Timeline for Compatibility conditions for quadratic equations
Current License: CC BY-SA 4.0
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| Feb 17, 2023 at 3:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 18, 2023 at 16:15 | comment | added | Michael Schindler | This is a very useful link. In particular, the described method by Kronecker generates quartic and cubic conditions. The latter are the determinant of the coefficients in three quadratic equations. This explains why I also observe both of them. | |
| Jan 18, 2023 at 3:04 | comment | added | John Doyle | Hi @Michael, this Math Stack Exchange discussion includes a reference that discusses several single-variable polynomials. Perhaps this could be useful. | |
| Jan 18, 2023 at 2:13 | answer | added | Max Alekseyev | timeline score: 1 | |
| Jan 17, 2023 at 18:10 | comment | added | Michael Schindler | Thank you, John Doyle, for your quick help. I had a look at both types of resultants in the links to Wikipedia you proposed. They apply well to the case of two equations, but unfortunately I need to extend to N. The Macaulay resultant needs homogeneous polynomials, which can be achieved by adding another variable, but still I found that theory only for two equations. Do you have another idea where I could look for, say N>2 quadratic equations? | |
| Jan 16, 2023 at 22:07 | comment | added | John Doyle | The quartic expression you've given in your example is the resultant of the polynomials $A_1x^2 + B_1x + C_1$ and $A_2x^2 + B_2x + C_2$. In general, given two single-variable polynomials $f$ and $g$, the resultant is a polynomial in the coefficients of $f$ and $g$ that vanishes if and only if $f$ and $g$ have a common zero. I might suggest taking a look at the multivariate version (the Macaulay resultant) and its variants as a starting point. | |
| Jan 16, 2023 at 17:31 | history | edited | Michael Schindler |
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| Jan 16, 2023 at 17:28 | history | edited | Michael Schindler | CC BY-SA 4.0 |
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| S Jan 16, 2023 at 17:08 | review | First questions | |||
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| S Jan 16, 2023 at 17:08 | history | asked | Michael Schindler | CC BY-SA 4.0 |