one man

Alexey Ivanov

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8 years, 258 days
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     There is a chance to get all the solutions on connected subsets of solutions. Perhaps this is one connected subset. Here's an example where three variables and one equation.
http://www.mapleprimes.com/posts/200684-------Method-For-Solving-Underdetermined
     Can do similarly.  After receiving a set of solutions, we choose the ones that satisfy constrains.

       We are talking about a transformation of coordinates? To do this, we can transform corresponding equations. An example of the program (it's small and simple) transformation equations for surface motion in space.
http://www.mapleprimes.com/posts/200578-3d-Model-Of-A-Cam-Mechanism-Animation


And the example of the rigid body motion with six degrees of freedom.


https://vk.com/doc242471809_383336706

 

(But the calculation of geometry, kinematics and mechanisms animations I produce universal method based on solving systems of nonlinear equations underdetermined.)

Parameterization.mw
Maple15.
Numerical parameterization with an auxiliary surface. Always works in the local case and sometimes “global”.
Obtain the curve of intersection of the two surfaces, and then move it in any direction along the surface. Numerate and remember the point on the curve in each of its position. You can get a MxN matrix and use it as the index parameters of the surface.
Examples in the form of animation.
https://vk.com/doc242471809_375450085
https://vk.com/doc242471809_375799361
https://vk.com/doc242471809_375837573
https://vk.com/doc242471809_375682684  

   I think you would be able to help yourself consider "a" as a function of a = a (x, y). Approximate considerations in text.

Fa.mw    

Yuri Nikolaevich, using  print() suit you?
PRICONV.mw

     Numerically for the curve given any kind of equations. With geom3d  you construct the plane equation for any three points of the curve that does not lie on one line. In a cycle of successively take point of the curve, substitute them in the equation of the plane and monitor the absolute value of the discrepancy.



Many choices
on the same basis.
PAR.mw

restart:
a := [x+1, x+2, x+3, x+4];
a := convert(a, set);
a :=minus(a, {x+2});
a := convert(a, list);

restart;
a := [x+1, x+2, x+3, x+4];
a := subs(x+2 = NULL, a);
nops(a);
op(2, a);

restart: with(plots):
t := [1, 2, 3];
f(t[1]) := [3, 4]; f(t[2]) := [11, 12]; f(t[3]) := [41, 1];
pointplot([f(t[1]), f(t[2]), f(t[3])], color = RGB(7, .3, 4), style = line, symbol = solidcircle, thickness = 5);
pointplot3d([1, op(f(t[1])), 2, op(f(t[2])), 3, op(f(t[3]))], color = RGB(7, .3, 4), style = line, symbol = solidcircle, thickness = 5);

combine(-ln(x)+ln(y), symbolic);

restart;
f := x1^2/(x2^3*x3^2);
op(1, op(2, f))^sign(op(2, op(2, f)));
op(1, op(3, f))^sign(op(2, op(3, f)));
f := algsubs(1/x2 = x2b, f);
f := algsubs(1/x3 = x3b, f);

restart;

(diff(f(x), x))/(diff(ln(x), x));

 

for example:

restart;

f := sin(x);

(diff(f, x))/(diff(ln(x), x));

Skeptik18(_for_d1.mw

 For a start point “a” = 0.5 any number of solutions. It depends on the "smax".

   1, [(0.8013209420000008)], 2.70183810879842667*10^-8                                                            

   2, [(1.0938038328000006)], 1.75716205141895898*10^-7                                                        

      3, [(1.5165511908)], 3.19181676505797540*10^-8                                                        

   4, [(1.9061358998000002)], 4.58627091859398206*10^-9                                                           

   5, [(2.1833650214000007)], 4.36816931514982798*10^-8                                                            

   6, [(2.5877177300000005)], 1.71876049503971729*10^-7                                                            

    7, [(2.937538889999998)], 9.29630750157173224*10^-9                                                           

    8, [(3.219756611999996)], 2.01128799837135830*10^-7                                                            

   9, [(3.6180527559999964)], 4.55144026911824540*10^-8                                                           

   10, [(3.953152181999997)], 3.39347172584325562*10^-8                                                            

   11, [(4.239272189999994)], 2.57192325658905930*10^-7                                                           

   12, [(4.635025125999992)], 3.01111789280383846*10^-7                                                         

   13, [(4.962516473999992)], 9.20600748965938465 10^-8                                                            

   14, [(5.2514410039999975)], 2.19850920579744980*10^-7                                                           

   15, [(5.645899321999999)], 1.82685308214303177*10^-7                                                         

   16, [5.968760335999992)], 2.30153605063065925*10^-8                                                          

   17, [6.2597571959999945)], 2.33606770816408017*10^-7                                                           

   18, [(6.653469225999989)], 1.16942534766906194*10^-7                                                           

    19, [(6.97322109999999)], 7.71696275769784279*10^-8                                                          

   20, [(7.265801703999997)], 4.86139439814792240*10^-8                                                           

   21, [(7.659044969999998)], 4.08131656026711200*10^-7                                                          

   22, [(7.976567196000005)], 6.48611420128730742*10^-8                                                    

   23, [(8.270394148000008)], 1.66075897922723926*10^-7                                                           

   24, [(8.663323925999999)], 2.60858493916771295*10^-7                                                      

      25, [(8.979170028)], 7.82206077687419565*10^-8                                                           

   26, [(9.274002000000005)], 1.76298078358172460*10^-8                                                           

   27, [(9.666711878000001)], 5.96099682503847818*10^-7                                                        

      28,[(9.981252484)], 2.84982932807764656*10^-8                                                            

   29, [(10.276911416000011)], 2.49167541710448860*10^-7 

...

The Draghilev method. Read, for example: http://www.mapleprimes.com/posts/145360-The-Dragilev-Method-1-Some-Mathematical

 

restart;
Digits := 30; 2^29.403243784;

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