On Wed, Aug 19, 2009 at 2:10 AM, Viny<hje...@hotmail.com> wrote:
>
> I have got the same problem of memory with maxima than Mani Chandra
> few days ago and I decided to make an interface to mathematica for
> solving the symbolic linear system which demand too much memory. The
> expression in my former mail, it's the symbolic answer expression of
> this linear system with mathematica.
> This memory limit it's a big problem. Maxima can't use the whole 12
> giga of RAM of my system while mathematica can. That why i turned
> toward mathematica.
> If I don't understand very well how to get away with? Sorry it' quite
> diffucult to me to write and understand english very well i'm from
> France.
You might try posting a French version of your question, since there
are a couple of French people around this list...
> Is there something to change in maxima source files or a
> function to put in the code for reallocation of memory?? Is it
> possible to put this function in a .sage file writting with python?
>
> Thankx
>
> On 19 août, 10:22, Robert Bradshaw <rober...@math.washington.edu>
> wrote:
>> On Aug 19, 2009, at 12:48 AM, Viny wrote:
>>
>>
>>
>> > Hi !
>>
>> > phi, v, u, Cxy are functions of (x,y). I use the command sage_eval
>> > (string, locals = { 'E':E, 'u':u, 'v':u, 'phi'=phi, ......}). string
>> > it's the expression. It's the only way i found for chang it to
>> > expression but it generate an error. Perhaps this come from the
>> > function the eval of phi[x,y], v[x,y],
>>
>> Ah, so this is a Mathematica string where a[x,y] is actually a
>> function application. You might be able to get away with
>>
>> s.replace("[", "(").replace("]", ")")
>>
>>
>>
>> > On 18 août, 11:02, Robert Bradshaw <rober...@math.washington.edu>
>> > wrote:
>> >> On Aug 17, 2009, at 3:45 AM, Viny wrote:
>>
>> >>> Hello!
>>
>> >>> Is it possible to have the equivalent sage expression of the
>> >>> following
>> >>> string, by using sage_eval() or another function without getting
>> >>> this
>> >>> error in while the transcription :
>>
>> >> There was talk a while back about x[1] giving a sub-scripted x, but I
>> >> don't think anything concrete came of it (IIRC there were bigger
>> >> symbolic changes going on at the time). What is phi, v, etc. in your
>> >> context?
>>
