Sharedsupport / 2015-05-13-111552.sagewsOpen in CoCalc
Examples for support purposes...

c23c1050-6ece-4a8b-9133-84d20901fd52
R.<x> = RDF[]
p = 331776*x^36 - 11943936*x^34 + 195747840*x^32 - 1932263424*x^30 + 12809871360*x^28 - 60216016896*x^26 + 206610186240*x^24 - 524928024576*x^22 + 991718940672*x^20 - 1386996203520*x^18 + 1415900528640*x^16 - 1026732589056*x^14 + 505483296768*x^12 - 158084628480*x^10 + 28283240448*x^8 - 2378170368*x^6

p.roots()
[(-2.002061769233494, 1), (0.0, 6), (2.0019692379514833, 1)]
p.roots(CDF)
[(-2.002061769233494, 1), (0.0, 6), (2.0019692379514833, 1), (-1.9989726631542863 - 0.0018799310334743384*I, 1), (-1.9989726631542863 + 0.0018799310334743384*I, 1), (-1.9491204848785912 - 0.0438260977666023*I, 1), (-1.9491204848785912 + 0.0438260977666023*I, 1), (-1.8335921409220832 - 0.06885614642262637*I, 1), (-1.8335921409220832 + 0.06885614642262637*I, 1), (-1.7672112908697883 - 0.29094074586911356*I, 1), (-1.7672112908697883 + 0.29094074586911356*I, 1), (-1.0884589210361526 - 0.4723685573016453*I, 1), (-1.0884589210361526 + 0.4723685573016453*I, 1), (-0.8164516294478674 - 0.15463773142849763*I, 1), (-0.8164516294478674 + 0.15463773142849763*I, 1), (-0.48375342827963264 - 0.17658017537451084*I, 1), (-0.48375342827963264 + 0.17658017537451084*I, 1), (0.48375342827963247 - 0.17658017537451232*I, 1), (0.48375342827963247 + 0.17658017537451232*I, 1), (0.816451629447875 - 0.15463773142850787*I, 1), (0.816451629447875 + 0.15463773142850787*I, 1), (1.088458921036147 - 0.4723685573017288*I, 1), (1.088458921036147 + 0.4723685573017288*I, 1), (1.767211290890328 - 0.29094074587044855*I, 1), (1.767211290890328 + 0.29094074587044855*I, 1), (1.8335921531554762 - 0.06885615377916224*I, 1), (1.8335921531554762 + 0.06885615377916224*I, 1), (1.9491208653682 - 0.04382607882375571*I, 1), (1.9491208653682 + 0.04382607882375571*I, 1), (1.9990185360517412 - 0.0017925795209700309*I, 1), (1.9990185360517412 + 0.0017925795209700309*I, 1)]
p.roots(RealField(200))
[(-2.0020617692334941040144258295185863971710205078125000000000, 1), (0.00000000000000000000000000000000000000000000000000000000000, 6), (2.0019692379514832936138191143982112407684326171875000000000, 1)]
p.roots(ComplexField(200))
[(-2.0020617692334941040144258295185863971710205078125000000000, 1), (0.00000000000000000000000000000000000000000000000000000000000, 6), (2.0019692379514832936138191143982112407684326171875000000000, 1), (-1.9989726631542863444224167324136942625045776367187500000000 - 0.0018799310334743383685274231709172454429790377616882324218750*I, 1), (-1.9989726631542863444224167324136942625045776367187500000000 + 0.0018799310334743383685274231709172454429790377616882324218750*I, 1), (-1.9491204848785912417952204123139381408691406250000000000000 - 0.043826097766602296890159351505644735880196094512939453125000*I, 1), (-1.9491204848785912417952204123139381408691406250000000000000 + 0.043826097766602296890159351505644735880196094512939453125000*I, 1), (-1.8335921409220832245523524761665612459182739257812500000000 - 0.068856146422626371417230473070958396419882774353027343750000*I, 1), (-1.8335921409220832245523524761665612459182739257812500000000 + 0.068856146422626371417230473070958396419882774353027343750000*I, 1), (-1.7672112908697883426611952017992734909057617187500000000000 - 0.29094074586911355950746838061604648828506469726562500000000*I, 1), (-1.7672112908697883426611952017992734909057617187500000000000 + 0.29094074586911355950746838061604648828506469726562500000000*I, 1), (-1.0884589210361526046000335554708726704120635986328125000000 - 0.47236855730164528655024014369701035320758819580078125000000*I, 1), (-1.0884589210361526046000335554708726704120635986328125000000 + 0.47236855730164528655024014369701035320758819580078125000000*I, 1), (-0.81645162944786742187375239154789596796035766601562500000000 - 0.15463773142849762676220848334196489304304122924804687500000*I, 1), (-0.81645162944786742187375239154789596796035766601562500000000 + 0.15463773142849762676220848334196489304304122924804687500000*I, 1), (-0.48375342827963263570012486525229178369045257568359375000000 - 0.17658017537451084488786534620885504409670829772949218750000*I, 1), (-0.48375342827963263570012486525229178369045257568359375000000 + 0.17658017537451084488786534620885504409670829772949218750000*I, 1), (0.48375342827963246916667117147881072014570236206054687500000 - 0.17658017537451231593337297454127110540866851806640625000000*I, 1), (0.48375342827963246916667117147881072014570236206054687500000 + 0.17658017537451231593337297454127110540866851806640625000000*I, 1), (0.81645162944787497139031984261237084865570068359375000000000 - 0.15463773142850786856961065041105030104517936706542968750000*I, 1), (0.81645162944787497139031984261237084865570068359375000000000 + 0.15463773142850786856961065041105030104517936706542968750000*I, 1), (1.0884589210361470534849104296881705522537231445312500000000 - 0.47236855730172877532169195546885021030902862548828125000000*I, 1), (1.0884589210361470534849104296881705522537231445312500000000 + 0.47236855730172877532169195546885021030902862548828125000000*I, 1), (1.7672112908903279127059704478597268462181091308593750000000 - 0.29094074587044854718342890009807888418436050415039062500000*I, 1), (1.7672112908903279127059704478597268462181091308593750000000 + 0.29094074587044854718342890009807888418436050415039062500000*I, 1), (1.8335921531554761898519245733041316270828247070312500000000 - 0.068856153779162238004474261288123670965433120727539062500000*I, 1), (1.8335921531554761898519245733041316270828247070312500000000 + 0.068856153779162238004474261288123670965433120727539062500000*I, 1), (1.9491208653681999507512045965995639562606811523437500000000 - 0.043826078823755706959097722119622630998492240905761718750000*I, 1), (1.9491208653681999507512045965995639562606811523437500000000 + 0.043826078823755706959097722119622630998492240905761718750000*I, 1), (1.9990185360517411794489817111752927303314208984375000000000 - 0.0017925795209700308777134303284128691302612423896789550781250*I, 1), (1.9990185360517411794489817111752927303314208984375000000000 + 0.0017925795209700308777134303284128691302612423896789550781250*I, 1)]
plot(p, -5, 5, ymax=10, ymin=-10)
complex_plot(p, (-3,3), (-3,3))