Thank you ;)
On Fri, Jul 16, 2010 at 2:08 PM, Ralf Hemmecke
<address@hidden> wrote:
On 07/16/2010 12:52 PM, Vladimir Skokov wrote:
The problem is that my function contains logs, it is not just Taylor series.
For instance, I'd like to expand f(x,y)log(x) + g(x,y) at x=0, y=0.
So I expect to obtain
(expansion of f(x,y)) * log(x) + expansion of g(x,y)
Do you want to have a taylor series in x which has coefficients being taylor series in y? Or do you want the same with roles of x and y exchanged? Or do you want a *univariate* power series whose coefficients are (homogeneous) polynomials in x and y with a degree corresponding to the degree of the power in the taylor series?
Specify exactly what you want otherwise nobody will be able to help you.
I am not willing to guess your specification.
e.g. for one variable "series" does a good job
series(sin(x)*log(x),x=0)
(5) ->
(5)
log(x) 3 log(x) 5 log(x) 7 log(x) 9 log(x) 11
log(x)x - ------ x + ------ x - ------ x + ------ x - -------- x
6 120 5040 362880 39916800
+
12
O(x )
Type: GeneralUnivariatePowerSeries(_expression_
Integer,x,0)
However this is not Taylor series and therefore I cannot extract
coefficients as you specified.
????
Look at the type. So we have
(3) -> coefficient(s,1)
(3) log(x)
Type: _expression_(Integer)
I agree, that this might not be what you expected, but that is the problem with your input. You haven't exactly specified what you wanted.
Believe it or not, Axiom considers "log(x)" as a separate variable.
More natural would be something like
U := UnivariateTaylorSeries(Fraction Integer, 'x, 1)
x: U := x::U
log(x)
(3)
1 2 1 3 1 4 1 5 1 6
(x - 1) - - (x - 1) + - (x - 1) - - (x - 1) + - (x - 1) - - (x - 1)
2 3 4 5 6
+
1 7 1 8 1 9 1 10 11
- (x - 1) - - (x - 1) + - (x - 1) - -- (x - 1) + O((x - 1) )
7 8 9 10
Type: UnivariateTaylorSeries(Fraction(Integer),x,1)
Now the error message
(6) -> sin x
>> Error detected within library code:
"sincos: series expansion involves transcendental constants"
should be clear. The result is simply not representable, by a series with just rational coefficients.
Try
V := UnivariateTaylorSeries(_expression_ Integer, 'y, 1)
y: V := y::V
sin(y)
sin(y)*log(y)
instead.
It all depends on what you want. AXIOM *is* different from other CAS.
Of course the example I have written is oversimplified. I do not know
the structure of the function, it can contain sin(log(x)) for example.
But you know what you want as a result.
Mathematica allows repeated series expansion, however it fails with
complicated expressions due to some memory limitation.
A Mathematica Series is a *truncated* series. Remove the initial terms and all you are left with is an O(x^10) _expression_ which will not deliver any more coefficients. AXIOM's series really represent infinite objects.
Ralf
--
_____________________________________________
Dr. Vladimir Skokov
Theory Division
GSI Helmholtzzentrum für Schwerionenforschung GmbH
Planckstraße 1
D-64291 Darmstadt
------------------------------------------------------------------------
email: address@hidden
phone: +49 6159-71 2751
fax : +49 6159-71 2990