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2013-07-08 12:06:47 -0500 | commented answer | multivariate polynomial root-finding Yes, there are multiple solutions $\bar{q}(p)$. I've found a workaround that involves numerical root-finding for high-degree polynomials, let me know if you want to see it. |

2013-07-08 09:53:42 -0500 | commented answer | multivariate polynomial root-finding I'm afraid that's mathematically incorrect. Treating the polynomial I provided as a system of polynomials eliminates solutions. They don't all have to be zero in order for the problem to be solved. |

2013-07-08 07:10:36 -0500 | asked a question | multivariate polynomial root-finding I have a series of large, high-degree, bivariate polynomials in two variables, p and q. For example, one of these polynomials is: $p^7 (25/4 q^6 - 75 q^5 + 525/2 q^4 - 400 q^3 + 300 q^2 - 120 q + 20) + p^6 (-175/8 q^6 + 525/2 q^5 - 3675/4 q^4 + 1400 q^3 - 1050 q^2 + 420 q - 70) + p^5 (255/8 q^6 - 765/2 q^5 + 2655/2 q^4 - 1980 q^3 + 1425 q^2 - 540 q + 84) + p^4 (-25 q^6 + 300 q^5 - 8175/8 q^4 + 1450 q^3 - 1875/2 q^2 + 300 q - 35) + p^3 (45/4 q^6 - 135 q^5 + 1785/4 q^4 - 580 q^3 + 300 q^2 - 60 q) + p^2 (-45/16 q^6 + 135/4 q^5 - 855/8 q^4 + 120 q^3 - 75/2 q^2) + p (5/16 q^6 - 15/4 q^5 + 45/4 q^4 - 10 q^3) + 1$ I would like to find all values of $q$ for which this polynomial is equal to $1-p$. The following code block illustrates my problem: All Sage returns is another multivariate polynomial, which doubtless has many solutions $\bar{q}(p)$. Is there something I can do to get these solutions? |

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