ElementaryFunctionsUnivariatePuiseuxSeries(Coef, ULS, UPXS, EFULS)

efupxs.spad line 1 [edit on github]

• 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

PartialTranscendentalFunctions UPXS