Hello.
I am new to axiom and so far it is very appealing to me.
So, I have been trying to apply it to some of my current problems
(numerical computations mainly).
I need to evaluate higher order derivatives of Lewis integral (
10.1103/PhysRev.102.537 , Appendix A, eq. 9) for further fortran export.
With a straightforward approach (see -----v1 below), I'm running out of
memory already on the second derivative.
I was able to progress slightly further (see ----v2) adapting an example
from the 'Derivatives' chapter of the axiom book (sec.1.11), but
i don't know how to export results into fortran, since after evaluation of
dLidMudAdB I need to somehow define and export all functions like
D(bt(mu,a,b),[a,b,mu]),
D(bt(mu,a,b),[b,mu]) and so on.
All in all, my question is: what is the best way to compute, say, 5th
derivative of 'Li' function from examples below and
export this result to fortran?
P.S: I was under impression that attachements to mail lists are not a good
idea.
If they are fine actually, next time i'll try to use them to include code.
P.P.S: sorry for my english.
--------------- v1
)clear all
LiBt :=_
mu * ((qx-px)^2 + (qy-py)^2 + (qz-pz)^2 + (a+b)^2 )_
+ b * ( mu^2 + qx^2 + qy^2 + qz^2 + a^2 )_
+ a * ( mu^2 + px^2 + py^2 + pz^2 + b^2 );
LiAg :=_
( (qx-px)^2 + (qy-py)^2 + (qz-pz)^2 + (a+b)^2 )_
* ( qx^2 + qy^2 + qz^2 + (mu+a)^2 )_
* ( px^2 + py^2 + pz^2 + (mu+b)^2 );
LiD := sqrt( LiBt^2 - LiAg );
Li := %pi^2 / LiD * log( (LiBt + LiD) / (LiBt - LiD) );
dLidMudA := D(Li,[mu,a]);
----------- v2
)clear all
dt := operator 'dt
bt := operator 'bt
ag := operator 'ag
Li := (%pi^2 / dt(bt(mu,a,b),ag(mu,a,b)))_
* log(_
( bt(mu,a,b) + dt( bt(mu,a,b), ag(mu,a,b)))_
/ ( bt(mu,a,b) - dt( bt(mu,a,b), ag(mu,a,b))) )
dLidMudAdB := D(Li,[mu,a,b])
--
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