To have more fun, I have this:
ma...@asus-eee:/opt/sage$ ./sage
----------------------------------------------------------------------
| Sage Version 4.1.2, Release Date: 2009-10-14 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: t=var('t')
sage: a=sqrt((sin(t))^2 + (cos(t))^2)
sage: integrate(a, t, 0, 2*pi)
pi
sage:
And this is maxima session:
;;; Loading #P"/opt/sage/local/lib/ecl/defsystem.fas"
;;; Loading #P"/opt/sage/local/lib/ecl/cmp.fas"
;;; Loading #P"/opt/sage/local/lib/ecl/sysfun.lsp"
Maxima 5.19.1 http://maxima.sourceforge.net
Using Lisp ECL 9.8.4
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(1784072509+1));
<sage-display>(%o1) 0
<sage-display>(%o2) __SAGE_SYNCHRO_MARKER_1784072510
(%i3) display2d:false; domain: complex; keepfloat: true; load
(topoly_solver);
<sage-display>
(%o3) false
<sage-display>
(%o4) complex
<sage-display>
(%o5) true
<sage-display>
(%o6) "/opt/sage/local/share/maxima/5.19.1/share/contrib/
topoly_solver.mac"
(%i7) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(572821093+1));
<sage-display>
(%o7) 0
<sage-display>
(%o8) "__SAGE_SYNCHRO_MARKER_572821094"
(%i9) nolabels:true;
<sage-display>
(%o9) true
(%i10) :lisp (defun tex-derivative (x l r) (tex (if $derivabbrev (tex-
dabbrev x) (tex-d x '\\partial)) l r lop rop ))
0;sconcat("__SAGE_SYNCHRO_MARKER_",(86715755+1));
TEX-DERIVATIVE
(%i10) <sage-display>
(%o10) 0
<sage-display>
(%o11) "__SAGE_SYNCHRO_MARKER_86715756"
(%i12) 0;
<sage-display>
(%o12) 0
(%i13) sage0 : (((sin(t))^(2))+((cos(t))^(2)))^(1/2)$
<sage-display>
(%i14) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(1995813336+1));
<sage-display>
(%o14) 0
<sage-display>
(%o15) "__SAGE_SYNCHRO_MARKER_1995813337"
(%i16) sage1 : t$
<sage-display>
(%i17) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(1953885597+1));
<sage-display>
(%o17) 0
<sage-display>
(%o18) "__SAGE_SYNCHRO_MARKER_1953885598"
(%i19) sage2 : 0$
<sage-display>
(%i20) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(333161657+1));
<sage-display>
(%o20) 0
<sage-display>
(%o21) "__SAGE_SYNCHRO_MARKER_333161658"
(%i22) sage3 : (%pi)*(2)$
<sage-display>
(%i23) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(1111779811+1));
<sage-display>
(%o23) 0
<sage-display>
(%o24) "__SAGE_SYNCHRO_MARKER_1111779812"
(%i25) sage4 : integrate(sage0,sage1,sage2,sage3)$
<sage-display>
(%i26) kill(sage3)$kill(sage2)$kill(sage1)$kill(sage0)$kill(sage3)$kill
(sage2)$kill(sage1)$kill(sage0)$0;sconcat("__SAGE_SYNCHRO_MARKER_",
(2067936922+1));
<sage-display><sage-display><sage-display><sage-display><sage-display>
(%o30) 0
<sage-display>
(%o31) "__SAGE_SYNCHRO_MARKER_2067936923"
(%i32) sage5 : 0$
<sage-display>
(%i33) 0;sconcat("__SAGE_SYNCHRO_MARKER_",(1769152096+1));
<sage-display>
(%o33) 0
<sage-display>
(%o34) "__SAGE_SYNCHRO_MARKER_1769152097"
(%i35) sage6 : gen(sage5)$
<sage-display>
(%i36) kill(sage5)$kill(sage5)$0;sconcat("__SAGE_SYNCHRO_MARKER_",
(1390469140+1));
<sage-display><sage-display>
(%o37) 0
<sage-display>
so maxima is doing
sage0 : (((sin(t))^(2))+((cos(t))^(2)))^(1/2)$
sage1 : t$
sage2 : 0$
sage3 : (%pi)*(2)$
sage4 : integrate(sage0,sage1,sage2,sage3)
Lets try it:
----------------------------------------------------------------------
| Sage Version 4.1.2, Release Date: 2009-10-14 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: t=var('t')
sage: a=sqrt((sin(t))^2 + (cos(t))^2)
sage: integrate(a, t, 0, 2*pi)
pi
sage: maxima("(sage0:(((sin(t))^(2))+((cos(t))^(2)))^(1/2),sage1 : t,
sage2 : 0, sage3 : (%pi)*(2), sage4 : integrate
(sage0,sage1,sage2,sage3))")
%pi
Tests within maxima
1. maxima from debian package:
ma...@asus-eee:~$ maxima --batch-string="integrate(sqrt(sin(x)^2+cos(x)
^2),x,0,2*%pi);"
Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
2 2
(%i1) integrate(sqrt(sin (x) + cos (x)), x, 0, 2 %pi)
(%o1) 2 %pi
ma...@asus-eee:~$
2. maxima in Sage:
ma...@asus-eee:/opt/sage$ ./sage
----------------------------------------------------------------------
| Sage Version 4.1.2, Release Date: 2009-10-14 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: maxima("integrate(sqrt(sin(t)^2+cos(t)^2),t,0,2*%pi)")
%pi
sage:
Broken version of Maxima? Did Maxima in Sage passed tests? Maxima
commes with many tests from upstream. Have these tests been tested?
Robert
On 16 říj, 20:28, Jason Grout <jason-s...@creativetrax.com> wrote:
> Something is seriously wrong with simple integration in 4.1.2:
>
> sage: a=sqrt((sin(t))^2 + (cos(t))^2)
> sage: integrate(a, t, 0, 2*pi) # WRONG!
> pi
> sage: a.simplify_full().simplify_trig()
> 1
> sage: integrate(a.simplify_full().simplify_trig(), t, 0, 2*pi)
> 2*pi
>
> Any idea what is going on?
>
> Thanks,
>
> Jason
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