Timeline for Intersection Solutions of four nonlinear equations
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2018 at 18:05 | comment | added | Sara yaqob | I don't understand what is the problem ..you answered to my question. | |
| Dec 26, 2018 at 17:43 | comment | added | user64494 | After that edit dropbox.com/s/mkvvskm0i0m5mtx/screen26.12.2018.docx?dl=0 the question was edited one more time without any notice. This is not a good practice. | |
| Dec 26, 2018 at 16:43 | history | edited | Iosif Pinelis |
edited tags
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| Dec 26, 2018 at 9:45 | comment | added | user64494 | What was edited in your question? Please notice it. | |
| S Dec 26, 2018 at 7:04 | history | suggested | vidyarthi |
appropriate tag classification
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| Dec 26, 2018 at 6:34 | review | Suggested edits | |||
| S Dec 26, 2018 at 7:04 | |||||
| Dec 25, 2018 at 20:59 | vote | accept | Sara yaqob | ||
| Dec 25, 2018 at 20:21 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Dec 25, 2018 at 19:49 | comment | added | Jan-Christoph Schlage-Puchta | The most straightforward way is by computing resultants. If $P, Q$ are polynomials in $x, y, z, \ldots$, then Resultant[P, Q, x] gives a polynomial in $y, z, \ldots$, which vanishes at $(y_0, z_0, \ldots)$ if and only if there exists some $x_0$, such that $(x_0, y_0, \ldots)$ is a common zero of $P$ and $Q$. Thus you can pass from a system of $n$ equations in $n$ variables to a system of $n-1$ equations in $n-1$ variables. Unfortunately the degree increases, so in this case it would be wise to exploit (3) and (4) as Noam Elkies described first. | |
| Dec 25, 2018 at 17:55 | comment | added | Sara yaqob | I have two differential linear systems with centers the first one has a first integral H1(x,y)=k, the second one has the first integral H2(x,y)=h, I am looking for the number of intersection points between H1(x,y)=k, H2(x,y)=h, and the curve y^2-x^3=0......I suppose that there are two pairs (\alpha, \beta) and (\gamma, \delta) satisfying the four following equations .(it is necessary)....................1) H1(\alpha, \beta) =H1(\gamma, \delta) ....2) H2(\alpha, \beta) =H2(\gamma, \delta) ...3) \beta^2-\alpha^3=0 ............4) \delta^2-\gamma^3=0. | |
| Dec 25, 2018 at 17:21 | comment | added | Noam D. Elkies | Again I ask: why is this particular system of equations of interest, and in what context do you "need to solve" it? Knowing where a problem comes from (and why you expect that it has only two (real? complex?) solutions) is often useful in finding a solution $-$ and also in motivating others to help you with it. | |
| Dec 25, 2018 at 16:15 | review | Close votes | |||
| Dec 29, 2018 at 16:58 | |||||
| Dec 25, 2018 at 16:03 | comment | added | Sara yaqob | I need to solve this system of equation to prove that it has only two solutions, I used Mathematica software but it's very complicated | |
| Dec 25, 2018 at 16:02 | history | edited | user44191 | CC BY-SA 4.0 |
TeXing
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| Dec 25, 2018 at 15:59 | comment | added | Noam D. Elkies | Where do those equations come from $-$ i.e. why do you care about this particular system with its complicated coefficients? $$ $$ (3) and (4) mean that $(\alpha,\beta) = (x^2, x^3)$ and $(\gamma,\delta) = (y^2, y^3)$ for some $x,y$. So now you have two equations in two variables and can use a resultant to eliminate one of them. Then you still have to deal with the $\sqrt 3$'s in the coefficients, though some packages know how to do this. | |
| Dec 25, 2018 at 15:55 | review | First posts | |||
| Dec 25, 2018 at 16:04 | |||||
| Dec 25, 2018 at 15:53 | history | asked | Sara yaqob | CC BY-SA 4.0 |