QEtaAlgebra CΒΆ
qetaalg.spad line 98 [edit on github]
QEtaAlgebra(C) lists the minimal signatures for running algebra functions in the QEtaPackage. Mathematically seen is it a C-algebra.
- 0: %
0 is the neutral element with respect to +.
- 1: %
1 is the neutral element with respect to *.
- *: (%, %) -> %
Commutative multiplication
- *: (C, %) -> %
Multiplication by a coefficient.
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
Commutative addition.
- -: % -> %
-xreturns an elementysuch thatx+y=0.
- -: (%, %) -> %
Inverse operation to addition.
x-yreturns an elementszsuch thatx=z+y.
- ^: (%, NonNegativeInteger) -> %
Exponentiation (repeated multiplication)
- ^: (%, PositiveInteger) -> %
from Magma
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- 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
- recip: % -> Union(%, failed)
from MagmaWithUnit
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from MagmaWithUnit
- subtractIfCan: (%, %) -> Union(%, failed)
- traceout: NonNegativeInteger -> % -> OutputForm
traceout(verbosity)(x) coercesxinto OutputForm for tracing purposes. A higherverbosityvalue shows more information. Smaller values might show only partial information.
- zero?: % -> Boolean
zero?(x)returnstrueifxis the neutral element with respect to +.