Re: Re: Why is the negative root?

*To*: mathgroup at smc.vnet.net*Subject*: [mg69657] Re: [mg69642] Re: Why is the negative root?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 20 Sep 2006 02:44:00 -0400 (EDT)*References*: <200609130803.EAA18412@smc.vnet.net><eejais$2ta$1@smc.vnet.net> <eel28n$dsf$1@smc.vnet.net> <200609190944.FAA28301@smc.vnet.net>

p-valko at tamu.edu wrote: > I am a bit surprised by the "elitism" of the responses. Paul and Andrej > and previously Daniel Lichtbau all defend the Root objects without > telling the whole story. I am hard pressed to figure out what might earn one this bit of name calling. It's not exactly new territory (in the States one gets called elitist for things as simple as political major party affiliation). But it is a bit unusual on MathGroup. I particularly wonder what part of the story I missed. Frankly, I can't even figure out what part I told: I see nothing to indicate I replied in MathGroup to this thread, and unless I replied from my home machine via webmail interface (possible, but unlikely), there is no evidence in my outgoing mailbox that I replied at all. > In my opinion those objects are just > pseudo-useful. If you plot > Plot[Root[-1 + b #1 + #1^3 &, 1], {b,-10,10}] > you will see that they are defending a monster. It is discontinuous at a root crossing. I tend to think of parametrized roots as an ensemble, rather than as individual root functions, and thus regard this as less a problem than, say, dealing with the spurious imaginary parts of a numericized radical formulation. All the more so in situations where one has roots to a quartic, or where one has no chance to obtain a radical form of roots. > But I am not going to start (continue) a debate on faith. Rather I am > trying to formulate my question on a language even hard-core Mathematica > defenders can accept: > > "Assuming that the coefficients are real and I am interested only in > real roots, how do I persuade Reduce to give the formulas 69 - 72 of > > http://mathworld.wolfram.com/CubicFormula.html ? > (I do not mind if Mathematica gives two different result depending on the sign > of the determinant.)" > Regards > Peter > [...] Could try the method in: http://library.wolfram.com/infocenter/Conferences/337/ See section: "Radical solutions vs. Root objects. vs. trigs for cubic equations". Whether this "works" will depend on what exactly you want in an arctrig formulation, and (I think) on some details of ComplexExpand. An aside: if you want to think of this as some sort of battle with myself amongst defenders of Root[] functions, you are sort of out on your own. If this ever was a battle, it was won many years ago. Though as best I can tell it was generally recognized (both in symbolic and numeric computation circles), before the appearance of Root[] functions (and equivalents in other programs), that these were the needed representation for sensible handling of algebraic functions. Daniel Lichtblau Wolfram Research

**References**:**Why is the negative root?***From:*p-valko@tamu.edu

**Re: Why is the negative root?***From:*p-valko@tamu.edu

**Re: an equation containg radicals**

**Re: Re: attention 64 bit Mathematica users - would you please test a command for me?**

**Re: Why is the negative root?**

**Re: Why is the negative root?**