Timeline for Calculating multiplication in a finite dimensional algebra over $\mathbb{Q}$
Current License: CC BY-SA 4.0
9 events
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| Jan 28, 2022 at 17:43 | comment | added | F Zaldivar | As I understand the question, the OP is considering a finite field extension $L$ of ${\mathbb Q}$ of degree $n$. Thus, there is a primitive element $\alpha\in L$ such that $1,\alpha,\ldots,\alpha^{n-1}$ is a basis of $L$ over ${\mathbb Q}$ and from that basis somehow the OP wants to compute or find formulas for the products $ab$, for general $a,b\in L$. For the degree $n=8$ that the OP specifically mentions at the end of the post, there are useful comments in the related post mathoverflow.net/questions/414814/… by the same OP. | |
| Jan 28, 2022 at 16:24 | history | edited | Sky | CC BY-SA 4.0 |
added 29 characters in body
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| Jan 27, 2022 at 20:14 | comment | added | GH from MO | I changed title and tags to match content. Please polish the main text, e.g. the second sentence is incomplete. | |
| Jan 27, 2022 at 20:13 | history | edited | GH from MO | CC BY-SA 4.0 |
edited tags
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| Jan 27, 2022 at 20:07 | history | edited | RobPratt | CC BY-SA 4.0 |
deleted 20 characters in body; edited tags
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| Jan 27, 2022 at 18:21 | comment | added | Max Alekseyev | Yes. See example in the documentation. | |
| Jan 27, 2022 at 18:15 | comment | added | Sky | Yes here is finite dimensional algebra over $\mathbb Q$ and multiplication table are given. So can we determine the product of arbitrary two elements? | |
| Jan 27, 2022 at 18:08 | comment | added | Max Alekseyev | Sage supports finite-dimensional algebras defined by multiplication tables for the basis elements. Is this what you want? | |
| Jan 27, 2022 at 17:52 | history | asked | Sky | CC BY-SA 4.0 |