Hi Raymond,
If you know what your coefficients are and what operations you want to
perform with series, you can also do it in this way.
(2) -> C==>UnivariatePolynomial('a, Integer)
Type:
Void
(3) -> K==>Fraction C
Type:
Void
(4) -> S==>UnivariateLaurentSeries(K, 'x, 0)
Type:
Void
(5) -> x: S := 'x
(5) x
Type:
UnivariateLaurentSeries(Fraction(UnivariatePolynomial(a,Integer)),x,0)
(6) -> aS: S := 'a
(6) a
Type:
UnivariateLaurentSeries(Fraction(UnivariatePolynomial(a,Integer)),x,0)
(7) -> a: K := 'a
(7) a
Type:
Fraction(UnivariatePolynomial(a,Integer))
(8) -> 1/(1-a*x)
(8)
2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9
10 10
1 + a x + a x + a x + a x + a x + a x + a x + a x + a x + a x
+
11
O(x )
Type:
UnivariateLaurentSeries(Fraction(UnivariatePolynomial(a,Integer)),x,0)
(10) -> coefficient(s,5)
5
(10) a
Type:
Fraction(UnivariatePolynomial(a,Integer))
(11) -> ds := differentiate s
(11)
2 3 2 4 3 5 4 6 5 7 6 8 7 9 8
10 9
a + 2a x + 3a x + 4a x + 5a x + 6a x + 7a x + 8a x + 9a x +
10a x
+
11 10 11
11a x + O(x )
Type:
UnivariateLaurentSeries(Fraction(UnivariatePolynomial(a,Integer)),x,0)
(12) -> xds := x*ds
(12)
2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9
a x + 2a x + 3a x + 4a x + 5a x + 6a x + 7a x + 8a x + 9a x
+
10 10 11 11 12
10a x + 11a x + O(x )
Type:
UnivariateLaurentSeries(Fraction(UnivariatePolynomial(a,Integer)),x,0)
See also http://axiom-wiki.newsynthesis.org/TaylorSeries
Ralf
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