# trying to write complex equation with parentheses

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ali on 27 Feb 2024
Answered: Sam Chak on 27 Feb 2024
iam trying to write the following formula for the area ratio at Ma =1 but i think that iam missing a parentheses
note: im only trying to write the right side of the equation
code:
((k+1)/2)^(-(k+1)/(2*(k-1)))*(1+((k-1)/2)*(Ma)^2)^((k+1)/2*(k-1))/Ma
Walter Roberson on 27 Feb 2024
syms gamma M
k = gamma;
Ma = M;
f = ((k+1)/2)^(-(k+1)/(2*(k-1)))*(1+((k-1)/2)*(Ma)^2)^((k+1)/2*(k-1))/Ma
f =
... I think that's the same.
Dyuman Joshi on 27 Feb 2024
@Walter, the (gamma -1) in the power of numerator should be in denominator.

Dyuman Joshi on 27 Feb 2024
You were missing a pair of parenthesis -
syms gamma M
k = gamma;
Ma = M;
% v v
f = ((k+1)/2)^(-(k+1)/(2*(k-1)))*(1+((k-1)/2)*(Ma)^2)^((k+1)/(2*(k-1)))/Ma
f =
VBBV on 27 Feb 2024
Edited: VBBV on 27 Feb 2024
Yes, @Dyuman Joshi it seems the denominator should have a pair of parenthesis. Good catch

Sam Chak on 27 Feb 2024
Hi @ali
When inputting a lengthy equation with multiple parentheses into the programming code, I usually adopt a "divide-and-conquer" approach. This helps reduce the chances of human error and enables me to cross-verify it effortlessly with the original equation.
Consider the function
,
where the numerator N and the denominator D are given by
,
.
syms gamma M
%% numerator elements
na = 1 + (gamma - 1)/2*M^2;
nb = M;
nc = gamma + 1;
nd = 2*(gamma - 1);
%% denominator elements
da = gamma + 1;
db = 2;
dc = nc;
dd = nd;
%% the function
N = (na^(nc/nd))/nb; % numerator
D = (da/db)^(dc/dd); % denominator
f = N/D
f =

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