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give the code to seperate out two terms

asked 2016-04-14 10:37:59 -0500

santoshi gravatar image

p=5 K.=GF(p^2);K.modulus() R.<z>=PolynomialRing(K); f=(z+2*a+4).truncate(1)

m=f.list() m the above code after execution give the result (2a+4) . i want to seperate out terms (2a) and 4. How to seperate?
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slelievre gravatar imageslelievre ( 2016-04-15 07:30:58 -0500 )edit

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answered 2016-04-14 11:17:27 -0500

tmonteil gravatar image

With:

sage: m=f.list()[0]
sage: m
2*a + 4

you get an element of the field of size 25:

sage: m.parent()
Finite Field in a of size 5^2

To separate 2*a and 4, you need to see it as a polynomial on the field on 5 elements (with indeterminate a):

sage: m.polynomial()
2*a + 4
sage: m.polynomial().parent()
Univariate Polynomial Ring in a over Finite Field of size 5

So, you can get the coefficients as follows:

sage: p = m.polynomial()
sage: p.dict()
{0: 4, 1: 2}
sage: p.dict().items()
[(0, 4), (1, 2)]

So you can get the list you want as follows:

sage: [a^i*j for i,j in p.dict().items()]
[4, 2*a]
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Asked: 2016-04-14 10:37:59 -0500

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Last updated: Apr 14 '16