Run the solve command in symbolic math toolbox ?

I want to solve 12 equations containing 12 variables using the solve command but my college doesn't have the symbolic math toolbox. can anyone pls solve these and post the results, i'll be really grateful as my whole project depends on these.

Equations:

1)(x1-xf1)^2+(y1-yf1)^2+(z1-zf1)^2-9^2=0

2)(x2-xf2)^2+(y2-yf2)^2+(z2-zf2)^2-11^2=0

3)(x3-xf3)^2+(y3-yf3)^2+(z3-zf3)^2-10^2=0

4)(x4-xf4)^2+(y4-yf4)^2+(z4-zf4)^2-8^2=0

5)(x1-xp)^2+(y1-yp)^2+(z1-zp)^2-12.065^2=0

6)(x2-xp)^2+(y2-yp)^2+(z2-zp)^2-10.25^2=0

7)(x3-xp)^2+(y3-yp)^2+(z3-zp)^2-10.25^2=0

8)(x4-xp)^2+(y4-yp)^2+(z4-zp)^2-12.065^2=0

9)(x1-x2)^2+(y1-y2)^2+(z1-z2)^2-4.5^2=0

10)(x1-x3)^2+(y1-y3)^2+(z1-z3)^2-4*(4.5^2)=0

11)(x1-x4)^2+(y1-y4)^2+(z1-z4)^2-9*(4.5^2)=0

12)(x3-x2)^2+(y3-y2)^2+(z3-z2)^2-4.5^2=0

I want to find x1,x2,x3,x4,y1,y2,y3,y4,z1,z2,z3,z4 in terms of the other variables so that i can use them in further calculation.

[Ivan van der Kroon]

Can you post a working m-file?

[Walter Roberson]

I started this executing in Maple, but it is taking quite a bit of time.

Are there restrictions that can be placed on the variables? For example are they all real-valued? Non-negative?

With a set of equations as large as that, branching through all the real vs complex possibilities takes a long time.

[Walter Roberson]

I ran this for about 4 1/2 hours, but it grew past 2 Gb so I had to kill it.

If there were constraints on the value, the run-time would potentially be much less.

Is the task to find the intersection of several spheres? If so then Roger Stafford has written about the algebra of that several times; the most common answer once past 2 spheres is "you can't satisfy all those constraints simultaneously". It would depend, though, on the geometry of the situation.

[Walter Roberson]

m-file equivalent:

syms x1 x2 x3 x4 y1 y2 y3 y4 z1 z2 z3 x4

syms xf1 xf2 xf3 xf4 yf1 yf2 yf3 yf4 zf1 zf2 zf3 zf4

syms xp yp zp

eq1 = (x1-xf1)^2+(y1-yf1)^2+(z1-zf1)^2-9^2;

eq2 = (x2-xf2)^2+(y2-yf2)^2+(z2-zf2)^2-11^2;

eq3 = (x3-xf3)^2+(y3-yf3)^2+(z3-zf3)^2-10^2;

eq4 = (x4-xf4)^2+(y4-yf4)^2+(z4-zf4)^2-8^2;

eq5 = (x1-xp)^2+(y1-yp)^2+(z1-zp)^2-12.065^2;

eq6 = (x2-xp)^2+(y2-yp)^2+(z2-zp)^2-10.25^2;

eq7 = (x3-xp)^2+(y3-yp)^2+(z3-zp)^2-10.25^2;

eq8 = (x4-xp)^2+(y4-yp)^2+(z4-zp)^2-12.065^2;

eq9 = (x1-x2)^2+(y1-y2)^2+(z1-z2)^2-4.5^2;

eq10 = (x1-x3)^2+(y1-y3)^2+(z1-z3)^2-4*(4.5^2);

eq11 = (x1-x4)^2+(y1-y4)^2+(z1-z4)^2-9*(4.5^2);

eq12 = (x3-x2)^2+(y3-y2)^2+(z3-z2)^2-4.5^2;

sols = solve(eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,x1,x2,x3,x4,y1,y2,y3,y4,z1,z2,z3,z4);

for K = 1 : length(sols)

fprintf('\nSolution #%d\n\n',K);

sols(K)

end

[Sourabh Bajaj]

Pls help me with running the simulation as i dont have the simulation and really need the solution. is there some other way to solve these as you can't do it on paper.

[Sourabh Bajaj]

All the variables are real no. and the problem is about spheres.

[Sourabh Bajaj]

The equations would satisfy to give a distinct and discrete solution as I have checked that. The other constant come in such a manner that it'll give a solution. I want a generalized formula for the variables so that i can use it in some other program.

[Walter Roberson]

"Pls help me with running the simulation" -- I've been running it for the last 12 hours, the last 4 or so hours of which have been constrained to real numbers. There are still a lot of cases to check.

[Walter Roberson]

It was too large for me to run constrained to real numbers.

Even just equations 1, 2, and 9 together are giving the system problems. I recommend that you read Roger Stafford's postings about intersecting spheres.

[Sourabh Bajaj]

will it help if we eliminate the equations 4,8,11 and then reduce it to 9. also if we limit the variables from -100 to 100. i think that might significantly reduce the iterations.

I have also simplified the equations to reduce non linearity so i'll post them.

