# simplify roots with mulitple inbedded roots

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.

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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!

( 2013-12-26 14:40:45 -0600 )edit

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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

more

hmm thanks! Sage astonishes me more and more hehe

( 2013-12-23 01:25:25 -0600 )edit