# Unable to solve for a variable

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Jonas Freiheit on 6 Oct 2021
Commented: Jonas Freiheit on 10 Oct 2021
Hi all,
I am trying to solve for a variable 'a' and saving it into an array, However, I am left with an inifinitely long running program. What should I do?
Heres a section of the code:
clc, clear, clear all
J_value=0.5
syms a;
for TonTc=.01:0.01:.99
sig_sigo_1=((2*J_value+1)/2*J_value)*coth((2*J_value+1)/2*J_value)*a-(1/2*J_value)*coth(a/2*J_value);
sig_on_sigo_2=((J_value+1)/3*J_value)*TonTc*a;
z=sig_sigo_1-sig_on_sigo_2;
for k=1:99
val_a(k)=vpasolve(z,a);
end
end
Cheers

Walter Roberson on 7 Oct 2021
J_value=0.5;
syms a;
TonTc_vals = .01:0.01:.99;
num_Tonc = length(TonTc_vals);
val_a = zeros(num_Tonc, 1);
for k = 1 : num_Tonc
TonTc = TonTc_vals(k);
sig_sigo_1=((2*J_value+1)/2*J_value)*coth((2*J_value+1)/2*J_value)*a-(1/2*J_value)*coth(a/2*J_value);
sig_on_sigo_2=((J_value+1)/3*J_value)*TonTc*a;
z=sig_sigo_1-sig_on_sigo_2;
sol = vpasolve(z, a, -1);
if isempty(sol)
val_a(k) = nan;
else
val_a(k) = sol(1);
end
if k == 1
fplot([z, 0], [0.5 1])
title("plot for TonTc = " + TonTc)
ylim([-2 2])
end
end figure
plot(TonTc_vals, val_a)
title("a vs TonTc") That first plot makes it clear that there is no root at 0.75
Jonas Freiheit on 10 Oct 2021
Yes, Sorry How would I plug in the second solutions?
Just trying to test to see if that gives me the theoretical results. This is the equation I'm supposed to follow to obtain sigma/sigma0 which I think I've correctly used in the code. ### More Answers (1)

David Hill on 6 Oct 2021
What are you solving? You need to set z equal to something.
z=sig_sigo_1-sig_on_sigo_2==0;%what do you want z to be?
Jonas Freiheit on 7 Oct 2021
Hi,
For some reason when I do z==0 and do vpasolve(z,a) for TonTc=0.1 I get 0.972 when the actual correct answer is 0.75 from my calculator? Howcome is this wrong?
Thanks
Also solve doesn't work and has to be vpasolve