Timeline for EXACT number of intersection points of two algebraic curves
Current License: CC BY-SA 4.0
6 events
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| Jan 16, 2021 at 8:34 | comment | added | François Brunault | This is not equivalent: Bézout's theorem only gives the number of points over the complex numbers, not the reals. To get the number of real intersection points, you need to use Hilmar-Smyth and count the number of real embeddings of the number fields that appear. | |
| Jan 16, 2021 at 4:04 | comment | added | BobSS | @FrançoisBrunault Thanks for your help!To be simple I just want to know how many common points do Three ellipses have on the R^2 plane.And that's equivalent to how many common points do two algebraic curves have.I would read the paper through and try Magma as soon as possible after I finish my homework before the deadline.Thanks again! | |
| Jan 15, 2021 at 18:06 | comment | added | François Brunault | Also, what is your field $k$? Do you mean the $k$-rational points? Do you include the points at infinity? | |
| Jan 15, 2021 at 17:04 | comment | added | François Brunault | It depends on whether you take into account the multiplicities of intersection or not. Assuming you just want the cardinality of the set-theoretic intersection, this is done in the following nicely written paper: arxiv.org/abs/0907.0361 This has been implemented in Magma: magma.maths.usyd.edu.au/magma/handbook/text/1386#15457 (you can use Magma with the online calculator). | |
| Jan 15, 2021 at 15:56 | review | First posts | |||
| Jan 15, 2021 at 17:33 | |||||
| Jan 15, 2021 at 15:55 | history | asked | BobSS | CC BY-SA 4.0 |