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I'm new at using Maxima, so when I wanted to solve these simultaneous equations:

$$y_1=-\left(\frac{2ax+c+ey}
{2by+d+ex}\right)x_1+\left[y+\left(\frac{2ax+c+ey}
{2by+d+ex}\right)x\right]$$

and

$$ax^2+by^2+cx+dy+exy+f=0$$

where the variables are $x, y$, maxima showed:

$[\;]$

as the otput. I inserted the system of equation through the solve algebraic system option available under the equation option in the status bar of the GUI wxmaxima.

So what should I do to get a proper answer as output, please suggest.

Peyman Mohamadpour
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Soham Sarkar
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  • Can you post a pretty print of the system – chiliNUT Jun 08 '20 at 03:18
  • I asked the same question here https://math.stackexchange.com/q/3708784/570799 in stack exchange mathematics where I used latex typesettings to write the same above equations. But sadly there I got no answers. – Soham Sarkar Jun 08 '20 at 09:06
  • I see. Yeah, I think what the comment on your other post is getting at, is that you have 2 equations with much more than 2 variables. what are you trying to do exactly, get y and x in terms of the other variables? – chiliNUT Jun 08 '20 at 15:54
  • Yes exactly. Actually I'm trying to get the general expression for the contact point of any tangent (passing from a fixed point) to the general equation of second degree. – Soham Sarkar Jun 08 '20 at 16:29
  • (1) Can you please post the actual input which you entered and the actual output, as plain text. It's very important for others to know exactly what you typed in. (2) When `solve` returns an empty list `[]` , it means that it was unable to solve the equation. `solve` isn't too strong; that is a real weakness of Maxima, I'm sorry for that. It might be possible to make progress in some way. If you post the actual input, we can go from there. – Robert Dodier Jun 08 '20 at 17:19
  • My input was algsys([y_1=-(2*a*x+c+e*y)/(2*b*y+d+e*x)*x_1+y+(2*a*x+c+e*y)/(2*b*y+d+e*x)*x, a*x^2+b^y^2+c*x+d*y+e*x*y+f=0], [x,y]); – Soham Sarkar Jun 08 '20 at 17:29
  • I think you need to enclose the inputs in backticks, i.e., like this: `` `2*x*y` ``, in order to correctly show the multiplication signs. Aside from that, the equations you showed are actually pretty complex. If you clear the fractions (i.e., multiply by the denominators) you'll get a big messy polynomial in a degree of 4 or something like that. Now a polynomial of degree 4 has a exact solution in terms of radicals, but in the general case, with all the coefficients undetermined, it is a gigantic mess, and not practical to solve because you can't actually use the solution. – Robert Dodier Jun 08 '20 at 19:57
  • My advice is to try to find definite values for some of the coefficients so that you don't have to solve the equations in full generality. Also look for structure in the problem -- perhaps you can solve a smaller problem first and use that the solve the original problem, or something like that. – Robert Dodier Jun 08 '20 at 19:58
  • Can i solve this in mathematica or matlab? – Soham Sarkar Jun 09 '20 at 13:37

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