Why the results are different when use different letters?

I solve same equations in different ketters and got fifferent results as follow:

But rs=a, xs=b, rp=c and xp=d. the equations are same!

>> syms rs xs rp xp;

>> [rp,xp]=solve(rs*rp^2+rs*xp^2==xp^2*rp,xs*rp^2+xs*xp^2==rp^2*xp)

rp =

-(rp*(rs*(rp - rs))^(1/2))/(rp - rs)

(rp*(rs*(rp - rs))^(1/2))/(rp - rs)

xp =

-(rs*(rp - rs))^(1/2)

(rs*(rp - rs))^(1/2)

-------------------------------------------------------------

>> syms a b c d

>> [c,d]=solve(a*c^2+a*d^2==c^2*d,b*c^2+b*d^2==d^2*c)

c =

0

(a^2 + b^2)/b

d =

0

(a^2 + b^2)/a

Answer 1

[Walter Roberson]

You are not specifying which two variables to solve for, so solve() is using symvar() and picking the first two variables.

With the different names involved, the relative order of the variables in symvar() is different than you are expecting.

[Xizeng Feng]

Thank you for your reminding!

But how can I specify the variables to solve for? Or can I specify the order of the variables?

[Walter Roberson]

syms rs xs rp xp
[rp,xp]=solve(rs*rp^2+rs*xp^2==rp^2*xp,  xs*rp^2+xs*xp^2==xp^2*rp, [rp, xp])

rp = 

xp = 

[Xizeng Feng]

thank you very much for your kindly help. I learned more about the symbolic operations now.

Answer 2

[DGM]

They are not the same.

syms rs xs rp xp;
[rp,xp] = solve( rs*rp^2+rs*xp^2 == xp^2*rp,  xs*rp^2+xs*xp^2 == rp^2*xp)

syms a b c d
[c,d] = solve( a*c^2+a*d^2 == c^2*d,  b*c^2+b*d^2 == d^2*c)

The RHS of both equations don't correspond. You'll have to decide which one is which.

[Xizeng Feng]

thanks for your reminding!

Answer 3

[Jan]

Because the equations are different:

syms rs xs rp xp
syms a  b  c  d
[rp, xp] = solve(rs * rp^2 + rs * xp^2 == xp^2 * rp, xs * rp^2 + xs * xp^2 == rp^2 * xp)
[c,  d]  = solve(a  * c^2  + a  * d^2  == c^2  * d,  b  * c^2  + b  * d^2  == d^2  * c)
%                                         ^ ?!                                       ^

You see, the replacement is not performed exactly. The term xp is converted twice to c instead of d.

[Xizeng Feng]

thank you very much!

[Xizeng Feng]

I corrected it but still not have the same results as follow:

syms a b c d ;
[c,   d]=solve( a* c^2  +a*d^2==   c^2*d,   b*  c^2  +b*d^2   ==d^2* c)

c = 

d = 

syms rs xs rp xp;
[rp,xp]=solve(rs*rp^2+rs*xp^2==rp^2*xp,  xs*rp^2+xs*xp^2==xp^2*rp)

rp = 

xp = 

[Jan]

The equations are still not the same. Did you see, that I have inserted spaces around the operators? Note the differences between [a b], [a + b] and [a +b] ! Without a space on the right but one on the left, the + is interpreted as unary operator:

syms a b c d;
[a* c^2  +a*d^2==   c^2*d,   b*  c^2  +b*d^2   ==d^2* c]

ans = 

syms rs xs rp xp;
[rs*rp^2+rs*xp^2==rp^2*xp,  xs*rp^2+xs*xp^2==xp^2*rp]

ans = 

[Xizeng Feng]

That is not the key point, Mr. Walter Roberson gave a right answer. But I thank you too!

[Jan]

It is an important point to see, that the equations are not equal and that spaces around operators do matter.

[Xizeng Feng]

Yes, I'll remember this point.