Timeline for Number of distinct entries in a rotation invariant cube
Current License: CC BY-SA 4.0
22 events
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| Dec 3, 2022 at 18:36 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Dec 3, 2022 at 18:26 | vote | accept | Jacob Helwig | ||
| Dec 2, 2022 at 17:06 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Dec 1, 2022 at 23:47 | comment | added | Daniel Sebald | @MaartenHavinga SO(3) actually does contain S3, inside A5. | |
| Dec 1, 2022 at 21:47 | vote | accept | Jacob Helwig | ||
| Dec 2, 2022 at 17:07 | |||||
| Dec 1, 2022 at 21:30 | vote | accept | Jacob Helwig | ||
| Dec 1, 2022 at 21:47 | |||||
| Dec 1, 2022 at 19:45 | answer | added | Maarten Havinga | timeline score: 1 | |
| Dec 1, 2022 at 19:13 | comment | added | Maarten Havinga | @JacobHelwig it seems to me more that you mean 90 degree rotations of functions from $Z_N^3$ to some other algebra, where $Z_N$ is the integers modulo $N$. For you cannot apply 3D rotations to $N×N×N$ tensors in general. | |
| Dec 1, 2022 at 8:47 | review | Close votes | |||
| Dec 10, 2022 at 3:03 | |||||
| Dec 1, 2022 at 0:26 | comment | added | Jacob Helwig | @LSpice Sure, I edited my question | |
| Dec 1, 2022 at 0:26 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Dec 1, 2022 at 0:24 | comment | added | Jacob Helwig | @MaartenHavinga I do not follow your comment - is my proposed answer right? | |
| Dec 1, 2022 at 0:23 | comment | added | Jacob Helwig | @GerryMyerson Similar to how $\mathbb R^{5\times5}$ is the space of $5\times5$ matrices, $\mathbb R^{5\times5\times5}$ is the space of $5\times5\times5$ tensors. I'm imagining rotating a tensor $X$ by a rotation tensor $R$, similar to a rotation matrix. Then what I mean by unchanged is that $R\cdot X = X$ | |
| Nov 30, 2022 at 22:54 | comment | added | Gerry Myerson | I don't understand the notation. If $N$ is, say, $5$, then $X$ is a cube in the $125$-dimensional space ${\bf R}^{5\times5\times5}={\bf R}^{125}$. I don't know what it means for $X$ to be a cube in this space. So, maybe you mean a cube in ${\bf R}^3$, measuring five on each side. Then what does "the result is unchanged" mean? What result? Unchanged from what? | |
| Nov 30, 2022 at 20:37 | comment | added | Maarten Havinga | No wait. Since N is odd, elements at an n-th index can be rotated to other elements at an n-th index: (3,1,n) to (3,n,1) as x-axis rotation. That only counts for these edge cases with a 1 index and an n index. | |
| Nov 30, 2022 at 20:20 | comment | added | Maarten Havinga | Since SO(3), the group of all rotations in 3D, contains A3 but not S3, the odd permutations are excluded. So there are twice as much 3 different index unique elements. I think you're correct after changing that. | |
| Nov 30, 2022 at 17:53 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Nov 30, 2022 at 17:46 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Nov 30, 2022 at 17:23 | history | edited | Jacob Helwig | CC BY-SA 4.0 |
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| Nov 30, 2022 at 17:00 | history | edited | Jacob Helwig |
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| S Nov 30, 2022 at 16:59 | review | First questions | |||
| Dec 1, 2022 at 8:26 | |||||
| S Nov 30, 2022 at 16:59 | history | asked | Jacob Helwig | CC BY-SA 4.0 |