Maxima 5.20.1. The minimal version of it is:
I(x,y):=f+dxf*x+dyf*y+(1/2)*(d2xf*x^2+2*dxyf*x*y+d2yf*y^2)+(1/6)*(d3xf*x^3+3*d2xyf*x^2*y+3*dx2yf*x*y^2+d3yf*y^3)+(1/24)*(d4xf*x^4+4*d3xyf*x^3*y+6*d2x2yf*x^2*y^2+4*dx3yf*x*y^3+d4yf*y^4)+(1/120)*(d5xf*x^5+5*d4xyf*x^4*y+10*d3x2yf*x^3*y^2+10*d2x3yf*x^2*y^3+5*dx4yf*x*y^4+d5yf*y^5)$
DxI(x,y):=dxf+d2xf*x+dxyf*y+(1/2)*(d3xf*x^2+2*d2xyf*x*y+dx2yf*y^2)+(1/6)*(d4xf*x^3+3*d3xyf*x^2*y+3*d2x2yf*x*y^2+dx3yf*y^3)+(1/24)*(d5xf*x^4+4*d4xyf*x^3*y+6*d3x2yf*x^2*y^2+4*d2x3yf*x*y^3+dx4yf*y^4)$
DyI(x,y):=dyf+dxyf*x+d2yf*y+(1/2)*(d2xyf*x^2+2*dx2yf*x*y+d3yf*y^2)+(1/6)*(d3xyf*x^3+3*d2x2yf*x^2*y+3*dx3yf*x*y^2+d4yf*y^3)+(1/24)*(d4xyf*x^4+4*d3x2yf*x^3*y+6*d2x3yf*x^2*y^2+4*dx4yf*x*y^3+d5yf*y^4)$
eq1: I(deltax,0) = f(i+1,j)$
eq2: DxI(deltax,0) = dxf(i+1,j)$
eq3: DyI(deltax,0) = dyf(i+1,j)$
eq4: I(0,deltay) = f(i,j+1)$
eq5: DxI(0,deltay) = dxf(i,j+1)$
eq6: DyI(0,deltay) = dyf(i,j+1)$
eq7: I(deltax,deltay) = f(i+1,j+1)$
eq8: DxI(deltax,deltay) = dxf(i+1,j+1)$
eq9: DyI(deltax,deltay) = dyf(i+1,j+1)$
eq10: I(-deltax,-deltay) = f(i-1,j-1)$
eq11: DxI(-deltax,-deltay) = dxf(i-1,j-1)$
eq12: DyI(-deltax,-deltay) = dyf(i-1,j-1)$
eq13: I(-deltax,0) = f(i-1,j)$
eq14: DxI(-deltax,0) = dxf(i-1,j)$
eq15: DyI(-deltax,0) = dyf(i-1,j)$
eq16: I(deltax,-deltay) = f(i+1,j-1)$
eq17: DxI(deltax,-deltay) = dxf(i+1,j-1)$
eq18: DyI(deltax,-deltay) = dyf(i+1,j-1)$
eq19: I(0,-deltay) = f(i,j-1)$
eq20: DxI(0,-deltay) = dxf(i,j-1)$
eq21: DyI(0,-deltay) = dyf(i,j-1)$
eq22: I(-deltax,deltay) = f(i-1,j+1)$
eq23: DxI(-deltax,deltay) = dxf(i-1,j+1)$
eq24: DyI(-deltax,deltay) = dyf(i-1,j+1)$
linsolve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17,eq18,eq19,eq20,eq21,eq22,eq23,eq24],[dxyf,d2xf,d2yf,d3xf,d2xyf,dx2yf,d3yf,d4xf,d3xyf,d2x2yf,dx3yf,d4yf,d5xf,d4xyf,d3x2yf,d2x3yf,dx4yf,d5yf]);
2011/11/14 Stavros Macrakis <macrakis at alum.mit.edu>
> Could you please include a self-contained, reproducible example (ideally
> minimal)? That might help us figure out the problem. It would also be
> useful to report the version of Maxima you are using -- use bug_report() to
> get that information.
>
> By self-contained and reproducible, I mean that it can be run as a batch
> file in a fresh Maxima and doesn't require the tester to guess at
> appropriate parameter values, etc.
>
> -s
>
> On Mon, Nov 14, 2011 at 11:36, Fernanda Farias <feboccaccio at gmail.com>wrote:
>
>> Dear list members,
>>
>> I have been trying to use "solve" with 24 equations and expecting maxima
>> to give me 18 unknown variables. But when I try to do this all at once it
>> does not work, all I get is "[ ]". For the simplest case, I can give the
>> code which equations (about 3 or 6) are necessary for obtaining one
>> variable correctly, but this is enough since I am looking for the general
>> case.
>>
>> I wrote the equations as following and I give the values for 8 points
>> (giving the total of 24 equations), for example:
>>
>> One given point:
>> eq1: I(deltax,0) = f(i+1,j)$
>> eq2: DxI(deltax,0) = dxf(i+1,j)$
>> eq3: DyI(deltax,0) = dyf(i+1,j)$
>>
>> Equations:
>>
>> I(x,y):=f+dxf*x+dyf*y+(1/2)*(d2xf*x^2+2*dxyf*x*y+d2yf*y^2)+(1/6)*(d3xf*x^3+3*d2xyf*x^2*y+3*dx2yf*x*y^2+d3yf*y^3)+(1/24)*(d4xf*x^4+4*d3xyf*x^3*y+6*d2x2yf*x^2*y^2+4*dx3yf*x*y^3+d4yf*y^4)+(1/120)*(d5xf*x^5+5*d4xyf*x^4*y+10*d3x2yf*x^3*y^2+10*d2x3yf*x^2*y^3+5*dx4yf*x*y^4+d5yf*y^5)$
>>
>>
>> DxI(x,y):=dxf+d2xf*x+dxyf*y+(1/2)*(d3xf*x^2+2*d2xyf*x*y+dx2yf*y^2)+(1/6)*(d4xf*x^3+3*d3xyf*x^2*y+3*d2x2yf*x*y^2+dx3yf*y^3)+(1/24)*(d5xf*x^4+4*d4xyf*x^3*y+6*d3x2yf*x^2*y^2+4*d2x3yf*x*y^3+dx4yf*y^4)$
>>
>>
>> DyI(x,y):=dyf+dxyf*x+d2yf*y+(1/2)*(d2xyf*x^2+2*dx2yf*x*y+d3yf*y^2)+(1/6)*(d3xyf*x^3+3*d2x2yf*x^2*y+3*dx3yf*x*y^2+d4yf*y^3)+(1/24)*(d4xyf*x^4+4*d3x2yf*x^3*y+6*d2x3yf*x^2*y^2+4*dx4yf*x*y^3+d5yf*y^4)$
>>
>> Any ideas?
>>
>> Regards.
>> --
>>
>>
>>
>>
>>
>> _______________________________________________
>> Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>
>>
>
--
Msc Fernanda Farias
DMM-PEMM/COPPE/UFRJ