InnerTaylorSeries CoefΒΆ

taylor.spad line 1

Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a Stream of Ring elements. For univariate series, the Stream elements are the Taylor coefficients. For multivariate series, the nth Stream element is a form of degree n in the power series variables.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Coef) -> %
x*c returns the product of c and the series x.
*: (%, Integer) -> %
x*i returns the product of integer i and the series x.
*: (Coef, %) -> %
c*x returns the product of c and the series x.
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean if Coef has IntegralDomain
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coefficients: % -> Stream Coef
coefficients(x) returns a stream of ring elements. When x is a univariate series, this is a stream of Taylor coefficients. When x is a multivariate series, the nth element of the stream is a form of degree n in the power series variables.
coerce: % -> % if Coef has IntegralDomain
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
commutator: (%, %) -> %
from NonAssociativeRng
exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain
from EntireRing
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
order: % -> NonNegativeInteger
order(x) returns the order of a power series x, i.e. the degree of the first non-zero term of the series.
order: (%, NonNegativeInteger) -> NonNegativeInteger
order(x, n) returns the minimum of n and the order of x.
pole?: % -> Boolean
pole?(x) tests if the series x has a pole. Note: this is false when x is a Taylor series.
recip: % -> Union(%, failed)
from MagmaWithUnit
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
series: Stream Coef -> %
series(s) creates a power series from a stream of ring elements. For univariate series types, the stream s should be a stream of Taylor coefficients. For multivariate series types, the stream s should be a stream of forms the nth element of which is a form of degree n in the power series variables.
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
unit?: % -> Boolean if Coef has IntegralDomain
from EntireRing
unitCanonical: % -> % if Coef has IntegralDomain
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %) if Coef has IntegralDomain
from EntireRing
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra % if Coef has IntegralDomain

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

CommutativeRing if Coef has IntegralDomain

CommutativeStar if Coef has IntegralDomain

EntireRing if Coef has IntegralDomain

IntegralDomain if Coef has IntegralDomain

LeftModule %

Magma

MagmaWithUnit

Module % if Coef has IntegralDomain

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown