2020-02-28 08:20:07 +0100 | commented answer | solving system of equations over number field "then using the vector space structure of $K$ and changing the ring of the vectors to a polynomial ring in the same variables over $\mathbb{Q}$" Didn't know I could do that, thanks for that idea! |

2020-02-27 02:49:58 +0100 | received badge | ● Editor (source) |

2020-02-23 23:05:24 +0100 | asked a question | solving system of equations over number field I am trying to solve two, 2-variable polynomial equations over $F:=\mathbb{Q}(i)$ modulo $K:=F(\sqrt{2})$. Specifically, if p1 = $a^2+6b^2$, p2 = $3a^2+2b^2$, and $K^{\ast4}:=\langle k^4\vert k\in K\setminus 0 \rangle$ i.e. the group of 4th powers of nonzero elements of $K$. I want to find (all?) $a$ and $b$ in $F$ such that p1$\equiv$1 modulo $K^{\ast4}$ and p2$\equiv$-1 modulo $K^{\ast4}$. Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it. |

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2015-06-24 23:16:15 +0100 | commented answer | Multiplying matrices with different parents? Thank you for looking into this for me! As a new user, I'm glad to know it wasn't something ridiculous on my part. Also, thanks for the suggestion to use the polynomial ring. That will get me through what I need to do. |

2015-06-24 22:52:19 +0100 | received badge | ● Student (source) |

2015-06-24 18:44:09 +0100 | commented answer | Sage is not returning all solutions to equations modulo n Thanks! This will fix my current problem, but I am still concerned for when I use larger matrices, and/or a different modulus. If anyone has ideas on a really efficient way to do this in general, I would love to hear them. |

2015-06-24 18:39:06 +0100 | asked a question | Multiplying matrices with different parents? I want to conjugate a symbolic matrix, Sigma, by a matrix, garbage, over Z/9Z. If I define both matrices as symbolic matrices, I get the right answer. If I define garbage over Z/9Z, I get confusing answers. Can anyone explain my results? |

2015-06-24 18:05:16 +0100 | asked a question | Sage is not returning all solutions to equations modulo n I am trying to find all 2x2 matrices $S$ over $Z/9Z$ such that $S^3=I$, where I is the identity matrix. I am currently using the following procedure: The list of solutions (there are 207) I receive does not include |

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