ListMonoidOps(S, E, un)ΒΆ

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This internal package represents monoid (abelian or not, with or without inverses) as lists and provides some common operations to the various flavors of monoids.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: S -> %

from CoercibleFrom S

latex: % -> String

from SetCategory

leftMult: (S, %) -> %

leftMult(s, a) returns s * a where * is the monoid operation, which is assumed non-commutative.

listOfMonoms: % -> List Record(gen: S, exp: E)

listOfMonoms(l) returns the list of the monomials forming l.

makeMulti: List Record(gen: S, exp: E) -> %

makeMulti(l) returns the element whose list of monomials is l.

makeTerm: (S, E) -> %

makeTerm(s, e) returns the monomial s exponentiated by e (e.g. s^e or e * s).

makeUnit: () -> %

makeUnit() returns the unit element of the monomial.

mapExpon: (E -> E, %) -> %

mapExpon(f, a1\^e1 ... an\^en) returns a1\^f(e1) ... an\^f(en).

mapGen: (S -> S, %) -> %

mapGen(f, a1\^e1 ... an\^en) returns f(a1)\^e1 ... f(an)\^en.

nthExpon: (%, Integer) -> E

nthExpon(l, n) returns the exponent of the n^th monomial of l.

nthFactor: (%, Integer) -> S

nthFactor(l, n) returns the factor of the n^th monomial of l.

outputForm: (%, (OutputForm, OutputForm) -> OutputForm, (OutputForm, OutputForm) -> OutputForm, Integer) -> OutputForm

outputForm(l, fop, fexp, unit) converts the monoid element represented by l to an OutputForm. Argument unit is the output form for the unit of the monoid (e.g. 0 or 1), fop(a, b) is the output form for the monoid operation applied to a and b (e.g. a + b, a * b, ab), and fexp(a, n) is the output form for the exponentiation operation applied to a and n (e.g. n a, n * a, a ^ n, a\^n).

retract: % -> S

from RetractableTo S

retractIfCan: % -> Union(S, failed)

from RetractableTo S

reverse!: % -> %

reverse!(l) reverses the list of monomials forming l, destroying the element l.

reverse: % -> %

reverse(l) reverses the list of monomials forming l. This has some effect if the monoid is non-abelian, i.e. reverse(a1\^e1 ... an\^en) = an\^en ... a1\^e1 which is different.

rightMult: (%, S) -> %

rightMult(a, s) returns a * s where * is the monoid operation, which is assumed non-commutative.

size: % -> NonNegativeInteger

size(l) returns the number of monomials forming l.

BasicType

CoercibleFrom S

CoercibleTo OutputForm

RetractableTo S

SetCategory