mpsolve runs forever and other issues

[parisseb]

If you divide the Mandelbrot polynomial of degree 255 by x^3+2x^2+x+1 and call mpsolve with 30 digits and goal approximate, it runs forever. This is a polynomial of degree 252 (I paste the coefficients at the end of this message).

I have another issue trying to integrate mps in giac/xcas: for the same polynomial, with mps_context_select_algorithm(s, MPS_ALGORITHM_SECULAR_GA); mps_context_set_output_goal (s, MPS_OUTPUT_GOAL_APPROXIMATE); mps_context_set_output_prec (s, nmps); after a call to mps_mpsolve and mps_context_get_roots_m (s, &mroot, &drad), I don't understand what's in drad. I was expecting to get for each root a radius of a circle containing the root. But here for a radius of about 1e-50, I get some roots near -2 with a small imaginary part of about 1e-20 instead of a real root and that should not happen with a radius of 1e-50. Is this a bug or did I miss something about radius using the secular algorithm? If you want to reproduce this, you can compile this source file https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/mps.cc (see first line for compilation command, it requires installing giac). Then run ./a.out -1e-30 bug1 where bug1 contains quo(x*(x*(x*(x*(x*(x*(x*(x+1)^2+1)^2+1)^2+1)^2+1)^2+1)^2+1)^2+1,x^3+2x^2+x+1)

The file content that runs forever with mpsolve: !mand252 dri 0 252 1 0 0 4 10 24 84 287 951 2997 9178 27687 82556 243856 714585 2078280 5998812 17186929 48889915 138114909 387573696 1080521975 2993201892 8239628896 22541699645 61292110635 165648278291 444993617790 1188285124297 3154274100432 8323365625136 21833611738404 56935515935122 147595804188348 380362965100104 974440000395468 2481664860255580 6282905072767168 15812679064764308 39561848766736998 98394972185596230 243273059572206654 597915751348686360 1460869301670406434 3548207176726510040 8567100294413053988 20563028996235601018 49064758617351911624 116381070793653314652 274426190054250116886 643278853540344137698 1499004645324515350418 3472446557055584539388 7996415371966954046646 18305431438069836678640 41656854387498307358540 94234787788137846291862 211909348279228052595706 473694408447088023970366 1052568436777891016642880 2324879849307308568372858 5104373412871346915808664 11139593594723103421807956 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