I've got this error while installing mdcs:

Building Maple archive mdc.mla
smarch -c mdc.mla
/bin/bash: smarch: command not found
make: *** [mdc.mla] Error 127

I couldn't find how to install the command "smarch". Which package are you using?

@vv if V is required to be a proper vector. We can formulate a non-zero vector V:=<c,d,e>;

Then solve the system of equations that involve the vars: a,b,c,d,e

Is it possible?

@vv Let's say V is a non-zero vector with norm = 1, is it possible? Could you please explain more?

@vv yes, I'm looking for other ways to formulate it: 

I already have 2 methods:

1. det(J) = 0;

2. J.V=0 (V is a non-zero vector)

@vv In the J matrix, I have some unknowns 

So the question is writing some sort of equations that make the J rank deficient.

From that, I could solve the equation(s) to get the solution for the unknowns that make J lose rank.

@vv I agree that the inequalities do count, as I said, the inequalities in this system are used to isolate the solution, choose the positive solutions, to be specific. However, the system f1->f7 defines the curves.

I've used your suggestion, tried to derive f7 and subs it into other equations, I got the new system on x,y,t1 which is good. Thanks for that.

But actually, my goal is to find a general method for this kind of problem. This is a small system; there are systems where I have to deal with a large number of equations. I though there would be the method that reduces the system into a characteristic polynomial. Then we could use some sort of rational parametrization to plot the set easily (the set would be lines, curves, or surfaces).

Anyway, for this general problem, it seems I have to use solve or the tools in DirectSearch package to get the solution.  

@Markiyan Hirnyk this is very close to the desired solution. I've tried your method and get some sort of curves below (without taking to account the inequalities). Would be awesome if knowing how to deal with the inequalities, because there are some extraneous solutions that lead to the redundant curves.

@Christian Wolinski thanks for your attempt. it sounds odd. There should be some mistakes. We have 8 vars, but only 7 equations involved (doesn't count the last 3 eqs because it is used to isolate the solutions), so the solution must be some set of curves.

Could you please post the previous code? we can look at it and figure out the problem, it looks close to the desired solution. The figure I posted was generated by a numerical software.  

@Markiyan Hirnyk Thanks for your help

Actually, I expected something like the method we could use to reduce a system of equations into a characteristic polynomial. Then, we can try the rational parametrization to generate the parametric curves or surfaces, then we can easily plot the solution, it would be faster, I guess so. This is my idea, I'm not familiar with this, but any suggestion in this approach would help me a lot. Thanks

@Markiyan Hirnyk I see that this approach is not optimal in terms of computational time, it took me minutes to get the solution of 200 points. Do you think so? 

I would love to know if there is a method to do it faster, because if there is a case where we have to generate the surface of solutions where thousands of points appear. Anyway, this is also the general method for any system of equations. Thank you very much!

@Christian Wolinski hi, it looks closed to the desired solution, in fact some solution are missing. Here is the top projection in (x,y). Could you post the code so everybody can discuss about it?

@Carl Love yes, they are meant to be equal to 0, I remove the "=" sign to put it into Maple

@vv Thanks for your help, i get it.

This is just an example to a general problem, cannot be extended to use in other system of equations. I believe there is a general and consistent way to do this.

@Markiyan Hirnyk I want to get the parameterized system on x,y and t1, so I can plot it in 3d and get some sort of curves or surfaces

the result of that system project into (x,y,t1) should be like this:

@Markiyan Hirnyk Hello, thanks for your asking, I had a mistake. it should be (x,y,t1) in this case. I've edited it.

If we combine those equations, will x and y be eliminated? let's say I want to project the surfaces or curves in the range x[-10,10] y[-10,10] t1[-Pi,Pi], all the other vars has the range [-Pi,Pi]