2020-01-18 17:04:03 +0100 | commented answer | Testing whether polynomial is in algebra of other polynomials Hey. Thanks a lot for your answer! I still need to play around with it some more. In the meantime, do you think there's any way to also spit out how, for example, $x_0x_1+x_0x_2+x_1x_2$ came from the given algebra, i.e. what combination of stuff in our algebra yields $x_0x_1+x_0x_2+x_1x_2$? |

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2020-01-18 11:29:57 +0100 | asked a question | Testing whether polynomial is in algebra of other polynomials A collection $\Sigma$ of polynomials is an algebra if: (1) $\lambda f + \eta g \in \Sigma$ for any $f,g \in \Sigma, \lambda,\eta \in \mathbb{R}$ and (2) $f,g \in \Sigma$ implies $fg \in \Sigma$. We say that $P$ is in the algebra of ${P_1,\dots,P_n}$ if $P$ is in the smallest algebra containing $P_1,\dots,P_n$. I was wondering if there was a way to check whether a given $P$ as in the algebra of a given collection $P_1,\dots,P_n$.
I'd appreciate any help. |

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