warning all the time, don't know what is wrong

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Xiao yang
Xiao yang 2024-3-22
评论： Dyuman Joshi 2024-3-29
Ran in:
syms m n p a x y z lambda real
g = x + y + z -a;
L = (x).^m.*(y).^n.*(z).^p - lambda.*g
L = 
Lx = diff(L,x)
Lx = 
Ly = diff(L,y)
Ly = 
Lz = diff(L,z)
Lz = 
sol = solve([Lx==0,Ly==0,Lz==0,g==0],[x y z lambda])
Warning: Unable to find explicit solution. For options, see help.
sol = struct with fields:
x: [0x1 sym] y: [0x1 sym] z: [0x1 sym] lambda: [0x1 sym]
sol.x
ans = Empty sym: 0-by-1
sol.y
ans = Empty sym: 0-by-1
sol.z
ans = Empty sym: 0-by-1

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回答（1 个）

Walter Roberson
Walter Roberson 2024-3-22
移动：Walter Roberson 2024-3-22
Ran in:
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]
solution1 = 
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]
solution2 = 
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]
solution3a = 
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]
solution3b = 
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]
solution3c = 
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Dyuman Joshi
Dyuman Joshi 2024-3-29
Hello @Xiao yang, if this answer solved your problem, please consider accepting the answer.
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