1)(xp-xf1)*(2*x1-xp-xf1)+(yp-yf1)*(2*y1-yp-yf1)+(zp-zf1)*(2*z1-zp-zf1)-9*9+12.065*12.065

2) 2*xp*xp-2*xp*(x1+x2)+2*x1*x2+2*yp*yp-2*yp*(y1+y2)+2*y1*y2+2*zp*zp-2*zp*(z1+z2)+2*z1*z2-10.25*10.25-12.065*12.065+4.5*4.5

3) xf1*xf1+xf2*xf2-2*x1*xf1-2*x2*xf2+2*x1*x2+yf1*yf1+yf2*yf2-2*y1*yf1-2*y2*yf2+2*y1*y2+zf1*zf1+zf2*zf2-2*z1*zf1-2*z2*zf2+2*z1*z2-9*9-11*11+4.5*4.5

4)

(xp-xf2)*(2*x2-xp-xf2)+(yp-yf2)*(2*y2-yp-yf2)+(zp-zf2)*(2*z2-zp-zf2)-11*11+10.25*10.25

5) 2*xp*xp-2*xp*(x1+x3)+2*x1*x3+2*yp*yp-2*yp*(y1+y3)+2*y1*y3+2*zp*zp-2*zp*(z1+z3)+2*z1*z3-10.25*10.25-12.065*12.065+4*4.5*4.5

6) xf1*xf1+xf3*xf3-2*x1*xf1-2*x3*xf3+2*x1*x3+yf1*yf1+yf3*yf3-2*y1*yf1-2*y3*yf3+2*y1*y3+zf1*zf1+zf3*zf3-2*z1*zf1-2*z3*zf3+2*z1*z3-9*9-10*10+4*4.5*4.5

7) (xp-xf3)*(2*x3-xp-xf3)+(yp-yf3)*(2*y3-yp-yf3)+(zp-zf3)*(2*z3-zp-zf3)-10*10+10.25*10.25

8) 2*xp*xp-2*xp*(x3+x2)+2*x3*x2+2*yp*yp-2*yp*(y3+y2)+2*y3*y2+2*zp*zp-2*zp*(z3+z2)+2*z3*z2-10.25*10.25-10.25*10.25+4.5*4.5

9) xf3*xf3+xf2*xf2-2*x3*xf3-2*x2*xf2+2*x3*x2+yf3*yf3+yf2*yf2-2*y3*yf3-2*y2*yf2+2*y3*y2+zf3*zf3+zf2*zf2-2*z3*zf3-2*z2*zf2+2*z3*z2-10*10-11*11+4.5*4.5

variables : x1,x2,x3,y1,y2,y3,z1,z2,z3

[Sourabh Bajaj]

I have simplified the equations further to generate a system of linear equations.

(x2-xf1)*(2*x1-xf1-x2)+(y2-yf1)*(2*y1-yf1-y2)+(z2-zf1)*(2*z1-zf1-z2)-f1*f1+d*d

(xf1-xp)*(2*x1-xf1-xp)+(yf1-yp)*(2*y1-yf1-yp)+(zf1-zp)*(2*z1-zf1-zp)-l1*l1+f1*f1

(xp-x2)*(2*x1-xp-x2)+(yp-y2)*(2*y1-yp-y2)+(zp-z2)*(2*z1-zp-z2)-d*d+l1*l1

(x3-xf2)*(2*x2-xf2-x3)+(y3-yf2)*(2*y2-yf2-y3)+(z3-zf2)*(2*z2-zf2-z3)-f2*f2+d*d

(xf2-xp)*(2*x2-xf2-xp)+(yf2-yp)*(2*y2-yf2-yp)+(zf2-zp)*(2*z2-zf2-zp)-l2*l2+f2*f2

(xp-x3)*(2*x2-xp-x3)+(yp-y3)*(2*y2-yp-y3)+(zp-z3)*(2*z2-zp-z3)-d*d+l2*l2

(x1-xf3)*(2*x3-xf3-x1)+(y1-yf3)*(2*y3-yf3-y1)+(z1-zf3)*(2*z3-zf3-z1)-f3*f3+4*d*d

(xf3-xp)*(2*x3-xf3-xp)+(yf3-yp)*(2*y3-yf3-yp)+(zf3-zp)*(2*z3-zf3-zp)-l2*l2+f3*f3

(xp-x1)*(2*x3-xp-x1)+(yp-y1)*(2*y3-yp-y1)+(zp-z1)*(2*z3-zp-z1)-4*d*d+l3*l3

x1,x2,x3,y1,y2,y3,z1,z2,z3

can you help with these.

Thank you for everything Mr. Walter Roberson, You're a great help.

[Walter Roberson]

These are not linear equations. Look at the first term of the first equation: it has x2 on the left side of the multiplication and x2 on the right side of the multiplication. You might have reduced the number of non-linear terms,but it is still non-linear.

I think you might have to proceed by elimination of variables. I did some of that last night, but may perhaps have done something wrong, as after only a few equations, a simple substitution of variables ran all night.

[Sourabh Bajaj]

I'll try and do as much as i can, what i meant was that now i have three linear equations and six with lesser non linearity. Will try to simplify as much as I can and then tell you.

[Sourabh Bajaj]

I don't think these non linear equations can be solved just with these many conditions. So I'll try and find someother equations if possible.