaning the edge from A to
B.
u0 v0 u1 v1 u2 v2, etc., all ≥
0, and plots a chart with two line graphs, one for
u and one for v.
StronglyConn.test(java.lang.String[]).
i0,j0 and of side s, it
is the identity.
M.
M.
this * b.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
b0 is a CSparse or
DenseMatrixZ, destructive to this if
b0 is an ElemMatrix.
this * b.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
b * this.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
b is a CSparse or DenseMatrixZ,
is destructive to it; otherwise is unsupported.
this and y, and whose index is that
of this.
newIndex and whose
value is the product of the values in this and
y.
SparseElt), producing values in the other domain.
int data type. q such
that q * y + this is as small as possible for
SparseEltEuc.eucNorm().
this, and whose index is that of
this.
this with its scalar product by -1.
j by -1.
i with its negative.
i by -1.
SparseElt), producing values in the other domain.
ordinal(58) is "fifty-eighth", for example.
MPDQ.getPivot().
s to make its length equal to
n.
[[2,3],[3,1]] to2^3 * 3.
v to stream as a dense vector
of length m, one entry per line.
Qvsps. repaint() on the main panel.
x, rounds it off to the nearest
dec_places decimal places, if any.
sig_figs) into the appropriate number of decimal
places, then passes off the work to Format.round(float, int).
this as SparseVs.
CSparseWin, a window showing the sparsity
pattern of the matrix as it changes in real time.
or of the appropriate SHOW_xxx
constants in this class.
ProgressMonitor, a dialog box with a few
statistics and with a progress bar indicating how far along the
computation is.
StatWins with line graphs showing the sparsity,
number of P's and Q's, etc., as they change
throughout the computation.
SparseV) over an integral domain D. SparseElts should implement this interface if
its underlying integral domain D is a Euclidean
domain.SparseElts should implement this interface if
its underlying integral domain is a field.val mod 2.
val is
true and 0 if val is false.
val
mod p.
BigIntegers).int to store the values. SparseElts representing a vector
over the integral domain that underlies the SparseElts. StatWin.show(double[], java.lang.String, int) displays a window with a line graph. StronglyConn.Graph, then
StronglyConn.getSCC(shh.util.StronglyConn.Graph, java.lang.Object) will find its strongly-connected components.this with its scalar product by the
value stored in s.
DenseMatrixZ.set(SparseElt, int).
UnsupportedOperationException.
corner should be assumed to be diagonal.
i-th data series
(default true).
s's index to s.
Format.tab(java.lang.StringBuffer).
this)
minus (value of y), and whose index is that of
this.
i-th and j-th
entries; it's required that
i < j.
t in tabStops
that's greater than the length of s, and pads
s with spaces until its length is t.
AB meaning the
edge from A to B.
PPT consisting of this
as a row vector times the matrix in mm.
DenseMatrixZ with the same size and entries
as this.
(index value).
((a e i m) (b f j n) (c g k o) (d h l p))
as in the constructor.
(1 0 1 1).
Qvsp.setName(java.lang.String), or
else returns a String like Q^17.
QvspMorphism.setName(java.lang.String);
otherwise, returns a printed representation, including the
matrix if it is small enough.
1 0 1 1.
NumThy.factor(int), is
fac.
UnivCoeff).
SparseV.updateNormSq() on all columns
j ≥ j0.
SparseV.getNormSq(),
and call it again if any operation changes the values of this
vector.
this CSparse from the entries in
ravelList, in row-major order.
SparseElt), producing values in the other domain.
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