ElementaryFunctionsUnivariateLaurentSeries(Coef, UTS, ULS)ΒΆ

efuls.spad line 1

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