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Group, this constructs an
AbelianGroup with the same elements.
chi to the character table.
HeckeAlgebraElt that's the sum of
this and y.
equals), put it in using CharTable.add(repthy.GpCharacter); if it is in
the table, do nothing.
g.
g of the source.
this(i).
(0
1), (1 2), up to (n-2 n-1) in
a minimal product equal to this.
GpCharacter.getRealType().
CharTable of G holds some or all of the
character of the irreducible representations of G. Group G that is
constant on conjugacy classes. Group.getConjClass(int)) is val[i].
doubles.Group.getCharTable(), not directly,
because the method makes sure to fill in the table the first
time.
Homomorphisms are immutable.
this and y commute.
this and the argument commute.
this.
y * this * y^(-1).
y * this * y^(-1).
y^(-1) * this * y.
Subgroup.leftCosetReps().
HeckeAlgebra.makeDblCosetReps().
dblCosetReps[i].
chi with respect to the current character
table.
Homomorphism from this to
a group H, iterates through each character currently in
H's character table, pulls it back by f, and
decomposes it with respect to the character table on
this.
a mod p.
this.
Set view of the key-value
pairs.
==.
HeckeAlgebras are
equal and the coefficients are termwise equal.
this and o belong to the same
G/H and are equal modulo H.
int arrays.
super method.
super method.
HeckeAlgebra.makeSubgroup().
Group
G, or an element of the Z-lattice generated by such
characters (a virtual character).
Group.getConjClass(int)) is val[i].
Group is a Set of GroupElts
satisfying the group axioms--existence of an identity element and
closure under GroupElt.mult(repthy.GroupElt) and GroupElt.inverse().
GroupElt is an Object supporting the group
operations GroupElt.mult(repthy.GroupElt) and GroupElt.inverse(), with an appropriate
notion of GroupElt.equals(java.lang.Object). int.
g in this group.
GpCharacters by the
degree.
i-th conjugacy class.
i-th conjugacy class as an
unmodifiable Set.
x is in the i-th
conjugacy class.
g is in the i-th
conjugacy class.
g is in the i-th
conjugacy class.
i-th conjugacy class.
Subgroup.
i such that the argument is in the
i-th double coset.
HeckeAlgebra.makeDblCosetReps().
PermGpElts that make
up the group.
g.
g.
GroupElt that is the identity for this group,
up to GroupElt.equals(java.lang.Object).
this.
AbelianGroup.getSNF()) to this
group.
AbelianGroup.getSNF()).
(G, H), where H is the set of
elements of G that map to the identity under the
representation associated to this character.
C_n.
C_n.
G.
{1,1,d} up to scalar multiples.
{1,1,d} up to scalar multiples.
GpCharacter.REAL if the (complex) representation
associated to this character is a real representation tensored
with C,
GpCharacter.QUATERNIONIC if it is quaternionic
(has a G-invariant conjugate-linear automorphism
J with J^2 = -I), and
GpCharacter.COMPLEX otherwise.
this,
but exhibited in Smith normal form with the ProductGroup structure as shown.
i.
Subgroup (G, H) that was used
to construct this group G/H.
this itself and
{1}.
Subgroup in which the underlying subgroup is a PGroup.
Subgroup in which the underlying subgroup is a PGroup.
Group backed by a HashSet
that holds one copy of each element of the group.set is a Set holding GroupElts.
Homomorphism backed by a
HashMap that contains one copy of each key-value
pair.sou to
tar.
HeckeAlgebra
HZ(G, H).1*(g) in the algebra.
Homomorphism that can be constructed from an
easier-to-use object HomomorphismFunc.Homomorphism is a Map from one Group to another satisfying the axioms for a homomorphism of groups.
apply. GroupElt.equals(java.lang.Object).
HeckeAlgebraElt.equals(java.lang.Object).
QuotientGroupElt.equals(java.lang.Object).
SortedSet.
Set that can't be modified once it's been created.chiH),
where chiH is a character on H.
G and G1 have the same elements
(that is, if G.equals(G1)), this method returns
the natural identity map from G to
G1.
this.
c.
GroupElts of its class.
this is in Jordan canonical form.
{1,1,d}
up to scalar multiples.
this is a subgroup of G1.
int.
byte entries modulo a
rational prime p. ravel function ρ (rho),
this constructor returns the n by n matrix whose
entries, in row major order, come from x.
C_n's whose orders are specified
by the arguments.
sou to
tar sending the generators souGen to
the corresponding elements tarImages, or returns
null to indicate that such a homomorphism does not exist.
this - chi.
this - chi.
this * y.
HeckeAlgebraElt that's the product
of this and y.
HeckeAlgebraElt that's
this times the scalar a.
this * y, that is, the permutation whose
value on i is this(y(i)).
this times the conjugate of
w.
GpCharacters on the same
group, and sorts them in ascending order of GpCharacter.normSqInt().
ClassFunction.innerProduct(repthy.ClassFunction) of this with
itself.
ClassFunction.normSq() to the nearest int.
ClassFunction.normSq() to the nearest long.
GpCharacter to a CharTable, but adding it would violate the condition that the
characters in the table form an orthonormal set.BigInteger.
BigInteger.
BigInteger.
BigInteger.
Group and a prime p, this constructs a
p-group with the same elements.
byte p as in the
superclass MatrixModp, but modulo scalar multiples of the
identity. MatrixModp.MatrixModp(byte[][],
byte).
MatrixModp.MatrixModp(int, byte[], byte).
PMatrixModp that's known at construction time to have
determinant equal to an n-th root of unity. PariProcess.send(java.lang.String) and PariProcess.receive() methods for communicating with it. HashGroup in which all the group elements are PermGpElts of the same degree.HashGroup.
HashGroup.
deg-1. PermGpElt from an array of length
n containing a permutation of the integers 0, 1,
..., n-1.
Groups.ProductGroup.(2 0 4)(3 1) to a
PermGpElt of the specified degree.
g.
long), then prints as if by Complex.toString().
chiT on the
target.
Homomorphisms are immutable.
Homomorphisms are immutable.
GpCharacter.getRealType().
Subgroup (G, H) where H is a
normal subgroup of G, this class is the quotient group
G/H, and provides the method QuotientGroup.getQuotientMap() for
obtaining the quotient homomorphism from G to G/H.GpCharacter.getRealType().
(Group, int) constructor to
construct the character of the regular representation.
H of the given
character on G.
PariProcess.send(java.lang.String).
Homomorphisms are immutable.
PermGp, is used with the
(Group, int) constructor to construct the
character that's 1 or -1 according to the sign of the
permutation.
PermGp, is used with the
(Group, int) constructor to construct the
character of the standard representation (the underlying
permutation representation minus the identity).
SortedSet, meaning a SortedSet
with exactly one element. Groups G ⊃ H where
H is a subgroup of G. HeckeAlgebraElt.toString() to return.
GpCharacter.getRealType().
Subgroup.getSubgroup().
SortedSet.
this + chi.
this and for chi.
this
direct-summed with itself n times.
this.
(Group, int) constructor to
construct the trivial character.
(G, int) constructor.
this if from is the unique
element of this set, and an empty SortedSet
otherwise.
this and for chi.
n * this.
this * chi.
C_12 X C_2 X C_2.
[a b; c d].
NumThy.factor(int), is
fac.
this.
(Group, int) constructor to
construct the zero character.
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