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Re: Convert expression to polynomial

• To: mathgroup at smc.vnet.net
• Subject: [mg70440] Re: Convert expression to polynomial
• From: dimmechan at yahoo.com
• Date: Mon, 16 Oct 2006 02:35:42 -0400 (EDT)
• References: <egsd96$cj7$1@smc.vnet.net>

x = 1 + (-t + t^2)^(-1) + 1/((-t + t^2)^2*(-t + t^4)) + 1/((-t +
t^2)^4*(-t + t^4)^2*(-t + t^8));

fun = FullSimplify[Together[x]]
(1 + (-1 + t)^4*t^4*(1 + t + t^2)*(1 + t + t^2 + t^3 + t^4 + t^5 +
t^6)*(1 + (-1 + t)^2*t^2*(1 + (-1 + t)*t)*(1 + t + t^2)))/
  ((-1 + t)^7*t^7*(1 + t + t^2)^2*(1 + t + t^2 + t^3 + t^4 + t^5 +
t^6))

PolynomialQuotient[Numerator[fun], Denominator[fun], t]
1

(*Check*)

PolynomialRemainder[Numerator[fun], Denominator[fun], t]
1 + t^4 - 2*t^5 + 2*t^6 - 4*t^7 + 5*t^8 - 4*t^9 + 6*t^10 - 7*t^11 +
5*t^12 - 5*t^13 + 7*t^14 - 6*t^15 + 4*t^16 - 6*t^17 +
  6*t^18 - 3*t^19 + 3*t^20 - 3*t^21 + t^22

1*Denominator[fun] + %
1 + t^4 - 2*t^5 + 2*t^6 - 4*t^7 + 5*t^8 - 4*t^9 + 6*t^10 - 7*t^11 +
5*t^12 - 5*t^13 + 7*t^14 - 6*t^15 + 4*t^16 - 6*t^17 +
  6*t^18 - 3*t^19 + 3*t^20 - 3*t^21 + t^22 + (-1 + t)^7*t^7*(1 + t +
t^2)^2*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6)

FullSimplify[%] == Numerator[fun]
True

Regards
Dimitris