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factor x^2 - 30*x + 2817 in sqrt(-2)

asked 2016-11-02 00:47:32 -0600

Sha gravatar image

Is there a way I can use SAGE to factor my polynomial x^2 - 30*x + 2817 in sqrt(-2).

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Note that we write Sage rather than SAGE.

slelievre gravatar imageslelievre ( 2016-11-02 10:56:35 -0600 )edit

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answered 2016-11-02 01:22:36 -0600

rtc gravatar image

updated 2016-11-02 01:46:04 -0600

I think you are looking for the roots of the polynomial:

f = x^2 - 30*x + 2817
f.roots()

which gives:

[(-36*I*sqrt(2) + 15, 1), (36*I*sqrt(2) + 15, 1)]

This would mean that your original function is equal to:

$$ x^2-30x+2817 = \left(x-(15-36 \sqrt{-2})\right)\left(x-(15+36\sqrt{-2})\right)$$

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yes this is what I am looking for.. thank you..

Sha gravatar imageSha ( 2016-11-02 03:07:24 -0600 )edit
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answered 2016-11-03 05:32:30 -0600

slelievre gravatar image

Note that you can also work over the field QQbar of algebraic numbers.

Here is how you would factor your polynomial there and find its roots.

sage: P.<x> = QQbar[]
sage: p = x^2 - 30*x + 2817
sage: p.factor()
(x - 15.00000000000000? - 50.91168824543143?*I) * (x - 15.00000000000000? + 50.91168824543143?*I)
sage: p.roots()
[(15.00000000000000? - 50.91168824543143?*I, 1),
 (15.00000000000000? + 50.91168824543143?*I, 1)]

If you want a radical expression for the roots:

sage: for r in p.roots():
....:     print(r[0].radical_expression())
....:     
-36*I*sqrt(2) + 15
36*I*sqrt(2) + 15
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Thank you for explaining this to me. It is so useful in my calculation.

Sha gravatar imageSha ( 2016-11-03 05:50:38 -0600 )edit

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Asked: 2016-11-02 00:47:32 -0600

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Last updated: Nov 03 '16