MaplePrimes - answers and comments on Question, Unable to compute coefficient

coeff(algsubs(1/r=k,a),k);

andrei bobrov — Mon, 09 Apr 2012 09:11:28 Z

coeff(algsubs(1/r=k,a),k);

Another way

Markiyan Hirnyk — Mon, 09 Apr 2012 09:22:33 Z

Up to http://www.mapleprimes.com/questions/40164-Retrieving-The-Constant-In-An-Equation ,

Worked

mgu — Mon, 09 Apr 2012 18:20:22 Z

Hi again, Markiyan. It certainly worked. Thank you for the solution and the post as well.

n=0

Pseudomodo — Mon, 09 Apr 2012 19:56:39 Z

We were not told that n is a positive integer, were we?

Is this suggested answer correct when n=0?

There are four special cases, where the powers of `r` involve n. Of those, the cases n={-3,-2,-1} also make the denominator vanish.

This is the only exceptional case

Markiyan Hirnyk — Mon, 09 Apr 2012 20:29:26 Z

@Pseudomodo The arguments:

> eval(a, n = -1);

Error, numeric exception: division by zero
> eval(a, n = -2);

Error, numeric exception: division by zero
> eval(a, n = -3);

Error, numeric exception: division by zero

for this example

Pseudomodo — Mon, 09 Apr 2012 20:54:26 Z

@Markiyan Hirnyk For this example, n=0 could get special treatment (unless we are informed that n::posint). And yes, I was aware of what happened for n in {-3,-2,-1}.

But for other examples, more work may be required. Suppose that the term -240*r^(2*n+4)*n^2 in the numerator of `a` had instead been -240*r^(2*n-4)*n^2. Then n=2 would be yet another special case that would render the approach eval(r*a,r=0) as invalid.

A safer method might be to apply expand, combine(...,power), collect w.r.t `r`, and then examine the powers of r. The examination could solve the various powers of `r` for `n`, and build up a piecewise result involving those solutions-in-n.

Maybe a result like this:

a := (1/11520)*(4518-4320*r^(2*n)-5760*_C1*n^4*r^2-97920*_C1*n^2*r^2-97920*_C1*n*r^2
     -40320*_C1*n^3*r^2+2020*r^6*n^3+1500*r^6*n^2-1440*r^(2*n+6)+60*r^8-2880*r^(2+2*n)
     -720*r^4-100*n^5-339*n^2+3018*r^2+4560*r^(2+2*n)*n-240*r^(2*n-4)*n^2
     -480*r^(2+2*n)*n^4+50*r^8*n-130*r^8*n^4-270*r^8*n^3-170*r^8*n^2-20*r^8*n^5
     +480*r^(2*n+6)*n+480*r^(2*n+6)*n^3-480*r^(2*n+6)*n^2-1680*r^(2+2*n)*n^3
     +160*n^5*r^6-102*n*r+320*r^2*n^5+1783*r^2*n^4-34560*_C1*r^2-360*r^4*n^5
     -102*n^2*r-42*n^3*r-6*n^4*r+551*r^2*n^2+2551*r^2*n-1440*n^2*r^4-3240*r^4*n
     +240*r^(2*n)*n^2+1200*r^(2*n)*n^3-5040*r^(2*n)*n+240*r^(2*n)*n^4
     +480*r^(2+2*n)*n^2+97920*_C1*n^2+97920*_C1*n+40320*_C1*n^3+5760*_C1*n^4
     +2140*n*r^6+2481*r^2*n^3+240*r^(2*n+4)*n^4-3600*r^4*n^3-2160*r^4*n^4
     +1020*r^6*n^4+1800*r^6-507*n^4-589*n^3+34560*_C1-36*r-1399*n)
     /((17*n^2+17*n+6+7*n^3+n^4)*r);

piecewise(n = 0, 11/3840+(1/2)*_C1,
          n = 2, (1/2)*_C1-277/34560,
          (1/11520)*
           (97920*_C1*n^2+97920*_C1*n+40320*_C1*n^3+5760*_C1*n^4+4518-507*n^4
            -339*n^2-589*n^3-100*n^5-1399*n+34560*_C1)/(17*n^2+17*n+6+7*n^3+n^4));

Naturally, it could be that the questioner's method of arriving at expression `a` precludes such powers as r^(2*n-4) in the numerator.