# FactoredFunctions M¶

manip.spad line 1 [edit on github]

computes various functions on factored arguments.

- log: Factored M -> List Record(coef: NonNegativeInteger, logand: M)
`log(f)`

returns`[(a1, b1), ..., (am, bm)]`

such that the logarithm of`f`

is equal to`a1*log(b1) + ... + am*log(bm)`

.

- nthRoot: (Factored M, NonNegativeInteger) -> Record(exponent: NonNegativeInteger, coef: M, radicand: List M)
`nthRoot(f, n)`

returns`(p, r, [r1, ..., rm])`

such that the`n`

th-root of`f`

is equal to`r * pth-root(r1 * ... * rm)`

, where`r1`

, …,`rm`

are distinct factors of`f`

, each of which has an exponent smaller than`p`

in`f`

.