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.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 »
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