ElementaryFunctionsUnivariateLaurentSeries(Coef, UTS, ULS)

efuls.spad line 1 [edit on github]

• Coef : Algebra(Fraction(Integer))
• UTS : UnivariateTaylorSeriesCategory(Coef)
• ULS : UnivariateLaurentSeriesConstructorCategory(Coef, UTS)

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.

^ : (ULS, Fraction(Integer)) -> ULS if Coef has Field

s ^ r raises a Laurent series s to a rational power r

acos : ULS -> ULS

acos(z) returns the arc-cosine of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

acosh : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

acot : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

acoth : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

acsc : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

acsch : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

asec : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

asech : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

asin : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

asinh : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

atan : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

atanh : ULS -> ULS

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

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

from PartialTranscendentalFunctions(ULS)

cos : ULS -> ULS

cos(z) returns the cosine of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

cosh : ULS -> ULS

cosh(z) returns the hyperbolic cosine of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

cot : ULS -> ULS

cot(z) returns the cotangent of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

coth : ULS -> ULS

coth(z) returns the hyperbolic cotangent of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

csc : ULS -> ULS

csc(z) returns the cosecant of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

csch : ULS -> ULS

csch(z) returns the hyperbolic cosecant of Laurent series z.

cschIfCan : ULS -> Union(ULS, "failed")

from PartialTranscendentalFunctions(ULS)

exp : ULS -> ULS

exp(z) returns the exponential of Laurent series z.

expIfCan : ULS -> Union(ULS, "failed")

from PartialTranscendentalFunctions(ULS)

log : ULS -> ULS

log(z) returns the logarithm of Laurent series z.

logIfCan : ULS -> Union(ULS, "failed")

from PartialTranscendentalFunctions(ULS)

nthRootIfCan : (ULS, NonNegativeInteger) -> Union(ULS, "failed")

from PartialTranscendentalFunctions(ULS)

sec : ULS -> ULS

sec(z) returns the secant of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

sech : ULS -> ULS

sech(z) returns the hyperbolic secant of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

sin : ULS -> ULS

sin(z) returns the sine of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

sinh : ULS -> ULS

sinh(z) returns the hyperbolic sine of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

tan : ULS -> ULS

tan(z) returns the tangent of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

tanh : ULS -> ULS

tanh(z) returns the hyperbolic tangent of Laurent series z.

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

from PartialTranscendentalFunctions(ULS)

PartialTranscendentalFunctions(ULS)