Cannot find ALL solutions to simultaneous equation
显示 更早的评论
Hi everyone, I would like to find ALL the solutions to this series of equations. Here is my code.
My problem is that it prompts me to use vpasolve, which doesn't give ALL the solutions. I tried "ReturnCondition", but to no avail.
My code is here:
clear all
syms x y z
eq1 = exp(x^2 + y^2 + z^2) == 9;
eq2 = x + x*y - z == 1;
eq3 = x + y + z == 1;
[solx,soly,solz] = solve([eq1,eq2,eq3],[x y z])
采纳的回答
David Goodmanson
2020-1-8
Hi CZ
If
exp(x^2+y^2+z^2) = 9
then
x^2+y^2+z^2 = log(9)
which is a lot less challenging for symbolic evaluation.
clear all
syms x y z C
eq1 = x^2 + y^2 + z^2 == C;
eq2 = x + x*y - z == 1;
eq3 = x + y + z == 1;
[solx,soly,solz] = solve([eq1,eq2,eq3],[x y z])
solz =
root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 1)
root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 2)
root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 3)
root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 4)
There are expressions that are twice as long for x and y. You can get numerical results by plugging in log(9) for C and using the roots function to get four solutions. I wish I knew how to get the coefficients in solx, soly and solz into the roots function in a convenient way, but I don't.
更多回答（1 个）
Walter Roberson
2020-1-8
0 个投票
Ookkay... The 55 kilobyte solution is attached.
Now what are you going to do with it?
5 个评论
Xinzhe Chai
2020-1-8
Walter Roberson
2020-1-8
I used Maple,
[allvalues](solve([exp(x^2 + y^2 + z^2) = 9, x*y + x - z = 1, x + y + z = 1]))
and then a fair bit of hand-editing to get the values into a form that could be loaded into MATLAB.
Xinzhe Chai
2020-1-8
Walter Roberson
2020-1-8
solve eq2 for x (in terms of y and z) . Substitute that x into eq3 and solve for z. substitute for x and then z into eq1, and solve for y asking solve for MaxDegree 4. The result will be four exact roots for y. simplify(). Now do back substitution.
Xinzhe Chai
2020-1-8
类别
在 帮助中心 和 File Exchange 中查找有关 Equation Solving 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
