@acer The added the datatype declaration to local A in LArip showed some improvements. This line is amazing:

Grid:-Map(subs(rr = r, MM = M, eval(k -> LArip(k, rr, MM))), [$ (1 .. r)])

Thanks again.  

Thank you for your insightfulness and quick response.

Hi,

I noticed your additional conditions: g is not a square of an integer number and your limits for b, d, and f. I incorporate these new conditions to mloops.mw. Again there many solutions and the real time is less than 5 minutes to complete the search. Please see new script.

  mloops_mod_2.mw

@Carl Love This problem was prosed by a user a year ago on Mapleprime: looking for a fast way to find 6 integer roots. I suggested a solution at that time. I am revisting it to see if I can speedup my original solution. I enjoyed reviewing your script. It will take me much time to understand it.

You appear to have found more than 2 possible 6 integer root solutions. I may be wrong, but I substituted the values for the 7 coefficients from Sols into the equation: abs(a*x + b) + abs(c*x + d) - t*x^2 + m*x - n and calculated the equation for the various roots (x). The results were not always zero. Please see script.

Roots_with_map_cl.mw

I hope I understood your question correctly about the possibilities of 8 integer roots instead of 6. It never occurred to me that there will be 8 integer roots. I modified the script called Roots_with_map.mw found in my original question. I changed the statement if nops(X) = 6 to if nops(X) = 8 and added and frac(X[7]) = 0 and frac(X[8]) = 0 in Procedure 2. I was not able to come up solution with 8 roots. Please show me how to get 8.

Thanks again for your help, I throughly enjoyed it.

@Carl Love I would never have come up your three methods to handle multiple agruements. You are right they did required as much time to complete as my old method. Thanks.

@dharr I like the Profile function. I will implement your the seq method and see what happens.

Thanks again. 

@acer  thanks for your explanantion, very helpful.

I also have struggled with problem of properly declaring the datatype.

Download thread_gl.mw

Two lines of code were added in red font to @acer's tutorial. They appear show some speed improvements when using map versus Threads:-Map. Please explain. Is this possible? Thank you.

Download thread_map_acc_mod.mw

@mmcdara 

Your explanation is right on. This is a Bayesian problem that was first solved in R. I did not fully understand the solution in R. I thought if I tried to solve it in Maple then I would have a better understanding of Bayesian Analysis. I turned to Maple because I can ask questions, if I get stuck, and get some really good answers and help from very knowledgable people. Thanks so much for your help again.

@acer 

It is wonderful to see how you can get so much speed from your code. Thank you 

@mmcdara 

I am still stuck in the world of for loops. Thank you.

@Carl Love Thank you, you solved two problems for me: one in Maple and R.

@acer Thanks so much. I am learning to use Maple, off and on. I thought turning one of my procedure into C code would be something interesting to understand. I am always like to learn about simplifing or improving code/script. Could you offer some suggestions that I may try.

Thank you. 

@Carl Love 

Another variation. I am learning alot today. Thanks.