trying to write complex equation with parentheses

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]

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]

@Walter, the (gamma -1) in the power of numerator should be in denominator.

Answer 1

[Dyuman Joshi]

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]

Yes, @Dyuman Joshi it seems the denominator should have a pair of parenthesis. Good catch

Answer 2

[Sam Chak]

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 =