I find some book teach motion planning in topology 

but do it need to formulate the equations for the environments such as a map with obstacle in 2d or 3D?  the environment is quite complex, how can these equations be formulated?

Can old maple version saved .m files in window be readable in maple 2015 Linux version?

i would like to to test and do hash on a 2d array and then predict this hash and then reverse back to another hash which can convert back to 2d array , how to do?

Is there lifting function for polynomials or algebra use?

expect input a list univariate polynomial , then output a list of polynomials of two variables.

it should be the reverse operation of projection.

Which library has this function in maple 12 or maple 2015?

sourcesamples := [evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
templatesamples := [A, evalf(-1-sqrt(7)), A, -2, A, 1, A, evalf(-1 + sqrt(7)), A, 2, A];
samples := [-4, evalf(-1-sqrt(7)), -3, -2, 0, 1, evalf(3/2), evalf(-1 + sqrt(7)), evalf(9/5), 2, 3]

want to insert value alternatively according to the template and neighbor values

Some inserted values come from

floor(evalf(-1-sqrt(7)))
ceil(evalf(-1-sqrt(7)))

(round(evalf(-1+sqrt(7)),0) + 1)/2;
(2 + 1)/2
=evalf(3/2)

(round(evalf(-1+sqrt(7)),1) + 2)/2;
(1.6 + 2)/2
=evalf(9/5);

how to generalize this method into general case function instead of manual inesrt?