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Re: notation using # with exponents and &

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  • Subject: [mg92929] Re: notation using # with exponents and &
  • From: David Bailey <dave at>
  • Date: Mon, 20 Oct 2008 07:33:17 -0400 (EDT)
  • References: <gdevcc$3mp$>

Molly Lipscomb wrote:
> Hi,
> When I ask Mathematica to solve one of my equations, at first it says that the response is long, and asks whether I want the full output, or the output with a size limit.  When I say that I want the full output it comes up with seven roots, each of which has a polynomial which is pages long.  At the end of each root, it has a notation which I haven't seen before and can't find in any documentation--it has a box that looks something like a # sign, 1 with an exponent, and then an & sign, a comma, and then a number.  Is this an abbreviation for something?  Does it mean that I don't have the full solution listed?  
> Also, I have been trying to get Mathematica to factor or simplify the solution, but when I enter Factor[%], it just repeats the same solution.  Does this mean that the solution just can't be simplified, or is there an alternative way to do this?
> Thanks so much for any ideas you have!
> Best,
> Molly
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There is a pure maths theorem which states that just like quadratic 
equations, cubic and quartic equations have a formula that gives the 
solutions. The theorem also states that general fifth order equations 
don't have such a formula (unless you use exotic special functions).

Mathematica, being Mathematica, is not going to cheat you of these 
results if you really want them, but in practice these solutions are so 
complicated that they are of no use, unless the equation happens to 
factorize. Therefore, it is usually best to use NSolve to solve such 
equations numerically, and forget the exact solutions.

David Bailey

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