>> >>> /lib/python2.6/site-packages/sage/misc/sage_eval.py", line 199, in
>> >>> sage_eval return eval(source, sage.all.__dict__, locals) File
>> >>> "<string>", line 1, in <module> TypeError:
>> >>> 'sage.symbolic.expression.Expression' object is unsubscriptable
>>
>> >>> A part of the string is:
>>
>> >>> [(dx**4*dy**4*E**(2*phi[0, 0])*epsr**2* ((16*ni*(Cxy[0, 0] + (phi[0,
>> >>> -1] - 2*phi[0, 0] + phi[0, 1])/dy**2 + (phi[-1, 0] - 2*phi[0, 0] +
>> >>> phi[1, 0])/dx**2 + (ni*(-(E**phi[0, 0]*u[0, 0]) + v[0, 0]/E**phi
>> >>> [0,
>> >>> 0]))/epsr))/ (E**phi[0, 0]*epsr) + (8*(dx**2 + dy**2)* (dx**2*
>> >>> ((-4 +
>> >>> phi[0, -1] - phi[0, 1])*v[0, -1] + 8*v[0, 0] + (-4 - phi[0, -1]
>> >>> + phi
>> >>> [0, 1])*v[0, 1]) + dy**2*((-4 + phi[-1, 0] - phi[1, 0])*v[-1, 0] +
>> >>> 8*v[0, 0] + (-4 - phi[-1, 0] + phi[1, 0])*v[1, 0])))/
>> >>> (dx**4*dy**4) +
>> >>> ((-4 + phi[0, 0] - phi[0, 2])* (dx**2*((-4 + phi[0, 0] - phi[0,
>> >>> 2])*v
>> >>> [0, 0] + 8*v[0, 1] + (-4 - phi[0, 0] + phi[0, 2])*v[0, 2]) +
>> >>> dy**2*
>> >>> ((-4 + phi[-1, 1] - phi[1, 1])*v[-1, 1] + 8*v[0, 1] + (-4 - phi[-1,
>> >>> 1] + phi[1, 1])*v[1, 1])))/(dx**2*dy**4) + ((-4 + phi[0, 0] - phi
>> >>> [2,
>> >>> 0])* (dx**2*((-4 + phi[1, -1] - phi[1, 1])*v[1, -1] + 8*v[1, 0]
>> >>> + (-4
>> >>> - phi[1, -1] + phi[1, 1])*v[1, 1]) + dy**2*((-4 + phi[0, 0] -
>> >>> phi[2,
>> >>> 0])*v[0, 0] + 8*v[1, 0] + (-4 - phi[0, 0] + phi[2, 0])*v[2, 0])))/
>> >>> (dx**4*dy**2)))/ (2*dx**4*(-8*dy**2*E**phi[0, 0]*epsr*ni*(2 +
>> >>> dy**2*Cxy[0, 0] + phi[0, -1] - 2*phi[0, 0] + phi[0, 1]) -
>> >>> 16*dy**4*ni**2*v[0, 0] + E**(2*phi[0, 0])*epsr**2*((-4 + phi[0,
>> >>> 0] -
>> >>> phi[0, 2])*v[0, 0] + 4*v[0, 1] + (-phi[0, 0] + phi[0, 2])*v[0,
>> >>> 2]))
>> >>> + dx**2*dy**2*E**phi[0, 0]*epsr*(-16*dy**2*ni*(2 + phi[-1, 0] -
>> >>> 2*phi
>> >>> [0, 0] + phi[1, 0]) + E**phi[0, 0]*epsr*((-4 + phi[-1, 1] - phi[1,
>> >>> 1])* v[-1, 1] + 8*v[0, 1] + (-4 + phi[1, -1] - phi[1, 1])*v[1, -1] +
>> >>> 8*v[1, 0] - (8 + phi[-1, 1] + phi[1, -1] - 2*phi[1, 1])*v[1, 1])) +
>> >>> 2*dy**4*E**(2*phi[0, 0])*epsr**2*((-4 + phi[0, 0] - phi[2, 0])*v
>> >>> [0, 0]
>> >>> + 4*v[1, 0] + (-phi[0, 0] + phi[2, 0])*v[2, 0])) -
>> >>> (dx**4*dy**4*E**
>> >>> (2*phi[0, 0])*epsr**2*(64*(dx**(-2) + dy**(-2))**2 + (16*ni**2)/
