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

Question

David 2013-10-21

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回答： David 2013-10-21

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 mupadengine.mupadengine>mupadengine.evalin at 97
  In mupadengine.mupadengine>mupadengine.feval at 150
  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.

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Answer 1

David 2013-10-21

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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])

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Answer 2

Walter Roberson 2013-10-21

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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.

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David 2013-10-21

编辑：David 2013-10-21

Thanks for your quick reply and suggestions. However, I would like to ask, how is that you got these solutions using the solve function where I couldn't? Were there any differences between how you and I called the solve function? Thanks again.

David

David 2013-10-21

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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])

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