Integrals Crash MMA

*To*: mathgroup <mathgroup at yoda.physics.unc.edu>*Subject*: Integrals Crash MMA*From*: Roberto Sierra <73557.2101 at compuserve.com>*Date*: 17 Jul 93 02:17:46 EDT

The following double integrals crash MMA 2.03 for the Mac. It takes a while, and you get some warnings about ComplexInfinities first, but they will crash eventually. I wonder if this problem has been fixed in MMA 2.2. The variables x, y, z, and sigma are constants within the integral. Integrate[ (Sqrt[r^2] r Cos[theta]) / (r^2 - 2 r x Cos[theta] - 2 r y Sin[theta])^(3/2), {theta,0,2Pi}, {r,0,R} ] Integrate[ (Sqrt[r^2] r Sin[theta]) / (r^2 - 2 r x Cos[theta] - 2 r y Sin[theta])^(3/2), {theta,0,2Pi}, {r,0,R} ] Integrate[ (Sqrt[r^2] sigma (x - r Cos[theta])) / (r^2 + x^2 + y^2 + z^2 - 2 r x Cos[theta] - 2 r y Sin[theta])^(3/2), {theta,0,2Pi}, {r,0,R} ] Integrate[ (Sqrt[r^2] sigma (y - r Sin[theta])) / (r^2 + x^2 + y^2 + z^2 - 2 r x Cos[theta] - 2 r y Sin[theta])^(3/2), {theta,0,2Pi}, {r,0,R} ] I tried to evaluate a related 1-D integral, and it took MMA a real long time before leaving the integral unevaluated. Why does it take MMA so long (hours) before rejecting this integral, whereas most unevaluable integrals are rejected within minutes or seconds? [Note that the reported timing requirements are considerably lower than what is actually required.] I want to avoid having to wait hours in the future -- I thought that MMA had crashed at first until I let it run overnight... In[1] := eqn = (lambda (x - R Cos[theta]) Sqrt[R^2 Cos[theta]^2 + R^2 Sin[theta]^2]) / (z^2 + (x - R Cos[theta])^2 + (y - R Sin[theta])^2)^(3/2) Out[1] = 2 2 2 2 lambda (x - R Cos[theta]) Sqrt[R Cos[theta] + R Sin[theta] ] --------------------------------------------------------------- 2 2 2 3/2 (z + (x - R Cos[theta]) + (y - R Sin[theta]) ) In[2] := Timing[eqn1 = Simplify[eqn]] Out[2] = {38.15 Second, 2 lambda Sqrt[R ] (x - R Cos[theta]) ------------------------------------------------------------} 2 2 2 2 3/2 (R + x + y + z - 2 R x Cos[theta] - 2 R y Sin[theta]) In[3] := Timing[int1 = Integrate[eqn1, {theta,0,2Pi}]] Out[3] = 2 {4044.6 Second, lambda Sqrt[R ] x - R Cos[theta] Integrate[------------------------------------------------------------, 2 2 2 2 3/2 (R + x + y + z - 2 R x Cos[theta] - 2 R y Sin[theta]) {theta, 0, 2 Pi}]} In[4] := Timing[int = Integrate[eqn, {theta,0,2Pi}]] Out[4] = {3856.17 Second, lambda Integrate[ 2 2 2 2 (x - R Cos[theta]) Sqrt[R Cos[theta] + R Sin[theta] ] --------------------------------------------------------, 2 2 2 3/2 (z + (x - R Cos[theta]) + (y - R Sin[theta]) ) {theta, 0, 2 Pi}]} -- Roberto Sierra Tempered MicroDesigns