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plurals

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20545619
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2013-12-12T14:02:40.620
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2013-12-12T14:02:40.620
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One problem could be that your coefficients contain floating point numbers. This often does not work with symbolic software. Using f=10000*simplify(re(poly)) and g=10000*simplify(im(poly)) and editing the results gives polynomials with integer coefficients. The CAS (Magma in my case) then can produce a triangular representation of the ideal of f and g, which is given as the polynomials <pre><code>a - 2483798807340123709959247/13545514719183259347425004828125*b^4 + 66732206412048596386372283/541820588767330373897000193125*b^3 - 3849759933277117021785191063/86691294202772859823520030900*b^2 + 9245906471290310401430681453/1733825884055457196470400618*b - 31414499425567273751868164900/866912942027728598235200309, b^5 - 189465979625/206648369*b^4 + 330827538698125/826593476*b^3 - 17645868534640625/206648369*b^2 + 1724106750659765625/206648369*b - 52548859891484375000/206648369 </code></pre> which tells us that 5 solutions exist. The numerical solutions for the second polynomial are <pre><code>174.10461010682254746847015187264557067610513554291323564643772 + 63.402741884833821878468926640811609033267039765104756747285816*i 174.104610106822547468470151872645570676105135542913235646437738 - 63.402741884833821878468926640811609033267039765104756747285804*i 258.006564009101655109715962546854008929462784282347754971379392 + 272.334426347869856080204881056671278679761260094680345276069337*i 258.006564009101655109715962546854008929462784282347754971379382 - 272.334426347869856080204881056671278679761260094680345276069359*i 52.62969633957523864698147679803879873180829265956656342643376 </code></pre> resulting in exactly one real solution. The numerical result of sympy was correct and complete.
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singulars
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1. POFinding all roots of a complex polynomial with SymPy
 singulars
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1. PTAnswer
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1. USLutzL
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