/usr/share/axiom-20170501/src/algebra/UPXSCAT.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | )abbrev category UPXSCAT UnivariatePuiseuxSeriesCategory
++ Author: Clifton J. Williamson
++ Date Created: 21 December 1989
++ Date Last Updated: 20 September 1993
++ Description:
++ \spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux
++ series in one variable.
UnivariatePuiseuxSeriesCategory(Coef) : Category == SIG where
Coef : Ring
NNI ==> NonNegativeInteger
RN ==> Fraction Integer
Term ==> Record(k:RN,c:Coef)
SIG ==> UnivariatePowerSeriesCategory(Coef,RN) with
series : (NNI,Stream Term) -> %
++ \spad{series(n,st)} creates a series from a common denomiator and
++ a stream of non-zero terms, where a term is an exponent-coefficient
++ pair. The terms in the stream should be ordered by increasing order
++ of exponents and \spad{n} should be a common denominator for the
++ exponents in the stream of terms.
multiplyExponents : (%,Fraction Integer) -> %
++ \spad{multiplyExponents(f,r)} multiplies all exponents of the power
++ series f by the positive rational number r.
if Coef has Algebra Fraction Integer then
integrate : % -> %
++ \spad{integrate(f(x))} returns an anti-derivative of the power
++ series \spad{f(x)} with constant coefficient 1.
++ We may integrate a series when we can divide coefficients
++ by rational numbers.
if Coef has integrate : (Coef,Symbol) -> Coef and _
Coef has variables : Coef -> List Symbol then
integrate : (%,Symbol) -> %
++ \spad{integrate(f(x),var)} returns an anti-derivative of the power
++ series \spad{f(x)} with respect to the variable \spad{var}.
if Coef has TranscendentalFunctionCategory and _
Coef has PrimitiveFunctionCategory and _
Coef has AlgebraicallyClosedFunctionSpace Integer then
integrate : (%,Symbol) -> %
++ \spad{integrate(f(x),y)} returns an anti-derivative of
++ the power series \spad{f(x)} with respect to the variable
++ \spad{y}.
RadicalCategory
--++ We provide rational powers when we can divide coefficients
--++ by integers.
TranscendentalFunctionCategory
--++ We provide transcendental functions when we can divide
--++ coefficients by integers.
if Coef has Field then Field
--++ Univariate Puiseux series over a field form a field.
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