NMRing

jnemo.spad line 13 [edit on github]

Parent category of Nemo ring domains.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> %

from JLObjectRing

*: (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

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: % -> NonNegativeInteger

characteristic(x) returns the characteristic of the base ring of x.

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Integer -> %

from NonAssociativeRing

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> String

from ConvertibleTo String

divide: (%, %) -> Record(quotient: %, remainder: %)

divide(x,y) returns a record containing both remainder and quotient.

equal?: (%, %) -> Boolean

equal?(x,y) checks whether or not x and y ar equal.

exact?: % -> Boolean

exact?(x) check whether or not x is exact.

exactDivide: (%, %) -> %

exactDivide(x,y) returns the exact division of x by y. Throws a Julia error if it is no an exact division.

inverse: % -> %

inverse(x) returns the inverse of x.

jlAbout: % -> Void

from JLObjectType

jlApply: (String, %) -> %

from JLObjectType

jlApply: (String, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %, %) -> %

from JLObjectType

jlDisplay: % -> Void

from JLObjectType

jlDump: JLObject -> Void

from JLObjectType

jlId: % -> JLInt64

from JLObjectType

jlNMRing: () -> String

jlNMRing(x) returns the FriCAS Nemo ring type of x used in Julia. For example: example{jlNMRing()$NMPadicInteger(17)}

jlObject: () -> String

jlObject() returns the internal Julia name of the module used.

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

mutable?: % -> Boolean

from JLObjectType

nothing?: % -> Boolean

from JLObjectType

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

string: % -> String

from JLType

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

unit?: % -> Boolean

unit?(x) checks whther or not x is a unit, i.e. invertible.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

ConvertibleTo String

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

Magma

MagmaWithUnit

Monoid

NMType

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown