> <\body> interface> completes by providing the user with special variants for polynomials with numerical type coefficients: <\itemize> |analyziz/polynomial_double.hpp>, |analyziz/polynomial_floating.hpp>, |analyziz/polynomial_ball.hpp>. Root finding is implemented: <\itemize> |analyziz/solver_aberth.hpp> contains an implementation of Aberth's method, |analyziz/solver_floating.hpp> uses the latter solver with gradual precision doubling, |analyziz/solver_ball.hpp> includes certification with ball coefficients. interface> <\session|mathemagix|default> <\input> <|input> use "analyziz" <\unfolded-io> <|unfolded-io> p: Polynomial Floating == polynomial (-1.0001, 0.0^^4, 1.0) <|unfolded-io> -1.000100000000000000000000000000000000003>: > <\unfolded-io> <|unfolded-io> bit_precision := 128; v == roots p <|unfolded-io> ,0.3090231744676361593283293244132217784405-0.9510755366646799096692339194573113113580*\,1.000019999200047996640255339572892528134-1.463023860841311977236202941830836428098e-98*\,0.3090231744676361593283293244132217784405+0.9510755366646799096692339194573113113610*\,-0.8090331740676601576484569941996680425059+0.5877970075273189885146125012659640572021*\|]>>: |)>> <\unfolded-io> <|unfolded-io> [ eval (p, a) \| a in v ] <|unfolded-io> ,-1.175494350822287507968736537222245677819e-38-7.315704507899035038550609833263372575725e-98*\,-1.469367938527859384960920671527807097273e-39*\,-1.175494350822287507968736537222245677819e-38|]>>: |)>> <\unfolded-io> <|unfolded-io> p: Polynomial Ball (Floating, Complex Floating) == \ \ polynomial (ball (-1.0001), (ball 0.0)^^4, ball 1.0) <|unfolded-io> +|)>*x+|)>*x+|)>*x+|)>*x-1.0001000000000000000000000000000000000>: |)>|)>> <\unfolded-io> <|unfolded-io> roots p <|unfolded-io> ,0.30902317446763615932832932441322178-0.95107553666467990966923391945731131*\,1.000019999200047996640255339572892528,0.30902317446763615932832932441322178+0.951075536664679909669233919457311311*\,-0.80903317406766015764845699419966804+0.587797007527318988514612501265964057*\|]>>: |)>|)>> . If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.> <\initial> <\collection>