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.

acosIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

acosh : UPXS -> UPXS

acosh(z) returns the inverse hyperbolic cosine of a Puiseux series z.

acoshIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

acot : UPXS -> UPXS

acot(z) returns the arc-cotangent of a Puiseux series z.

acotIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

acoth : UPXS -> UPXS

acoth(z) returns the inverse hyperbolic cotangent of a Puiseux series z.

acothIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

acsc : UPXS -> UPXS

acsc(z) returns the arc-cosecant of a Puiseux series z.

acscIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

acsch : UPXS -> UPXS

acsch(z) returns the inverse hyperbolic cosecant of a Puiseux series z.

acschIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

asec : UPXS -> UPXS

asec(z) returns the arc-secant of a Puiseux series z.

asecIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

asech : UPXS -> UPXS

asech(z) returns the inverse hyperbolic secant of a Puiseux series z.

asechIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

asin : UPXS -> UPXS

asin(z) returns the arc-sine of a Puiseux series z.

asinIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

asinh : UPXS -> UPXS

asinh(z) returns the inverse hyperbolic sine of a Puiseux series z.

asinhIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

atan : UPXS -> UPXS

atan(z) returns the arc-tangent of a Puiseux series z.

atanIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

atanh : UPXS -> UPXS

atanh(z) returns the inverse hyperbolic tangent of a Puiseux series z.

atanhIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

cos : UPXS -> UPXS

cos(z) returns the cosine of a Puiseux series z.

cosIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

cosh : UPXS -> UPXS

cosh(z) returns the hyperbolic cosine of a Puiseux series z.

coshIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

cot : UPXS -> UPXS

cot(z) returns the cotangent of a Puiseux series z.

cotIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

coth : UPXS -> UPXS

coth(z) returns the hyperbolic cotangent of a Puiseux series z.

cothIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

csc : UPXS -> UPXS

csc(z) returns the cosecant of a Puiseux series z.

cscIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

csch : UPXS -> UPXS

csch(z) returns the hyperbolic cosecant of a Puiseux series z.

cschIfCan : 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.

secIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

sech : UPXS -> UPXS

sech(z) returns the hyperbolic secant of a Puiseux series z.

sechIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

sin : UPXS -> UPXS

sin(z) returns the sine of a Puiseux series z.

sinIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

sinh : UPXS -> UPXS

sinh(z) returns the hyperbolic sine of a Puiseux series z.

sinhIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

tan : UPXS -> UPXS

tan(z) returns the tangent of a Puiseux series z.

tanIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

tanh : UPXS -> UPXS

tanh(z) returns the hyperbolic tangent of a Puiseux series z.

tanhIfCan : UPXS -> Union(UPXS, "failed")

from PartialTranscendentalFunctions(UPXS)

PartialTranscendentalFunctions(UPXS)