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Lifting polynomials

asked 2013-10-05 01:14:18 -0600

ogward gravatar image

Hello!

I have this polynomial 'fp' that I'd lite to lift to ZZ. How do I go about doing something like this in Sage online?

Univariate Quotient Polynomial Ring in y over Ring of integers modulo 127 with modulus Y^23 + 126     
fp=y^21 + 126*y^19 + y^17 + 126*y^16 + y^15 + y^14 + y^13 + y^12 + y^9 + 126*y^8 + 126*y^5 + 126*y^4 + 126*y^2 + 126*y +  1

Univariate Polynomial Ring in X over Integer Ring
Q.<X> = PolynomialRing(ZZ)

Best regards!

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answered 2013-10-05 02:20:16 -0600

Luca gravatar image

updated 2013-10-05 04:24:34 -0600

It's a two-step process. First you need to lift in $\mathbb{Z}/27\mathbb{Z}[y]$, then lift the coefficients in $\mathbb{Z}$:

fp.lift().change_ring(ZZ)

Or, if you want the result to live in your polynomial ring Q of variable X

Q(fp.lift())
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are you positive about this? I'm a bit confused as my Polynomial ring Q is defined by the variable 'X'(as shown above) and the variable in fp is 'y'. should't the answer be a polynomial with 'X'? my answer is show in his ring Qp.<y> = PolynomialRing(Zmod(p)).

ogward gravatar imageogward ( 2013-10-05 02:56:19 -0600 )edit

Edited my answer. Is this closer to what you were looking for?

Luca gravatar imageLuca ( 2013-10-05 04:24:58 -0600 )edit

that's exactly it! thanks a lot!

ogward gravatar imageogward ( 2013-10-05 05:19:21 -0600 )edit

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Asked: 2013-10-05 01:14:18 -0600

Seen: 121 times

Last updated: Oct 05 '13