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#192 new simpsum / taylor bug
This is a new simpsum / taylor bug. Note that I used a patched version of
Maxima, as described in the simpsum bug thread:
combin.lisp
933,935c927,929
< ;; nil ;; Kratt5 26.11.2002
< ; #-cl
< (let (*a *n (var *var*)) ; freevar expects "var", not "*var*"
---
> nil
> #-cl
> (let (*a *n)
(C1) build_info();
Maxima version: 5.9.0rc3
Maxima build date: 21:0 11/26/2002
host type: i686-pc-linux-gnu
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL-2-5.0
(D1)
(C2)
factsum3(mt,ej):=sum((-1)^(k+1)/(k*mt^k)*sum((1-l)^k-l^k,l,1,ej),k,1,INF)$
(C3) taylor(factsum3(mt,ej),[mt,0,3,ASYMP]);
ej ej ej
==== ==== ====
\ \ \ 3 2
> (- 2 l + 1) > (- 2 l + 1) > (- 2 l + 3 l - 3 l + 1)
/ / /
==== ==== ====
l = 1 l = 1 l = 1
(D3)/T/ ----------------- - ----------------- + -------------------------------
mt 2 3
2 mt 3 mt
+ . . .
(C4) taylor(factsum3(mt,ej),[mt,0,3,ASYMP]),simpsum;
2 2 4 2
l l l + l
(D4)/T/ - -- + ----- - ------- + . . .
mt 2 3
2 mt 6 mt
(C5)
This is nearly correct, only l should be changed to ej...
Martin
Logged In: YES
user_id=501686
The reported bug is not present in the current cvs version of
Maxima.
Thank you for your report. If you see this bug in a later version
of Maxima, please submit a new bug report.
Logged In: YES
user_id=501686
Reopening this bug report; it was closed by mistake. The
reported problem is still present in cvs Maxima.
For the record here is a more readable presentation of the
same example.
(%i2)
factsum3(mt,ej):=sum((-1)^(k+1)/(k*mt^k)*sum((1-l)^k-l^k,l,1,ej),k,1,inf);
(%o2) factsum3(mt,ej):=sum(
(-1)^(k+1)/(k*mt^k)*sum((1-l)^k-l^k,l,1,ej),k,1,
inf)
(%i3) taylor(factsum3(mt,ej),[mt,0,3,asymp]);
(%o3) ('sum(-2*l+1,l,1,ej))/mt-('sum(-2*l+1,l,1,ej))/(2*mt^2)
+('sum(-2*l^3+3*l^2-3*l+1,l,1,ej))
/(3*mt^3)
(%i4) ''%, simpsum;
(%o4) -(6*ej^2*mt^2-3*ej^2*mt+ej^4+ej^2)/(6*mt^3) <-- OK
(%i5) taylor(factsum3(mt,ej),[mt,0,3,asymp]), simpsum;
(%o5) -l^2/mt+l^2/(2*mt^2)-(l^4+l^2)/(6*mt^3) <-- OOPS
Diff:
Still present (5.29.1).
From what I can tell, if the operation is carried out in two steps it matches the expected result:
(%i2) factsum3(mt,ej):=sum((-1)^(k+1)/(kmt^k)sum((1-l)^k-l^k,l,1,ej),k,1,inf)$
(%i3) taylor(factsum3(mt,ej),[mt,0,3,asymp]);
(%o3) ('sum(-2l+1,l,1,ej))/mt-('sum(-2l+1,l,1,ej))/(2mt^2)
+('sum(-2l^3+3l^2-3l+1,l,1,ej))/(3mt^3)
(%i4) %, simpsum;
(%o4) -(6ej^2mt^2-3ej^2mt+ej^4+ej^2)/(6mt^3)
but if you try combining the two steps, you get result observed in the original report:
(%i5) taylor(factsum3(mt,ej),[mt,0,3,asymp]), simpsum;
(%o5) -l^2/mt+l^2/(2mt^2)-(l^4+l^2)/(6mt^3)
The bug only appears if simpsum is enable when taylor is called:
(%i6) factsum3 (mt, ej), simpsum;
(%o6) 'sum((-1)^(k+1)('sum((1-l)^k-l^k,l,1,ej))/(kmt^k),k,1,inf)
(%i7) taylor (%, [mt, 0, 3, asymp]);
(%o7) ('sum(-2l+1,l,1,ej))/mt-('sum(-2l+1,l,1,ej))/(2mt^2)
+('sum(-2l^3+3l^2-3l+1,l,1,ej))/(3*mt^3)
(%i9) taylor (%o6, [mt, 0, 3, asymp]), simpsum;
(%o9) -l^2/mt+l^2/(2mt^2)-(l^4+l^2)/(6mt^3)