HP Prime polynomial long division

[bluesun08]

If i calculate (x^3+x):(x^2+3) manually via polynomial long division the result is x-(2x)/(x^2+3)

How can i get this result with the HP Prime?

[Eddie W. Shore]

Quote:

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If i calculate (x^3+x):(x^2+3) manually via polynomial long division the result is x-(2x)/(x^2+3)

How can i get this result with the HP Prime?

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In CAS mode, use partfrac. Access: Toolbox, CAS, 1. Algebra, 6. Partial Fraction

Hope that helps.

[bluesun08]

Great, thank you!

[bluesun08]

A further question: What is the difference between partfrac and cpartfrac?

[Eddie W. Shore]

Quote:

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A further question: What is the difference between partfrac and cpartfrac?

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cpartfrac is the complex counterpart of partfrac

Example:

cpartfrac((x^3+x)/(x^2+3)) returns x - 1/(x+i*sqrt(3)) - 1/(x-i*sqrt(3))

[bluesun08]

o.k.

[CR Haeger]

Thanks. Does CAS Settings / Simplify need to be set to NONE or MINIMUM for this result? Appears that MAXIMUM will show the rational being "recomposed" as x^3+x : x^2+3.

Best

[Tim Wessman]

Yes, it will recombine them in your version unforuntately. Note that this will all work much better in the future. There is a reason we did not put it to anything but "none" by default in the initial release. :-)

TW

[Michael de Estrada]

Hi Tim,

A related issue. I want to expand and then recombine a symbolic polynomial to group the coefficients by powers, i.e.

(a-x)*(b-x) ---> a*b - (a+b)*x + x^2

If I enter this expression in CAS with simplify set to maximum in the settings the result I get is:

a*b - a*x - b*x + x^2

where the coefficients are not grouped for the power of x^1.

Is there some way to do this ?

[Michael de Estrada]

I found a solution in the CAS function "symb2poly".

symb2poly ((a-x)*(b-x)) ---> [1 -a-b a*b]

[CompSystems]

real collect

Poly:= (a-x)*(b-x)
Var:= x

sum( coeff( Poly, Var ) .* seq( Var^k, k, degree( Poly, Var ), 0, 1 )

[Wes Loewer]

Quote:

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In CAS mode, use partfrac.

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To see the results of polynomial long division, propfrac is more what he was looking for.

partfrac(((x^3+2*x²+3*x+4)/(x²-9))) returns the partial fractions
x+2+(29/3/(x-3))+7/3/(x+3)

while

propfrac(((x^3+2*x²+3*x+4)/(x²-9))) returns the proper fraction:
x+2+(12*x+22)/(x²-9)

-wes

[bluesun08]

"propfrac" is exactly the command i need. It's too bad that "propfrac" is not in CAS-Menü.

[parisse]

quo, rem and quorem are the CAS instructions to perform polynomial division.