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simplify roots with mulitple inbedded roots

asked 2013-12-23 06:45:40 +0200

Kuroth gravatar image

Hi everyone,

I know this questions has been asked quite some times before and I've browsed a couple of hours searching for the answer but I haven't found anything that worked yet. So here it is:

So I have these two functions and I need to calculate k. I've found you can use the maxima_methods, but as you can see, it doesn't work here either. (I tested the example question and I could simplify that one with these commands, so it's not the virtual machine)

I know you can calculate it by using the maxima engine itself on the virtual machine en then you should find 37/4+3*sqrt(7). But isn't there any method a bit less far-fetched, and I also still need to find a way to switch to maxima on the cloud, so this solution is for the virtual machine only...

I'm working on a project for school concerning Sage and so far this is the only problem I've encountered.

Thanks in advance!

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These kinds of questions are sort of tricky... look up Bombelli's experiments with the cubic formula to see more non-obvious examples!

kcrisman gravatar imagekcrisman ( 2013-12-26 21:40:45 +0200 )edit

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answered 2013-12-23 07:04:13 +0200

tmonteil gravatar image

updated 2013-12-23 07:05:07 +0200

Quick and dirty fix, look at the algebraic field:

sage: b = QQbar(k)
sage: b.as_number_field_element()
(Number Field in a with defining polynomial y^2 - 7,
 3*a + 37/4,
 Ring morphism:
  From: Number Field in a with defining polynomial y^2 - 7
  To:   Algebraic Real Field
  Defn: a |--> 2.645751311064591?)

Here, b is 3*a + 37/4, and a is the root of y^2 - 7 which is close to 2.645751311064591, so there should be a way to get your formula from this automatically from Sage.

Also, you can do things like:

sage: b.minpoly()
x^2 - 37/2*x + 361/16
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hmm thanks! Sage astonishes me more and more hehe

Kuroth gravatar imageKuroth ( 2013-12-23 08:25:25 +0200 )edit

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Asked: 2013-12-23 06:45:40 +0200

Seen: 328 times

Last updated: Dec 23 '13