Explicit root of symbolic equations

Question

Ductho Le 2019-10-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/486748-explicit-root-of-symbolic-equations

评论： Ductho Le 2019-10-22

I am trying to find the explicit roots of symbolic equations like the code bellow:

syms d1 d2 d3 d4 d5 d6 h11 h12 h13 h14 h21 h22 h23 h24 h41 h42 h45 h46 h51 h52 h55 h56 h61 h62 h65 h66
eq1 = h11*d1+h12*d2+h13*d3+h14*d4 == 0;
eq2 = h21*d1+h22*d2+h23*d3+h23*d4 == 0;
eq3 = d1+d2+d3+d4-d5-d6 == 0;
eq4 = h41*d1+h42*d2-h41*d3-h42*d4-h45*d5-h46*d6 == 0;
eq5 = h51*d1+h52*d2+h51*d3+h52*d4-h55*d5-h56*d6 == 0;
eq6 = h61*d1+h62*d2-h61*d3-h62*d4-h65*d5-h66*d6 == 0;
eq = [eq1,eq2,eq3,eq4,eq5,eq6];
var = [d1 d2 d3 d4 d5 d6];
S = solve(eq, var)

but the program return me the results like that

S = 
  struct with fields:
    d1: [1×1 sym]
    d2: [1×1 sym]
    d3: [1×1 sym]
    d4: [1×1 sym]
    d5: [1×1 sym]
    d6: [1×1 sym]

Can anybody please help me to find the explicit roots? Thanks you so much!

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Answer 1

Stephan 2019-10-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/486748-explicit-root-of-symbolic-equations#answer_397635

在 MATLAB Online 中打开

syms d1 d2 d3 d4 d5 d6 h11 h12 h13 h14 h21 h22 h23 h24 h41 h42...
    h45 h46 h51 h52 h55 h56 h61 h62 h65 h66
eq1 = h11*d1+h12*d2+h13*d3+h14*d4 == 0;
eq2 = h21*d1+h22*d2+h23*d3+h23*d4 == 0;
eq3 = d1+d2+d3+d4-d5-d6 == 0;
eq4 = h41*d1+h42*d2-h41*d3-h42*d4-h45*d5-h46*d6 == 0;
eq5 = h51*d1+h52*d2+h51*d3+h52*d4-h55*d5-h56*d6 == 0;
eq6 = h61*d1+h62*d2-h61*d3-h62*d4-h65*d5-h66*d6 == 0;
% Solve for d1...d6
sol_d1 = isolate(eq1,d1)
sol_d2 = isolate(eq2,d2)
sol_d3 = isolate(eq3,d3)
sol_d4 = isolate(eq4,d4)
sol_d5 = isolate(eq5,d5)
sol_d6 = isolate(eq6,d6)

gives:

sol_d1 =
 
d1 == -(d2*h12 + d3*h13 + d4*h14)/h11
 
sol_d2 =
 
d2 == -(d1*h21 + d3*h23 + d4*h23)/h22
 
sol_d3 =
 
d3 == d5 - d2 - d4 - d1 + d6
 
sol_d4 =
 
d4 == -(d3*h41 - d2*h42 - d1*h41 + d5*h45 + d6*h46)/h42
 
sol_d5 =
 
d5 == (d1*h51 + d2*h52 + d3*h51 + d4*h52 - d6*h56)/h55
 
sol_d6 =
 
d6 == -(d3*h61 - d2*h62 - d1*h61 + d4*h62 + d5*h65)/h66