ElementaryFunctionsUnivariateLaurentSeries(Coef, UTS, ULS)

efuls.spad line 1 [edit on github]

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.

acosh: ULS -> ULS

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

acoshIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

acosIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

acot: ULS -> ULS

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

acoth: ULS -> ULS

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

acothIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

acotIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

acsc: ULS -> ULS

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

acsch: ULS -> ULS

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

acschIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

acscIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

asec: ULS -> ULS

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

asech: ULS -> ULS

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

asechIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

asecIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

asin: ULS -> ULS

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

asinh: ULS -> ULS

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

asinhIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

asinIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

atan: ULS -> ULS

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

atanh: ULS -> ULS

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

atanhIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

atanIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

cos: ULS -> ULS

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

cosh: ULS -> ULS

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

coshIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

cosIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

cot: ULS -> ULS

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

coth: ULS -> ULS

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

cothIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

cotIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

csc: ULS -> ULS

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

csch: ULS -> ULS

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

cschIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

cscIfCan: 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.

sech: ULS -> ULS

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

sechIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

secIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

sin: ULS -> ULS

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

sinh: ULS -> ULS

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

sinhIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

sinIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

tan: ULS -> ULS

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

tanh: ULS -> ULS

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

tanhIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

tanIfCan: ULS -> Union(ULS, failed)

from PartialTranscendentalFunctions ULS

PartialTranscendentalFunctions ULS