In my ongoing interest in combinatorics there seems to be lapse in
Axiom/Fricas
In the attached script (repeated below) investigating "series(f,x=0)"
I can correctly differentiate, integrate, add, and subtract correctly;
but not multiply.
One of the rules for the Method of Coefficients is
[t^n](t*f(t))=[t^(n-1)] f(t)
The internal multiplication by the indexing variable is used elsewhere
as well.
Is there any way to append the multiply operation into
GeneralUnivariatePowerSeries or UnivariatePuiseuxSeries? Or do I have
to define a new domain or some such? That does seem to be a waste.
--
I guess that I will have to make a list [f(t),[t^n]f(t)] i.e.
[generating function, term n] in order to access the series for f(t) in
the blind. That is ask about [t^n]f(t) when n is not instantiated.
Even though the diff...add rules seem to have a grasp on the
coefficients and _seems_ to understand the generating function f(t) (I
could be wrong here).
--
Ray
s_test:= series(1/(1-a*x) ,x=0)
++ Now I can differentiate
D(s_test,x)
++ Integrate
integrate(s_test,x)
++ Add
s1_test:=series(1/(1-b*x),x=0)
ss_test:=s_test+s1_test
coefficient(ss_test,4)
++
++ But I can't multiply
sx_test:=x*s_test
coefficient(sx_test,4)
D(sx_test,x)
++ Random Leibniz product rule test
++ D(x*s_test,x)-x*D(s_test,x)-s_test
++
++ And just a puzzle to me
++ (x^2 * x^4)
++ x^r * x^s
--
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s_test:= series(1/(1-a*x) ,x=0)
++ Now I can differentiate
D(s_test,x)
++ Integrate
integrate(s_test,x)
++ Add
s1_test:=series(1/(1-b*x),x=0)
ss_test:=s_test+s1_test
coefficient(ss_test,4)
++
++ But I can't multiply
sx_test:=x*s_test
coefficient(sx_test,4)
D(sx_test,x)
++ Random Leibniz product rule test
++ D(x*s_test,x)-x*D(s_test,x)-s_test
++
++ And just a puzzle to me
++ (x^2 * x^4)
++ x^r * x^s
