Defining constants causes integration to hang

*To*: mathgroup at smc.vnet.net*Subject*: [mg114215] Defining constants causes integration to hang*From*: amannuc <amannuc at yahoo.com>*Date*: Sat, 27 Nov 2010 03:37:37 -0500 (EST)

Dear Mathematica group, I have found a situation where using the Constants option in Dt causes an indefinite integration to hang. This is unexpected behavior because when I don't provide the Constants information, the integration finishes quickly. I am surprised that in this case providing more information causes the problem. I am using Mathematica 7.0. The following works: n12[r_] := n1 - r dni/lD12 (* n1, dni and lD12 are actually constants *) g2[a_] := 2*a*Integrate[ Dt[n12[r], r] (n12[r]* Sqrt[n12[r]^2*r^2 - a^2]), {r, h2, h1}] and the resulting definite integral seems correct but contains a number of spurious derivatives such as: Dt[dni, r], Dt[lD12, r], etc. These derivatives are zero because n1, dni and lD12 are actually constants, not dependent on r. When I specify such in the Dt[n12[r], r] expression, the integral never finishes executing. That is, in the above expression I replace Dt[n12[r], r] with Dt[n12[r], r, Constants -> {n1, dni, lD12} ]. The integral now does not finish. So, if I do not use the Constants option in Dt, I have the spurious derivatives in the calculated expression (e.g. Dt[dni,r]) which I seek to remove. One way to do this is to use the transformation rule: Dt[dni, r] -> 0 (for example). It turns out that I can apply this type of rule one at a time, and once only. For example, the following works fine: g3[a] = g2[a] /. Dt[dni, r] -> 0 which removes the spurious derivatives of dni. If I try to remove another spurious derivative, the integral hangs. Thus, the following hangs (trying to remove Dt[dn1, r]: g4[a] = g3[a] /. Dt[dn1, r] -> 0 It turns out the key fact is that I apply the transformation twice. For example, I could switch the order of the above two transformation statements. In that case, the first one completes but the second one hangs. Any help/advice is appreciated. -Tony