[Maxima-bugs] [ maxima-Bugs-789048 ] allroots issues (doc and precision)

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Bugs item #789048, was opened at 2003-08-14 23:00
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: allroots issues (doc and precision)

Initial Comment:
The documentation doesn't say to what precision 
allroots calculates its argument: in fact, it gives full 
floating-point precision (even if the arguments are rats 
or bfloats).

allroots is advertised as "find[ing] all the ...roots of the 
real polynomial..." In fact it works on real AND complex 
polynomials, but requires that the coefficients all be 
explicit numbers (which is not stated).  The following get 
errors:

  allroots(x-sqrt(2)) => ALLROOTS: not a polynomial

  allroots(x-%pi) =>
** error while printing ERROR message **
ALLROOTS: polynomial not univariate: ~M

Shouldn't allroots simply float its argument?

allroots((x - 1)^10) gets answers about 20% off 
because it multiplies out the expression before looking 
for roots.  Shouldn't already-factored expressions be left 
that way?  (I am not sure what the right answer is to 
that, by the way -- perhaps it is more uniform to expand 
them all as floating-point polynomials?)  In any case, 
this should be documented.



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