Timeline for Dimensions of two spaces
Current License: CC BY-SA 3.0
10 events
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| Dec 4, 2014 at 15:24 | history | edited | Turbo | CC BY-SA 3.0 |
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| Dec 4, 2014 at 15:15 | history | edited | Turbo | CC BY-SA 3.0 |
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| Dec 4, 2014 at 15:08 | history | edited | Turbo | CC BY-SA 3.0 |
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| Dec 4, 2014 at 11:58 | history | edited | Turbo | CC BY-SA 3.0 |
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| Dec 4, 2014 at 11:53 | history | edited | Turbo | CC BY-SA 3.0 |
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| Dec 4, 2014 at 11:42 | comment | added | Turbo | @AlexDegtyarev Of course. Any ideal that produces a 'non-trivial' discrete set whose cardinality is exponential in $n$ would do. $\mathsf Z((x_1^2-x_1,\dots,x_n^2-x_n))$ is one such set and is of importance to computer science. This set describes the boolean cube. | |
| Dec 4, 2014 at 11:39 | comment | added | Alex Degtyarev | You can define multiplication to produce something of degree one in each argument, e.g., like you did, or factoring out $x_i^2$, or something else. My question was whether it makes sense. E.g., why $x_i^2-x_i$ and not just $x_i^2$? Is there any background? | |
| Dec 4, 2014 at 11:36 | comment | added | Turbo | @AlexDegtyarev $(x_{1} x_{2}+ x_{2} x_{3})^2 = (x_{1} x_{2}+ x_{2} x_{3} + 2 x_{1} x_{2} x_{3})$ So both $(x_{1} x_{2}+ x_{2} x_{3})$ and $(x_{1} x_{2}+ x_{2} x_{3} + 2 x_{1} x_{2} x_{3})$ are multilinear? | |
| Dec 4, 2014 at 11:34 | comment | added | Alex Degtyarev | Are you sure that what you describe are multilinear polynomials? Reading your posts, I was sure that multilinear were a subspace of the polynomial ring, which is not a ring. Does it really make much sense to multiply them? | |
| Dec 4, 2014 at 11:09 | history | asked | Turbo | CC BY-SA 3.0 |