# ElementaryFunctionsUnivariatePuiseuxSeries(Coef, ULS, UPXS, EFULS)ΒΆ

- Coef: Algebra Fraction Integer
- ULS: UnivariateLaurentSeriesCategory Coef
- UPXS: UnivariatePuiseuxSeriesConstructorCategory(Coef, ULS)
- EFULS: PartialTranscendentalFunctions ULS

This package provides elementary functions on any Laurent series domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide ‘partial functions’ which compute transcendental functions of Laurent series when possible and return “failed” when this is not possible.

- ^: (UPXS, Fraction Integer) -> UPXS if Coef has Field
`z ^ r`

raises a Puiseaux series`z`

to a rational power`r`

- acos: UPXS -> UPXS
`acos(z)`

returns the arc-cosine of a Puiseux series`z`

.

- acosh: UPXS -> UPXS
`acosh(z)`

returns the inverse hyperbolic cosine of a Puiseux series`z`

.- acoshIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- acosIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- acot: UPXS -> UPXS
`acot(z)`

returns the arc-cotangent of a Puiseux series`z`

.

- acoth: UPXS -> UPXS
`acoth(z)`

returns the inverse hyperbolic cotangent of a Puiseux series`z`

.- acothIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- acotIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- acsc: UPXS -> UPXS
`acsc(z)`

returns the arc-cosecant of a Puiseux series`z`

.

- acsch: UPXS -> UPXS
`acsch(z)`

returns the inverse hyperbolic cosecant of a Puiseux series`z`

.- acschIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- acscIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- asec: UPXS -> UPXS
`asec(z)`

returns the arc-secant of a Puiseux series`z`

.

- asech: UPXS -> UPXS
`asech(z)`

returns the inverse hyperbolic secant of a Puiseux series`z`

.- asechIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- asecIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- asin: UPXS -> UPXS
`asin(z)`

returns the arc-sine of a Puiseux series`z`

.

- asinh: UPXS -> UPXS
`asinh(z)`

returns the inverse hyperbolic sine of a Puiseux series`z`

.- asinhIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- asinIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- atan: UPXS -> UPXS
`atan(z)`

returns the arc-tangent of a Puiseux series`z`

.

- atanh: UPXS -> UPXS
`atanh(z)`

returns the inverse hyperbolic tangent of a Puiseux series`z`

.- atanhIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- atanIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- cos: UPXS -> UPXS
`cos(z)`

returns the cosine of a Puiseux series`z`

.

- cosh: UPXS -> UPXS
`cosh(z)`

returns the hyperbolic cosine of a Puiseux series`z`

.- coshIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- cosIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- cot: UPXS -> UPXS
`cot(z)`

returns the cotangent of a Puiseux series`z`

.

- coth: UPXS -> UPXS
`coth(z)`

returns the hyperbolic cotangent of a Puiseux series`z`

.- cothIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- cotIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- csc: UPXS -> UPXS
`csc(z)`

returns the cosecant of a Puiseux series`z`

.

- csch: UPXS -> UPXS
`csch(z)`

returns the hyperbolic cosecant of a Puiseux series`z`

.- cschIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- cscIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- exp: UPXS -> UPXS
`exp(z)`

returns the exponential of a Puiseux series`z`

.- expIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- log: UPXS -> UPXS
`log(z)`

returns the logarithm of a Puiseux series`z`

.- logIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- nthRootIfCan: (UPXS, NonNegativeInteger) -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- sec: UPXS -> UPXS
`sec(z)`

returns the secant of a Puiseux series`z`

.

- sech: UPXS -> UPXS
`sech(z)`

returns the hyperbolic secant of a Puiseux series`z`

.- sechIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- secIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- sin: UPXS -> UPXS
`sin(z)`

returns the sine of a Puiseux series`z`

.

- sinh: UPXS -> UPXS
`sinh(z)`

returns the hyperbolic sine of a Puiseux series`z`

.- sinhIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- sinIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS

- tan: UPXS -> UPXS
`tan(z)`

returns the tangent of a Puiseux series`z`

.

- tanh: UPXS -> UPXS
`tanh(z)`

returns the hyperbolic tangent of a Puiseux series`z`

.- tanhIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS
- tanIfCan: UPXS -> Union(UPXS, failed)
- from PartialTranscendentalFunctions UPXS