>> >>> (E**
>> >>> (2*phi[0, 0])*epsr**2) + (4 - phi[0, 0] + phi[0, 2])**2/ dy**4 +
>> >>> (4 -
>> >>> phi[0, 0] + phi[2, 0])**2/dx**4)* (-(((ni**2*(16/dx**4 + 16/dy**4
>> >>> + (u
>> >>> [0, 0] - u[0, 2])**2/dy**4 + (u[0, 0] - u[2, 0])**2/dx**4 +
>> >>> (16*ni*(-
>> >>> (E**phi[0, 0]*u[0, 0]) + v[0, 0]/E**phi[0, 0])*(Cxy[0, 0] + (phi[0,
>> >>> -1] - 2*phi[0, 0] + phi[0, 1])/dy**2 + (phi[-1, 0] - 2*phi[0, 0] +
>> >>> phi[1, 0])/dx** 2 + (ni*(-(E**phi[0, 0]*u[0, 0]) + v[0, 0]/E**phi
>> >>> [0,
>> >>> 0]))/ epsr))/epsr + 16*(2/dx**2 + 2/dy**2 + (E**phi[0, 0]*ni*u[0, 0]
>> >>> + (ni*v[0, 0])/E**phi[0, 0])/epsr)**2 + (v[0, 0] - v[0, 2])**2/
>> >>> dy**4 + (v[0, 0] - v[2, 0])**2/dx**4))/(4*epsr**2) + ((2*dx**4*
>> >>> (8*dy**2*E**phi[0, 0]*epsr*ni*(2 - phi[0, -1] + 2*phi[0, 0] - phi
>> >>> [0,
>> >>> 1]) + 8*dy**4*E**phi[0, 0]*ni*(-(epsr*Cxy[0, 0]) + 2* E**phi[0, 0]
>> >>> *ni*u[0, 0]) + epsr**2*((4 + phi[0, 0] - phi[0, 2])* u[0, 0] -
>> >>> 4*u[0,
>> >>> 1] + (-phi[0, 0] + phi[0, 2])*u[0, 2])) + dx**2*dy**2*epsr*
>> >>> (16*dy**2*E**phi[0, 0]*ni*(2 - phi[-1, 0] + 2* phi[0, 0] - phi
>> >>> [1, 0])
>> >>> + epsr*((4 + phi[-1, 1] - phi[1, 1])* u[-1, 1] - 8*u[0, 1] + (4
>> >>> + phi
>> >>> [1, -1] - phi[1, 1])* u[1, -1] - 8*u[1, 0] - (phi[-1, 1] + phi
>> >>> [1, -1]
>> >>> - 2*(4 + phi[1, 1]))*u[1, 1])) + 2*dy**4*epsr**2* ((4 + phi[0, 0] -
>> >>> phi[2, 0])*u[0, 0] - 4*u[1, 0] + (-phi[0, 0] + phi[2, 0])*u[2,
>> >>> 0]))*
>> >>> (2*dx**4*(-8*dy**2*E**phi[0, 0]*epsr*ni*(2 + dy**2*Cxy[0, 0] + phi
>> >>> [0, -1] - 2*phi[0, 0] + phi[0, 1]) - 16*dy**4*ni**2*v[0, 0] +
>> >>> E**
>> >>> (2*phi[0, 0])*epsr**2*((-4 + phi[0, 0] - phi[0, 2])*v[0, 0] + 4*
>> >>> v[0,
>> >>> 1] + (-phi[0, 0] + phi[0, 2])*v[0, 2])) + dx**2*dy**2*E**phi[0, 0]
>> >>> *epsr*(-16*dy**2*ni*(2 + phi[-1, 0] - 2* phi[0, 0] + phi[1, 0]) +
>> >>> E**phi[0, 0]*epsr* ((-4 + phi[-1, 1] - phi[1, 1])*v[-1, 1] + 8*v
>> >>> [0, 1]
>> >>> + (-4 + phi[1, -1] - phi[1, 1])*v[1, -1] + 8*v[1, 0] - (8 + phi
>> >>> [-1,
>> >>> 1] + phi[1, -1] - 2*phi[1, 1])*v[1, 1])) + 2*dy**4*E**(2*phi[0,
>> >>> 0])
>> >>> *epsr**2*((-4 + phi[0, 0] - phi[2, 0])* v[0, 0] + 4*v[1, 0] + (-
>> >>> phi[0,
>> >>> 0] + phi[2, 0])*v[2, 0])))/ (64*dx**8*dy**8*E**(2*phi[0, 0])
>> >>> *epsr**4))
>> >>> * ((((-8*(dx**2 + dy**2)*(dx**2*((4 + phi[0, -1] - phi[0, 1])*u
