[GAP Forum] Problems with Float Package

[Dr. Kashyap Rajeevsarathy]

Dear Forum,

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 ]

-- 
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