# Why does vpasolve work where solve doesn't for the following:

5 views (last 30 days)
David on 21 Oct 2013
Answered: David on 21 Oct 2013
When I pass the following equations into solve like so
eqn1 = (120*Lt*pi*Rt)/(14400*Lt^2*pi^2 + Rt^2)^(1/2) - 338920901889975/17592186044416
eqn2 = (42000*Lt*pi*Rt)/(1764000000*Lt^2*pi^2 + Rt^2)^(1/2) - 8473022547249375/17592186044416
S = solve([eqn1,eqn2],[Rt, Lt])
I get the following error:
Warning: 4 equations in 2 variables.
> In C:\Program Files (x86)\MATLAB\R2013a Student\toolbox\symbolic\symbolic\symengine.p>symengine at 56
In solve at 170
In Main at 152
Warning: Explicit solution could not be found.
> In solve at 179
In Main at 152
However, if I plug these same two equations into vpasolve like so
S = vpasolve([eqn1, eqn2], [Rt, Lt], [1e3, 1e-6]);
I get
double(S.Rt) = 482.866983 and
double(S.Lt) = 0.051144.
What am I doing wrong inside the solve function??? Thanks for any help.

David on 21 Oct 2013
Hey everyone,
It turns out, not surprisingly, that I needed to make eqn1 and eqn2 symbolic objects, which I did by wrapping sym() around each one. Now everything works fine. Yippee!
eqn1 = sym((120*Lt*pi*Rt)/(14400*Lt^2*pi^2 + Rt^2)^(1/2) - 338920901889975/17592186044416)
eqn2 = sym((42000*Lt*pi*Rt)/(1764000000*Lt^2*pi^2 + Rt^2)^(1/2) - 8473022547249375/17592186044416)
S = solve([eqn1, eqn2])

Walter Roberson on 21 Oct 2013
There are two solutions:
Lt = (135/7881299347898368)*sqrt(87986205389370659588312581)/pi,
Rt = (405/17592186044416)*sqrt(439931026946853297941562905)
and the negatives of those.
I suggest switching to symbolic numbers when you construct the equation:
eqn1 = sqrt(sym(120)*Lt*sym('pi')*Rt)/(sym(14400)*Lt^2*sym('pi')^2 + Rt^2) - sym('338920901889975')/sym('17592186044416')
eqn2 = sqrt(sym(42000)*Lt*sym('pi')*Rt)/(sym('1764000000')*Lt^2*sym('pi')^2 + Rt^2) - sym('8473022547249375')/sym('17592186044416')
I used sym(120) and other small numbers, but sym('17592186044416') and other large numbers, to avoid the possibility of losing precision in converting the double precision representation of the larger numbers to symbolic form.
##### 2 CommentsShowHide 1 older comment
David on 21 Oct 2013
Nevermind Walter, I figured out my problem. It turns out, not surprisingly, that I needed to make eqn1 and eqn2 symbolic objects, which I did by wrapping sym() around each one. Now everything works fine. Yippee!
eqn1 = sym((120*Lt*pi*Rt)/(14400*Lt^2*pi^2 + Rt^2)^(1/2) - 338920901889975/17592186044416)
eqn2 = sym((42000*Lt*pi*Rt)/(1764000000*Lt^2*pi^2 + Rt^2)^(1/2) - 8473022547249375/17592186044416)
S = solve([eqn1, eqn2])