ElementaryFunctionsUnivariatePuiseuxSeries(Coef, ULS, UPXS, EFULS)ΒΆ

efupxs.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.

^: (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