Dear Forum,
Kindly disregard my earlier email:
I have been having some issues computing the roots of polynomials using
"RootsFloat" function of the "Float" package. Please consider the following
example:
gap> a := last;
[ [ 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0 ] ]
gap> a = TransposedMat(a);
true
gap> LoadPackage("float");
Loading FLOAT 0.6.2 ...
true
gap> SetFloats(MPFR);
gap> pol := CharacteristicPolynomial(a);
x_1^20-40*x_1^18+610*x_1^16-8*x_1^15-4640*x_1^14+40*x_1^13+
19475*x_1^12-560*x_1^11-46380*x_1^10+5560*x_1^9+61610*x_1
^8-19600*x_1^7-42220*x_1^6+25784*x_1^5+8265*x_1^4-11560*
x_1^3+3700*x_1^2-400*x_1
gap> coeff := CoefficientsOfUnivariatePolynomial(pol);
[ 0, -400, 3700, -11560, 8265, 25784, -42220, -19600, 61610, 5560, -46380,
-560, 19475, 40, -4640, -8, 610, 0, -40, 0, 1 ]
gap> RootsFloat(coeff*1.0);
[ .0e0, .381966e0, .381966e0, .618034e0+.218005e-7ⅈ, .618034e0-.218005e-7ⅈ,
.618034e0+.807401e-7ⅈ, .618034e0-.807401e-7ⅈ, -.138197e1, .2e1, -.138197e1,
-.161803e1, -.161803e1-.141802e-8ⅈ, .2e1, -.161803e1+.136277e-8ⅈ,
-.161803e1, .261803e1, .261803e1, -.361803e1, -.361803e1, .4e1 ]
Note that that the RootsFloat function is showing complex roots
(eigenvalues) for the characteristic polynomial of a real symmetric matrix.
It would greatly help of you could me what's going wrong here.
Best regards,
Kashyap
--
Kashyap Rajeevsarathy
Assistant Professor,
Indian Institute of Science Education and Research (IISER) Bhopal,
Indore By-pass Road,
Bhauri, Bhopal - 462066,
Madhya Pradesh, India.
Phone: +91-755-669-2364
Website: https://home.iiserb.ac.in/~kashyap
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