Nspire CAS and Partial Fractions

[Nevil Hopley]

I'm wanting to know if it's possible to have Nspire CAS 'compare
coefficients' of polynomial expressions, as one does when manually
deriving partial fractions for example.

An example:
Consider splitting (x^2+3)/(x(1+x^2)) into partial fractions

I already know that to get Nspire CAS to turn this into partial
fractions in a single step you can type in:
expand((x^2+3)/(x(1+x^2)))

If I did it manually on paper, I would start off by:
(x^2+3)/(x(1+x^2)) = A/x + (Bx+C)/(1+x^2)

Then, by combining fractions on the RHS, I'd then compare the
polynomial coefficients of the numerators on both sides, and come up
with A=3, B=-2 and C=0

It's this process of taking the statement (x^2+3)/(x(1+x^2)) = A/x +
(Bx+C)/(1+x^2) and concluding the values of A, B and C that I am
interested in finding out if the Nspire can help process.

Any takers for this challenge?

One condition I'd like to uphold - the method of using Nspire for this
must not be long and convoluted and requiring umpteen steps to employ
for each term of polynomial term comparisons! Am I asking for too
much?

Thank you!

Nevil Hopley
www.CalculatorSoftware.co.uk

[Nelson Sousa]

Yes, it can be done (although not entirely on an automatic fashion without entering the realm of really complex stuff).

1. Comdenom - returns the expression in fraction form;

2. Getnum - returns the numerator of a faction;

3. Polycoeffs - returns the list of coefficients of a polynomial with respect to a certain variable;

4. Solve - this one is self-explanatory.

So, just create a function that accepts an equation such as that one and the number of variables and define:

Func

:Local lhslist,rhslist,eqstr,varlist,i,str

:polyCoeffs(getNum(comDenom(left(expression))),x)→lhslist

:polyCoeffs(getNum(comDenom(right(expression))),x)→rhslist

:{}→varlist

:""→eqstr

:For i,1,n

:  expr(char(96+i))→varlist[i]

:  eqstr&string(lhslist[i])&"="&string(rhslist[i])&" and "→eqstr

:EndFor

:left(eqstr,dim(eqstr)-5)→eqstr

:"solve("&eqstr&","&string(varlist)&")"→str

:Return expr(str)

:EndFunc

Cheers,

Nelson

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[Luke Setzer]

Was anyone able to get Nelson's proposed function to work in a public Library file?

[Samuel Hollis]

Yea, I was.  Probably too late of a reply