ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 26 Dec 2017 09:12:52 -0600Factor a quadratic in a quartic polynomialhttps://ask.sagemath.org/question/40304/factor-a-quadratic-in-a-quartic-polynomial/Hi, I have done this calculation using a very tedious way and have checked that it is correct. Can I possibly perform this using Sage only.
I have a polynomial :
D=M^2-(A/(2*p^4))*M+(B/(16*p^4))
where
A=18*p^{10} - 54*p^9 + 59*p^8 + 130*p^7 - 209*p^6 - 98*p^5 + 407*p^4 + 362*p^3 + 49*p^2 - 16*p + 8
and
B=9*( p + 1 )^2*(p^4 - 2*p^3 + 2*p^2 + 2*p + 1)*(4*p^8 - 52*p^7 + 373*p^6 + 68*p^5 - 445*p^4 + 72*p^3 + 163*p^2 - 48*p+ 9).
I have checked using multiple software that the factorization of D using the quartic in $p$
`v^2= p^4-2*p^3+5*p^2+8*p+4` gives
`[M-((A+2*F*v)/(4*p^4))]*[M-((A-2*F*v)/(4*p^4))]` where
`F=9*p^8-18*p^7-7*p^6+45*p^5-21*p^4-74*p^3-18*p^2+6*p-2`.
Can someone help me obtain the same result by using Sage only. Thank you.ShaTue, 26 Dec 2017 09:12:52 -0600https://ask.sagemath.org/question/40304/