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Science Forum Index » Math - Symbolic Forum » maxima, system of equations...
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| adriano meis... |
 Posted: Fri Jul 11, 2008 12:13 pm |
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Guest
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Hi,
I have win98 and Maxima 5.12.
Is it possible to solve this system of equations (variables=x,y) with
Maxima:
1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
?
I have tried with this instruction:
float(solve([3*x+exp(x)+y=8, 4*y+exp(y)+8*x=6], [x,y]));
but Maxima answers:
'algsys' cannot solve - system too complicated.
How can I do?
Do I need a different version of Maxim to solve it?
Do I need a different software to solve it(matlab,.. )?
Thanks,
adriano |
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| ... |
| Posted: Fri Jul 11, 2008 12:13 pm |
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Guest
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adriano meis schrieb:
Quote:
I have win98 and Maxima 5.12.
Is it possible to solve this system of equations (variables=x,y) with
Maxima:
1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
I have tried with this instruction:
float(solve([3*x+exp(x)+y=8, 4*y+exp(y)+8*x=6], [x,y]));
but Maxima answers:
'algsys' cannot solve - system too complicated.
How can I do?
Do I need a different version of Maxim to solve it?
Do I need a different software to solve it(matlab,.. )?
This sytem of equations is too complicated for a symbolic solution
regardless of the software used. Derive 6.10 reduces it to:
SOLVE([3*x+EXP(x)+y=8,4*y+EXP(y)+8*x=6],[x,y])
[EXP(EXP(y)/ *(3*EXP(3*y/2)+2*EXP(y/2)*(2*y+23))=8*EXP(3/4) AND ~
EXP(y)+8*x+4*y=6 AND EXP(EXP(y)/8+y/2)/=0]
A numerical solution, however, is possible of course:
[x=1.598455995 AND y=-1.740758807]
I expect Maxima top be able to do this as well.
Martin. |
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| G. A. Edgar... |
| Posted: Fri Jul 11, 2008 1:19 pm |
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Guest
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In article <6xMdk.25225$Ca.15040 at (no spam) twister2.libero.it>, adriano meis
<umiumiumi at (no spam) invalid.it> wrote:
Quote: Hi,
I have win98 and Maxima 5.12.
Is it possible to solve this system of equations (variables=x,y) with
Maxima:
1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
?
I have tried with this instruction:
float(solve([3*x+exp(x)+y=8, 4*y+exp(y)+8*x=6], [x,y]));
but Maxima answers:
'algsys' cannot solve - system too complicated.
How can I do?
Do I need a different version of Maxim to solve it?
Do I need a different software to solve it(matlab,.. )?
Thanks,
adriano
So you are solving the system algebraically, then converting the result
to floating point. Does Maxima have the Lambert W function (required
for the first step)? Maple does it this way...
Quote: eqs := {3*x+exp(x)+y=8,4*y+exp(y)+8*x=6};
{3 x + exp(x) + y = 8, 4 y + exp(y) + 8 x = 6}
RootOf(8*exp(_Z)-52+4*LambertW((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-Lambert
W((1/4)*exp(-2*_Z+3/2))-2*_Z+3/2)), y =
-3*RootOf(8*exp(_Z)-52+4*LambertW((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-Lamb
ertW((1/4)*exp(-2*_Z+3/2))-2*_Z+3/2))-exp(RootOf(8*exp(_Z)-52+4*LambertW
((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-LambertW((1/4)*exp(-2*_Z+3/2))-2*_Z+3
/2)))+8}
Quote: evalf(%);
{x = 1.598455995, y = -1.740758803}
Perhaps a better way would be to solve it numerically, and avoid the
need for the Lambert W function.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/ |
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| Axel Vogt... |
| Posted: Fri Jul 11, 2008 2:51 pm |
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G. A. Edgar wrote:
Quote: In article <6xMdk.25225$Ca.15040 at (no spam) twister2.libero.it>, adriano meis
umiumiumi at (no spam) invalid.it> wrote:
Hi,
I have win98 and Maxima 5.12.
Is it possible to solve this system of equations (variables=x,y) with
Maxima:
1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
?
