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Trying to analytically solve a practical matter, I came to the sophistry in the attached file. Maybe someone knows what the causes are.  Sophism.sm (30kb) downloaded 12 time(s).
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If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects |
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Good! You tell me that there are two solutions. I agree! But in this case the roots(2) function should mention them as such. In addition, the other intersection has coordinates x=-6.72537 and y=+21.20924. As a result, I (as a technician with a specialty other than mathematics) am confused. I understand that the other solution, I have to enter it from the console, in the case of a complicated and automated calculation?! My request is that you show me another method of calculation, which will offer me a solution automatically applicable to the case in question. Automatically, meaning without my intervention from the console. Edited by user 20 July 2023 16:27:46(UTC)
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Since Smath Studio ... has been replaced by Smath Solver, lots of Studio projects don't work anymore. Page 1 of this document solves line/intersection/circle. Further down red complains. Slope/Intercept are kaput Solver. You can rescue from the numerical code ... page 6 Eventually, you can solve any f(x,y), F(x,y) intersection(s). Hope it helps ... Jean. Solve Circle Line Intersect Normal.sm (171kb) downloaded 6 time(s).
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roots(3) solves intersection(s) of two symbolic differentiable functions.
Initialize wisely the third argument of roots(3)
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Originally Posted by: ola_nicolas  Good! You tell me that there are two solutions. I agree! But in this case the roots(2) function should mention them as such. In addition, the other intersection has coordinates x=-6.72537 and y= 21.20924. As a result, I (as a technician with a specialty other than mathematics) am confused. I understand that the other solution, I have to enter it from the console, in the case of a complicated and automated calculation?! My request is that you show me another method of calculation, which will offer me a solution automatically applicable to the case in question. Automatically, meaning without my intervention from the console. Previously explained.
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Originally Posted by: ola_nicolas Good! You tell me that there are two solutions. This is why we have roots(3). Solving without plotting is bad exercise. You may have full, correct and single answers without guesses for some equations. But sometimes you are gonna need to plot equations, find intersections and their coordinates. If you determine good guess points, it will show you nearest results to that coordinates. Regards 
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Thank you to everyone.
I was an engineer (currently retired) but I still have an intense activity related to my job. In engineering, although mathematics is a very useful tool (especially in engineering design), I cannot afford to waste time analyzing calculations. That's why I make any calculation from the beginning focused on the physical object of interest. That is precisely why I used an AutoCad-type program to sketch the geometric part, quoting in coordinates, instead of indicating the points of interest in a mathematical style. Admittedly, I haven't tried the roots(3) version. So I hope that the problem will be solved in this way. Thank you all at once.
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Hi Nicolas. Originally Posted by: ola_nicolas Good! You tell me that there are two solutions. I agree! But in this case the roots(2) function should mention them as such. Not in this case, because SMath's solve is a numerical procedure. You can demand that of maple's solve() or Maxima's Solve() . Originally Posted by: ola_nicolas In addition, the other intersection has coordinates x=-6.72537 and y=+21.20924. Not that fast ... the values for x are +6.7253 and -21.2093. Originally Posted by: ola_nicolas My request is that you show me another method of calculation, which will offer me a solution automatically applicable to the case in question. Automatically, meaning without my intervention from the console. Although I think that overlord's solution shows the correct solution, this other method does not require initial values, since it makes use of the knowledge that the solution implies a quadratic equation, assuming that the line M'N is not vertical .  Sophism.sm (36kb) downloaded 10 time(s).Best regards. Alvaro.
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 Originally Posted by: Razonar Not that fast ... the values for x are 6.7253 and -21.2093. The form in which the result of the roots(2) request is presented is as in the attachment. I thought (!?!?!?) that the elements of the vector represent the results x and y, respectively. Edited by user 21 July 2023 08:23:28(UTC)
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With a suitable pair of guess values, the problem will always indicate the pair of variables of the considered point, as can be seen in the attachment. Thanks for the guidance. 
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