Timeline for Spheres over rational numbers and other fields
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2010 at 23:16 | comment | added | Vipul Naik | In the three-dimensional case, with the standard dot product, the other two vectors for a vector $(a,b,c)$ on the sphere (with $a^2 + b^2 + c^2 = 1$) are: $b, (c^2 - ab^2)/(b^2 + c^2), -bc(1 + a)/(b^2 + c^2))$ and $(c, -bc(1 + a)/(b^2 + c^2), (b^2 - ac^2)/(b^2 + c^2))$ | |
| Feb 22, 2010 at 19:45 | history | edited | Bjorn Poonen | CC BY-SA 2.5 |
Described an algorithm for extending an orthonormal set
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| Feb 17, 2010 at 14:46 | comment | added | Vipul Naik | Thanks, that seems to settle it! Is the theorem constructive? i.e., is there an algorithm that works, say over the rational numbers or over finite fields? | |
| Feb 17, 2010 at 14:42 | vote | accept | Vipul Naik | ||
| Feb 17, 2010 at 2:46 | comment | added | Bjorn Poonen | This says that the answer to your question 1 is YES, and that the answer to your question 2 is always n+1, over any field of characteristic not 2, and for any n. | |
| Feb 17, 2010 at 2:37 | history | edited | Bjorn Poonen | CC BY-SA 2.5 |
simplified by replacing by a reference
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| Feb 17, 2010 at 2:32 | history | answered | Bjorn Poonen | CC BY-SA 2.5 |