I have tried with this instruction:
float(solve([3*x+exp(x)+y=8, 4*y+exp(y)+8*x=6], [x,y]));
but Maxima answers:
'algsys' cannot solve - system too complicated.
How can I do?
Do I need a different version of Maxim to solve it?
Do I need a different software to solve it(matlab,.. )?
Thanks,
adriano
So you are solving the system algebraically, then converting the result
to floating point. Does Maxima have the Lambert W function (required
for the first step)? Maple does it this way...
eqs := {3*x+exp(x)+y=8,4*y+exp(y)+8*x=6};
{3 x + exp(x) + y = 8, 4 y + exp(y) + 8 x = 6}
solve(eqs);
{x =
RootOf(8*exp(_Z)-52+4*LambertW((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-Lambert
W((1/4)*exp(-2*_Z+3/2))-2*_Z+3/2)), y =
-3*RootOf(8*exp(_Z)-52+4*LambertW((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-Lamb
ertW((1/4)*exp(-2*_Z+3/2))-2*_Z+3/2))-exp(RootOf(8*exp(_Z)-52+4*LambertW
((1/4)*exp(-2*_Z+3/2))+8*_Z-3*exp(-LambertW((1/4)*exp(-2*_Z+3/2))-2*_Z+3
/2)))+8}
evalf(%);
{x = 1.598455995, y = -1.740758803}
Perhaps a better way would be to solve it numerically, and avoid the
need for the Lambert W function.
This is: x a zero of 8*exp(z)-52-8*LambertW(1/4*exp(-2*z+3/2))+8*z
and y= -3*x-exp(x)+8. Now using Taylor in z=3/2 is approximated by
the polynomial -159713/2232+245259/5492*z+78353/4555*(z-3/2)^2+
60199/9457*(z-3/2)^3+50284/36513*(z-3/2)^4+24827/83197*(z-3/2)^5,
the desired x is quite well approximated through the only (?) real
root |
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| mark mcclure... |
| Posted: Mon Jul 14, 2008 7:50 am |
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On Jul 14, 12:53 pm, "adriano meis" <umiumi... at (no spam) invalid.it> wrote:
Quote: 1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
I don't want a symbolic solution. I want an approximated numerical solution
In maxima, use mnewton. You can also use implicit_plot to help locate
initial guesses for the roots. For example,
(%i1) f1 : 3*x+exp(x)+y-8$ f2 : 4*y+exp(y)+8*x-6$
(%i3) load(implicit_plot)$
(%i4) implicit_plot([f1=0,f2=0],[x,-2,2],[y,-2,2]);
Output file "/Users/markmcclure/maxplot.aqua".
(%o4) done
The picture indicates a root around (2,-2), so
(%i5) load(mnewton)$
(%i6) mnewton([3*x+exp(x)+y-8,4*y+exp(y)+8*x-6],[x,y],[2,-2]);
0 errors, 0 warnings
(%o6) [[x = 1.598455995475045, y = - 1.740758807198118]]
Incidently, you're likely to get maxima help specifically
from the maxima discussion group. You can browse messages
via gmane:
http://news.gmane.org/gmane.comp.mathematics.maxima.general
Also, it did not take me long to find the answer to your
question on Maxima's documentation page:
http://maxima.sourceforge.net/documentation.html
I find Maxima by Example (listed on that page) to be
particularly nice.
Have fun,
Mark McClure |
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| adriano meis... |
| Posted: Mon Jul 14, 2008 11:53 am |
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<clicliclic at (no spam) freenet.de> wrote in message
1fb7c3ce-d78e-4342-8e15-8c6564f119da at (no spam) z72g2000hsb.googlegroups.com...
Quote: 1) 3*x+exp(x)+y=8
2) 4*y+exp(y)+8*x=6
I have tried with this instruction:
float(solve([3*x+exp(x)+y=8, 4*y+exp(y)+8*x=6], [x,y]));
but Maxima answers:
'algsys' cannot solve - system too complicated.
How can I do?
This sytem of equations is too complicated for a symbolic solution
regardless of the software used.
I don't want a symbolic solution. I want an approximated numerical solution
(obtained by an
iterative method for example) of many systems like the one I have exposed.
What software could
I use? Can Maxima solve it numerically? How can Maxima do it?
Thanks,
adr |
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