Problem calculating an expression with roots

01312015, 08:16 AM
Post: #7




RE: Problem calculating an expression with roots
It takes much time to simplify your expression because of the way the CAS handles fractional powers. Everything is converted to a unique algebraic extension, here of degree 24, that depends on x. On a desktop with Xcas, you get an impressive rootof over a big denominator after a few seconds.
a:=normal(sqrt(x)*(2x)^(1/3)*(3x)^(1/4)) then normal(normal(b^12)) returns 432*x^13, therefore a seems to be (432*x^13)^(1/12) Of course, there are faster ways to handle expressions like that because there are only * and ^, but I did not implement anything for that, it's much too specific, while the general algorithm can handle +,,inv,*,/ (but is too slow on a calc). Just for fun, the denominator is 230844665274826752*x^211591866337624326144*x^20+427214488707388145664*x^19+12143550017802860494848*x^18383148224530214704644096*x^17+403326885144955994505216*x^16+24737181941124395515772928*x^15+23100313665974376526774272*x^14721159543494255466332020736*x^131879698125953101870690734592*x^121379343605380747369369610112*x^11343081635027894091463265792*x^1051960732759524362938918912*x^95636720287344516274888704*x^8376051106333108239073280*x^715740221526669160087552*x^653246666561770487808*x^5 and the minimal polynomial for the algebraic extension: [1,0,12*x,16*x,66*x^218*x,96*x^2,220*x^3+148*x^2,144*x^3432*x^2,495*x^4+198*x^3+135*x^2,384*x^410816*x^3,792*x^52448*x^4+4104*x^3,2016*x^5+37632*x^4+4320*x^3,924*x^6+4476*x^522748*x^4540*x^3,4032*x^626688*x^543776*x^4,792*x^7648*x^6183048*x^5+89640*x^4,4704*x^750912*x^6+48608*x^511232*x^4,495*x^86948*x^7+355338*x^6258660*x^5+1215*x^4,3456*x^8+104256*x^7163584*x^6+350784*x^5,220*x^9+9072*x^877640*x^7+710704*x^6+114372*x^5,1584*x^965664*x^8116064*x^7+148608*x^6+3888*x^5,66*x^104842*x^9+35172*x^8920100*x^7+804762*x^61458*x^5,416*x^10+9024*x^9+164352*x^81139776*x^7+289440*x^6,12*x^11+1044*x^1040248*x^9+371496*x^8876924*x^7+57348*x^6,48*x^11+3600*x^10+40608*x^9+610656*x^844496*x^7+11664*x^6,x^1234*x^115529*x^10115420*x^938561*x^829538*x^7+729*x^6] 

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