warning all the time, don't know what is wrong
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syms m n p a x y z lambda real
g = x + y + z -a;
L = (x).^m.*(y).^n.*(z).^p - lambda.*g
Lx = diff(L,x)
Ly = diff(L,y)
Lz = diff(L,z)
sol = solve([Lx==0,Ly==0,Lz==0,g==0],[x y z lambda])
sol.x
sol.y
sol.z
回答 (1 件)
Walter Roberson
2024 年 3 月 22 日
移動済み: Walter Roberson
2024 年 3 月 22 日
The 0^n and 0^(m-1) occur because there are not constraints on m and n, so there is the possibility that 0^0 is being generated, and 0^0 is 1 whereas 0^anything_else is 0
syms m n p a x y z lambda real
g = x + y + z -a;
L = (x).^m.*(y).^n.*(z).^p - lambda.*g;
Lx = diff(L,x);
Ly = diff(L,y);
Lz = diff(L,z);
eqns = [Lx==0,Ly==0,Lz==0,g==0];
partial_lambda = solve(eqns(1), lambda, 'returnconditions', true);
%partial_lambda.conditions
eqns2 = subs(eqns(2:end), lambda, partial_lambda.lambda);
partial_x = solve(eqns2(3), x);
eqns3 = subs(eqns2([1:2 4:end]), x, partial_x);
partial_y = solve(eqns3(1), y, 'returnconditions', true);
%partial_y.y
%partial_y.conditions
eqns4 = subs(eqns3(2:end), y, partial_y.y);
syms parameter1 parameter2 real
partial_z1 = subs(solve(eqns4(1,1), z, 'returnconditions', true), sym('x'), parameter1);
partial_z2 = subs(solve(eqns4(2,1), z, 'returnconditions', true), sym('x'), parameter2);
partial_z3 = solve(eqns4(3,1), z, 'returnconditions', true);
%partial_z3.z
%partial_z3.conditions
back_z1 = partial_z1.z;
back_y1 = subs(partial_y.y(1), z, back_z1);
back_x1 = subs(partial_x, {y, z}, {back_y1, back_z1});
back_lambda1 = subs(partial_lambda, {x, y, z}, {back_x1, back_y1, back_z1});
solution1 = [x == back_x1, y == back_y1, z == back_z1, lambda == back_lambda1.lambda]
back_z2 = partial_z2.z;
back_y2 = subs(partial_y.y(2), z, back_z2);
back_x2 = subs(partial_x, {y, z}, {back_y2, back_z2});
back_lambda2 = subs(partial_lambda, {x, y, z}, {back_x2, back_y2, back_z2});
solution2 = [x == back_x2, y == back_y2, z == back_z2, lambda == back_lambda2.lambda]
back_z3a = partial_z3.z(1);
back_y3a = subs(partial_y.y(3), z, back_z3a);
back_x3a = subs(partial_x, {y, z}, {back_y3a, back_z3a});
back_lambda3a = subs(partial_lambda, {x, y, z}, {back_x3a, back_y3a, back_z3a});
solution3a = [x == back_x3a, y == back_y3a, z == back_z3a, lambda == back_lambda3a.lambda]
back_z3b = partial_z3.z(2);
back_y3b = subs(partial_y.y(3), z, back_z3b);
back_x3b = subs(partial_x, {y, z}, {back_y3b, back_z3b});
back_lambda3b = subs(partial_lambda, {x, y, z}, {back_x3b, back_y3b, back_z3b});
solution3b = [x == back_x3b, y == back_y3b, z == back_z3b, lambda == back_lambda3b.lambda]
back_z3c = partial_z3.z(3);
back_y3c = subs(partial_y.y(3), z, back_z3c);
back_x3c = subs(partial_x, {y, z}, {back_y3c, back_z3c});
back_lambda3c = subs(partial_lambda, {x, y, z}, {back_x3c, back_y3c, back_z3c});
solution3c = [x == back_x3c, y == back_y3c, z == back_z3c, lambda == back_lambda3c.lambda]
5 件のコメント
Dyuman Joshi
2024 年 3 月 29 日
Accepting the answer indicates that your problem has been solved (which can be helpful to other people in future) and it awards the volunteer with reputation points for helping you.
You can accept only 1 answer for a question, but you can vote for as many answers as you want. Voting an answer also provides reputation points.
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