Hi Stan,
I don't think there is any other way to solve an equation such as that
in Sage. You can do it using Sage's interface to Maple (if you have
it installed / access to it), but it's not as clean as it should be
due to bug #3610.
sage:
var('wcnew,epsln,ysnew,delyu,sumsunew,sunlayersnew,delyu,nlayers,ysnew,cz,zr');
sage: eq = wcnew==epsln*(ysnew + ((delyu*sumsunew +
sunlayersnew*(delyu*(1 - nlayers) + sqrt((cz - ysnew)*(cz -
zr))))*sqrt((cz - ysnew)*(cz - zr)))/(cz - zr))
sage: meq = maple("%s = %s"%(repr(eq.lhs()), repr(eq.rhs())))
sage: ans = maple.solve(meq, ysnew)
sage: ans = sage_eval(str(ans).replace("\n",""),globals())
sage: ans
((-delyu*nlayers*sunlayersnew*(sqrt(-4*epsln*sunlayersnew*wcnew*zr +
4*epsln*wcnew*zr + 4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) +
delyu*sunlayersnew*(sqrt(-4*epsln*sunlayersnew*wcnew*zr +
4*epsln*wcnew*zr + 4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) +
delyu*sumsunew*(sqrt(-4*epsln*sunlayersnew*wcnew*zr + 4*epsln*wcnew*zr
+ 4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) + wcnew*zr -
cz*epsln*sunlayersnew*zr - cz*wcnew + cz^2*epsln*sunlayersnew)/
(epsln*(sunlayersnew - 1)*(cz - zr)),
(-delyu*nlayers*sunlayersnew*(-sqrt(-4*epsln*sunlayersnew*wcnew*zr +
4*epsln*wcnew*zr + 4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) + delyu*sunlayersnew*(-
sqrt(-4*epsln*sunlayersnew*wcnew*zr + 4*epsln*wcnew*zr +
4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) + delyu*sumsunew*(-
sqrt(-4*epsln*sunlayersnew*wcnew*zr + 4*epsln*wcnew*zr +
4*cz*epsln^2*sunlayersnew*zr - 4*cz*epsln^2*zr +
4*cz*epsln*sunlayersnew*wcnew - 4*cz*epsln*wcnew +
delyu^2*epsln^2*nlayers^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sunlayersnew^2 +
delyu^2*epsln^2*sunlayersnew^2 -
2*delyu^2*epsln^2*nlayers*sumsunew*sunlayersnew +
2*delyu^2*epsln^2*sumsunew*sunlayersnew - 4*cz^2*epsln^2*sunlayersnew
+ delyu^2*epsln^2*sumsunew^2 + 4*cz^2*epsln^2) +
delyu*epsln*nlayers*sunlayersnew - delyu*epsln*sunlayersnew -
delyu*epsln*sumsunew)/(2*(sunlayersnew - 1)) + wcnew*zr -
cz*epsln*sunlayersnew*zr - cz*wcnew + cz^2*epsln*sunlayersnew)/
(epsln*(sunlayersnew - 1)*(cz - zr)))
--Mike
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