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These are replies submitted by MDD

@dharr Thank you so much for your email and efforts. There is not any variable y[i] and all variables are x[i]. Thanks again. 


Thanks for the comprehensive explanations.

@Thomas Richard Thank you so much for your reply.


Thank you so much for your response. For example, I want to know the algorithm behind the "MTM:-rref" Maple command for computing the reduced row echelon form of a matrix. How to use the showstat for this?


Thank you so much. In fact, I want to use expand for sin(x+y) and so on. Expansion for (a+b)x=ax+bx is not different both of them are aA1+bA1. I try to expand the trigonometric function before using Dcoeffs. 


Thanks for your reply. Can we obtain the original ODE by saving all derivative and non-derivative terms in a sorted list with their corresponding Ai and using the subs command?

Also, I think there is a minor problem in the last file you sent. Please see the attached file. Why sin(x) is eliminated?


Thank you so much for your response and efforts. This is fine, and the final question is: How can I convert the obtained polynomial back into the original ODE? 


I need a*A4+b*A5 +c. I deal with any variables but usually x is variable.


Thank you again. This is okay, but I believe it is not working properly. Please see the attached


Thanks again, but I'm sorry, this also doesn't work in Maple 18!


Thank you so much for your answer. But, when I run your implementation an error appears. Please see the attached


Thanks, Yes, this is OK but I need an efficient implementation that receives a list of polynomials and returns as above. Also, it is possible that F contains subset F1,...Fm (Homogeneous polynomials ordered in ascending degrees and not necessarily in consecutive degrees). For example, the input is:
F=[F1={x-y}, F2={-x*y*z+z^3, x*y^2+y*z^2-z^3},F3={-x^2*y*z+z^4, x*y^3+y*z^3-z^4}].  We have to multiply F1 by all monomials in degree two in k[x,y,z] and add them to F2. Now, we must multiply F1 by all monomials in degree 4 multiply F2 by any monomials in degree 2, and add them to F3. 

@Joe Riel Thanks.
OK, I will use the homogeneous option to fix it. But, terms=1 means that a monomial, not -y-4!!

@Joe Riel A file attached namely Also, x^2-y-4 is not binomial while I used the following command in my procedure:

f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i)

@Axel Vogt Thank you so much. It is helpful almost. I am trying to implement a simple procedure too. Thanks again.

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