>> >>> [0, -1]
>> >>> - 8*u[0, 0] + (4 - phi[0, -1] + phi[0, 1])*u[0, 1]) + dy**2*((4 +
>> >>> phi[-1, 0] - phi[1, 0])*u[-1, 0] - 8*u[0, 0] + (4 - phi[-1, 0] + phi
>> >>> [1, 0])*u[1, 0])))/(dx**4*dy**4) + ((4 + phi[0, 0] - phi[0, 2])*
>> >>> (dx**2*
>> >>> ((4 + phi[0, 0] - phi[0, 2])* u[0, 0] - 8*u[0, 1] + (4 - phi[0, 0] +
>> >>> phi[0, 2])*u[0, 2]) + dy**2*((4 + phi[-1, 1] - phi[1, 1])*u[-1,
>> >>> 1] -
>> >>> 8*u[0, 1] + (4 - phi[-1, 1] + phi[1, 1])*u[1, 1])))/(dx**2*dy**4)
>> >>> + ((4 + phi[0, 0] - phi[2, 0])*(dx**2*((4 + phi[1, -1] - phi[1,
>> >>> 1])*
>> >>> u[1, -1] - 8*u[1, 0] + (4 - phi[1, -1] + phi[1, 1])* u[1, 1]) +
>> >>> dy**2*
>> >>> ((4 + phi[0, 0] - phi[2, 0])*u[0, 0] - 8*u[1, 0] + (4 - phi[0,
>> >>> 0] +
>> >>> phi[2, 0])*u[2, 0])))/ (dx**4*dy**2) - (16*E**phi[0, 0]*ni*(Cxy
>> >>> [0, 0]
>> >>> + (phi[0, -1] - 2*phi[0, 0] + phi[0, 1])/dy**2 + (phi[-1, 0] -
>> >>> 2*phi
>> >>> [0, 0] + phi[1, 0])/dx**2 + (ni*(-(E**phi[0, 0]*u[0, 0]) + v[0,
>> >>> 0]/
>> >>> E**phi[0, 0]))/epsr))/epsr)* (2*dx**4*(-8*dy**2*E**phi[0, 0]
>> >>> *epsr*ni*
>> >>> (2 + dy**2*Cxy[0, 0] + phi[0, -1] - 2*phi[0, 0] + phi[0, 1]) -
>> >>> 16*dy**4*ni**2*v[0, 0] + E**(2*phi[0, 0])*epsr**2*((-4 + phi[0,
>> >>> 0] -
>> >>> phi[0, 2])*v[0, 0] + 4* v[0, 1] + (-phi[0, 0] + phi[0, 2])*v[0,
>> >>> 2]))
>> >>> + dx**2*dy**2*E**phi[0, 0]*epsr*(-16*dy**2*ni*(2 + phi[-1, 0] - 2*
>> >>> phi[0, 0] + phi[1, 0]) + E**phi[0, 0]*epsr* ((-4 + phi[-1, 1] -
>> >>> phi[1,
>> >>> 1])*v[-1, 1] + 8*v[0, 1] + (-4 + phi[1, -1] - phi[1, 1])*v[1, -1] +
>> >>> 8*v[1, 0] - (8 + phi[-1, 1] + phi[1, -1] - 2*phi[1, 1])*v[1, 1])) +
>> >>> 2*dy**4*E**(2*phi[0, 0])*epsr**2*((-4 + phi[0, 0] - phi[2, 0])* v[0,
>> >>> 0] + 4*v[1, 0] + (-phi[0, 0] + phi[2, 0])*v[2, 0])))/
>> >>> (64*dx**4*dy**4*E**(2*phi[0, 0])*epsr**2) - ((2*dx**4*
>> >>> (8*dy**2*E**phi
>> >>> [0, 0]*epsr*ni*(2 - phi[0, -1] + 2*phi[0, 0] - phi[0, 1]) +
>> >>> 8*dy**4*E**phi[0, 0]*ni*(-(epsr*Cxy[0, 0]) + 2* E**phi[0, 0]*ni*u
>> >>> [0,
>> >>> 0]) + epsr**2*((4 + phi[0, 0] - phi[0, 2])* u[0, 0] - 4*u[0, 1]
>> >>> + (-
>> >>> phi[0, 0] + phi[0, 2])*u[0, 2])) + dx**2*dy**2*epsr*
>> >>> (16*dy**2*E**phi
>> >>> [0, 0]*ni*(2 - phi[-1, 0] + 2* phi[0, 0] - phi[1, 0]) + epsr*((4 +
>> >>> phi
