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Re: notation using # with exponents and &
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92941] Re: [mg92921] notation using # with exponents and &
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Mon, 20 Oct 2008 07:35:38 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
RootApproximant[Pi, 8] // InputForm
Root[-21 + 48*#1 - 19*#1^2 - 31*#1^3 + 17*#1^4 - 60*#1^5 - 4*#1^6 + 4*#1^7 + #1^8 & ,
2]
This is Pi approximated as the root of an eighth degree polynomial using a pure function. Look up Root and Function
Root[f, k] is the k-th root of the polynomial equation f[x] == 0
x /. Solve[#1^8 + 4*#1^7 - 4*#1^6 - 60*#1^5 + 17*#1^4 - 31*#1^3 -
19*#1^2 + 48*#1 - 21 &[x] == 0, x][[2]] // N
3.14159
Equivalently,
x /. Solve[x^8 + 4*x^7 - 4*x^6 - 60*x^5 + 17*x^4 - 31*x^3 -
19*x^2 + 48*x - 21 == 0, x][[2]] // N
3.14159
Bob Hanlon
---- Molly Lipscomb <molly_lipscomb at yahoo.com> 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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