MagmaWithUnitΒΆ

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MagmaWithUnit is the class of multiplicative monads with unit, i.e. sets with a binary operation and a unit element. Axioms leftIdentity(“*”:(%,%)->%,1) 1*x=x rightIdentity(“*”:(%,%)->%,1) x*1=x Common Additional Axioms unitsKnown—if “recip” says “failed”, that PROVES input wasn't a unit

1: %
1 returns the unit element, denoted by 1.
*: (%, %) -> %
from Magma
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
a^n returns the n-th power of a, defined by repeated squaring.
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
leftPower(a, n) returns the n-th left power of a, i.e. leftPower(a, n) := a * leftPower(a, n-1) and leftPower(a, 0) := 1.
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
leftRecip(a) returns an element, which is a left inverse of a, or "failed" if such an element doesn't exist or cannot be determined (see unitsKnown).
one?: % -> Boolean
one?(a) tests whether a is the unit 1.
recip: % -> Union(%, failed)
recip(a) returns an element, which is both a left and a right inverse of a, or "failed" if such an element doesn't exist or cannot be determined (see unitsKnown).
rightPower: (%, NonNegativeInteger) -> %
rightPower(a, n) returns the n-th right power of a, i.e. rightPower(a, n) := rightPower(a, n-1) * a and rightPower(a, 0) := 1.
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
rightRecip(a) returns an element, which is a right inverse of a, or "failed" if such an element doesn't exist or cannot be determined (see unitsKnown).
sample: %
sample yields a value of type %

BasicType

CoercibleTo OutputForm

Magma

SetCategory