>> >>> [-1, 1] - phi[1, 1])* u[-1, 1] - 8*u[0, 1] + (4 + phi[1, -1] -
>> >>> phi[1,
>> >>> 1])* u[1, -1] - 8*u[1, 0] - (phi[-1, 1] + phi[1, -1] - 2*(4 +
>> >>> phi[1,
>> >>> 1]))*u[1, 1])) + 2*dy**4*epsr**2* ((4 + phi[0, 0] - phi[2, 0])*u
>> >>> [0, 0]
>> >>> - 4*u[1, 0] + (-phi[0, 0] + phi[2, 0])*u[2, 0]))* ((16*ni*(Cxy
>> >>> [0, 0]
>> >>> + (phi[0, -1] - 2*phi[0, 0] + phi[0, 1])/dy**2 + (phi[-1, 0] -
>> >>> 2*phi
>> >>> [0, 0] + phi[1, 0])/dx**2 + (ni*(-(E**phi[0, 0]*u[0, 0]) + v[0, 0]/
>> >>> E**phi[0, 0]))/epsr))/ (E**phi[0, 0]*epsr) + (8*(dx**2 + dy**2)*
>> >>> (dx**2*((-4 + phi[0, -1] - phi[0, 1])*v[0, -1] + 8*v[0, 0] + (-4 -
>> >>> phi[0, -1] + phi[0, 1])*v[0, 1]) + dy**2*((-4 + phi[-1, 0] - phi[1,
>> >>> 0])*v[-1, 0] + 8*v[0, 0] + (-4 - phi[-1, 0] + phi[1, 0])*v[1,
>> >>> 0])))/
>> >>> (dx**4*dy**4) + ((-4 + phi[0, 0] - phi[0, 2])*(dx**2*((-4 + phi[0,
>> >>> 0] - phi[0, 2])* v[0, 0] + 8*v[0, 1] + (-4 - phi[0, 0] + phi[0,
>> >>> 2])* v
>> >>> [0, 2]) + dy**2*((-4 + phi[-1, 1] - phi[1, 1])*v[-1, 1] + 8*v
>> >>> [0, 1]
>> >>> + (-4 - phi[-1, 1] + phi[1, 1])*v[1, 1])))/ (dx**2*dy**4) + ((-4
>> >>> + phi
>> >>> [0, 0] - phi[2, 0])* (dx**2*((-4 + phi[1, -1] - phi[1, 1])*v[1,
>> >>> -1] +
>> >>> 8*v[1, 0] + (-4 - phi[1, -1] + phi[1, 1])*v[1, 1]) + dy**2*((-4 +
>> >>> phi[0, 0] - phi[2, 0])*v[0, 0] + 8*v[1, 0] + (-4 - phi[0, 0] + phi
>> >>> [2, 0])*v[2, 0])))/(dx**4*dy**2)))/ (64*dx**4*dy**4*epsr**2))) +
>> >>> ((ni**2*(2*dx**4*(8*dy**2*E**phi[0, 0]*epsr*ni*(2 - phi[0, -1] +
>> >>> 2*phi
>> >>> [0, 0] - phi[0, 1]) + 8*dy**4*E**phi[0, 0]*ni* (-(epsr*Cxy[0, 0]) +
>> >>> 2*E**phi[0, 0]*ni*u[0, 0]) + epsr**2*((4 + phi[0, 0] - phi[0, 2])*u
>> >>> [0, 0] - 4*u[0, 1] + (-phi[0, 0] + phi[0, 2])*u[0, 2])) +
>> >>> dx**2*dy**2*epsr* (16*dy**2*E**phi[0, 0]*ni*(2 - phi[-1, 0] + 2*phi
>> >>> [0, 0] - phi[1, 0]) + epsr*((4 + phi[-1, 1] - phi[1, 1])*u[-1, 1] -
>> >>> 8*u[0, 1] + (4 + phi[1, -1] - phi[1, 1])*u[1, -1] - 8*u[1, 0] -
>> >>> (phi
>> >>> [-1, 1] + phi[1, -1] - 2*(4 + phi[1, 1]))*u[1, 1])) +
>> >>> 2*dy**4*epsr**2*
>> >>> ((4 + phi[0, 0] - phi[2, 0])*u[0, 0] - 4*u[1, 0] + (-phi[0, 0] +
>> >>> phi
>> >>> [2, 0])*u[2,
>>
>> ...
>>
>> plus de détails »
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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