Problem calculating an expression with roots

[rprosperi]

(01-31-2015 08:16 AM)parisse Wrote:  ...Just for fun, the denominator is
230844665274826752*x^21-1591866337624326144*x^20+427214488707388145664*x^19+12143550017802860494848*x^18​-383148224530214704644096*x^17+403326885144955994505216*x^16+24737181941124395515​772928*x^15+23100313665974376526774272*x^14-721159543494255466332020736*x^13-1879698125953101870690734592*x^12-1379343605380747369369610112*x^11-343081635027894091463265792*x^10-51960732759524362938918912*x^9-5636720287344516274888704*x^8-376051106333108239073280*x^7-15740221526669160087552*x^6-53246666561770487808*x^5
and the minimal polynomial for the algebraic extension:
[1,0,-12*x,-16*x,66*x^2-18*x,96*x^2,-220*x^3+148*x^2,-144*x^3-432*x^2,495*x^4+198*x^3+135*x^2,-384*x^4-10816*x^3,-792*x^5-2448*x^4+4104*x^3,2016*x^5+37632*x^4+4320*x^3,924*x^6+4476*x^5-22748*x^4-540*x^3,-4032*x^6-26688*x^5-43776*x^4,-792*x^7-648*x^6-183048*x^5+89640*x^4,4704*x^7-50912*x^6+48608*x^5-11232*x^4,495*x^8-6948*x^7+355338*x^6-258660*x^5+1215*x^4,-3456*x^8+104256*x^7-163584*x^6+350784*x^5,-220*x^9+9072*x^8-77640*x^7+710704*x^6+114372*x^5,1584*x^9-65664*x^8-116064*x^7+148608*x^6+3888*x^5,66*x^10-4842*x^9+35172*x^8-920100*x^7+804762*x^6-1458*x^5,-416*x^10+9024*x^9+164352*x^8-1139776*x^7+289440*x^6,-12*x^11+1044*x^10-40248*x^9+371496*x^8-876924*x^7+57348*x^6,48*x^11+3600*x^10+40608*x^9+610656*x^8-44496*x^7+11664*x^6,x^12-34*x^11-5529*x^10-115420*x^9-38561*x^8-29538*x^7+729*x^6]

Although I must admit that seeing this result did make me smile, I cannot fully agree that this is fun. But thanks for taking the time to explain this.