PartitionΒΆ

prtition.spad line 1

Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus, (5 2 2 1) will represent s5 * s2^2 * s1.

0: %
from AbelianMonoid
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
<: (%, %) -> Boolean
from PartialOrder
<=: (%, %) -> Boolean
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean
from PartialOrder
>=: (%, %) -> Boolean
from PartialOrder
~=: (%, %) -> Boolean
from BasicType
coerce: % -> List Integer
coerce(p) coerces a partition into a list of integers
coerce: % -> OutputForm
from CoercibleTo OutputForm
conjugate: % -> %
conjugate(p) returns the conjugate partition of a partition p
convert: % -> List Integer
from ConvertibleTo List Integer
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
max: (%, %) -> %
from OrderedSet
min: (%, %) -> %
from OrderedSet
opposite?: (%, %) -> Boolean
from AbelianMonoid
partition: List Integer -> %
partition(li) converts a list of integers li to a partition
pdct: % -> Integer
pdct(a1^n1 a2^n2 ...) returns n1! * a1^n1 * n2! * a2^n2 * .... This function is used in the package CycleIndicators.
powers: List Integer -> List List Integer
powers(li) returns a list of 2-element lists. For each 2-element list, the first element is an entry of li and the second element is the multiplicity with which the first element occurs in li. There is a 2-element list for each value occurring in l.
sample: %
from AbelianMonoid
smaller?: (%, %) -> Boolean
from Comparable
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable

ConvertibleTo List Integer

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedSet

PartialOrder

SetCategory