Re: RSolve and known indexed variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg72337] Re: RSolve and known indexed variables*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Tue, 26 Dec 2006 06:46:51 -0500 (EST)*References*: <acbec1a40612181237t1539cdayed9c0eda52db15e9@mail.gmail.com>

A related question: Why don't the rules come back with patterns on the left hand sides? On 12/18/06, Chris Chiasson <chris at chiasson.name> wrote: > Here is an attempt to solve a recurrence relation for the moment[i] at > particular parts of a beam under constant shear. The index is i. > lever[i] stands for the length of a particular section of the beam. > > I would specify the "initial" condition for the moment at index 1, but > I want to show a problem into which I've run. > > RSolve[{moment[i+1]\[Equal]moment[i]+shear*lever@i, > moment[10]\[Equal]someMoment},{moment[i]},i] > > {{moment[i] -> someMoment - Sum[shear*lever[K$35], {K$35, K$36, 9}] + > Sum[shear*lever[K$35], {K$35, K$36, -1 + i}]}} > > Notice that the output includes two sums, both with an index of K$35. > However, the range of the sums start at K$36. K$36 has no value. From > looking at the output, I would guess that K$36 should have the value > 10 (the index at which I gave the initial condition for the moment). > > For now: I will try to work around this by specifying my own generated > parameter and then detecting the appropriate Sum structures to find > the variable to replace. > > I have also run into a problem where RSolve returns the input and an > RSolve::deqx error message if the input has one of these "known > indexed variables", even though the problem is actually separable (the > second part of the separate computation is shown above): > > RSolve[{moment[10] == someMoment, shear[10] == someShear, moment[1 + > i] == moment[i] + lever[i]*shear[i], > shear[1 + i] == shear[i]}, {shear[i], moment[i]}, i] > > So, uh, do you have any suggestions for making Mathematica handle the > combined problem? Do you have any methods for making Mathematica not > produce the K$36 variable in the output? > > Note: This is one of the few times I have ever attempted to use > RSolve, and probably the first time in more than a year. I could > easily be using it incorrectly. > > Second note: From the help browser documentation, it appears RSolve > was moved into the kernel from RSolve.m beginning with version 5, so > anyone with a version 4.x could probably view a copy of the source > code that is probably quite similar to what the internal code now > uses. I lack such a copy. > > -- > http://chris.chiasson.name/ > -- http://chris.chiasson.name/