Insert symbolic equation in another symbolic equation

Question

Mirko Rizzi 2023-4-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1948308-insert-symbolic-equation-in-another-symbolic-equation

评论： Mirko Rizzi 2023-4-17

Hello i have the equation eq5 that has been solved and is now only a function of y. I want now to insert this function (r) inside eq6 and solve that, but it gives me an error. How can i solve this?

eq5 = hw2*(q-r)==y;
r = solve(eq5,r);
eq6 = @(y) sigma*eps*((r^4)-T_inf^4)-y;
y0=0;
sol = fsolve(eq6,y0);

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Mirko Rizzi 2023-4-17

编辑：Mirko Rizzi 2023-4-17

if i use this:

% eq6 = sigma*eps*((r^4)-T_inf^4)==y;

% sol = solve(eq6,y)

it gives me a vector of 4 same elements:

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 1)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 2)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 3)

root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 4)

Mirko Rizzi 2023-4-17

if i view the entire function r, copy what it is written and substitute it inside works fine, but as it is in the cycle i can't copy and paste manually at every passage

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Answer 1

Dyuman Joshi 2023-4-17

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1948308-insert-symbolic-equation-in-another-symbolic-equation#answer_1217008

编辑：Dyuman Joshi 2023-4-17

在 MATLAB Online 中打开

Use vpa to get numerical values. Convert them to double() if you need the values to be in numeric data type.

syms z
%first root, copied from above
sol1=vpa(root(z^4 - (148549786974450477987*z^3)/27487790694400 + (66201117630463850684060566839278314716507*z^2)/6044629098073145873530880000 - (25694677813792110401306682574502596589303194435085805665710978025618652510443*z)/2420199345095688424498763567867944239211734959652864000000 + 3804255296569717375581777916032849021112749976946199317897911767146631227587687/1141798154164767904846628775559596109106197299200000000, z, 1))
sol1 = 549277.87721495737433337758873113
double(sol1)
ans = 5.4928e+05

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Dyuman Joshi 2023-4-17

在 MATLAB Online 中打开

They look same because the syntax of the output above is same except for the number of root.

Since solve() was unable to find the explicit value, it returns the solution as -

root(equation,variable,1)
root(equation,variable,2)
root(equation,variable,3)
root(equation,variable,4)

You can see at the end of the each expression there's a number, denoting which root it refers to. The value of roots will, of course, depend upon the coefficients.s

Mirko Rizzi 2023-4-17