Dear friends,

I need a procedure to classify a list of polynomials by their leading monomials. For example, if F = [x^2 - y - 1, y^2 - y, x^2 - 4, y^3 - 1, z^2 - 4] and a < be the lex ordering s.t. z<y<x, it should return [[x^2 - y - 1, x^2 - 4], [y^3 - y, y^3 - 1], [z^2 - 4]]. 

I appreciate any help you can provide.

Sincerely,

Hi

 I know that (G, A)=Basis(F,output=extended) computes reduced Groebner basis for polynomial ideal F, while  A is a list of lists.  If A is converted to a matrix, we get G=FA. Is there a command to compute matrix B such that F=GB?

Thank you. 

Hi all,

How Can I sort a list of polynomials with parametric coefficients based on the following criteria?
1. Fewer different parameters in the coefficients.
2. If the number of parameters is the same, the lower power of the parameters.
3. If the previous criteria are the same, sentences with parametric coefficients appear later.

Otherwise, the list is in order. For example, I want to obtain the sorted list 

[(a+2)*x[1]+3*x[2]-x[3]+(a-2)*x[4],2*x[1]+2*x[2]-b*x[3]+(c+1)*x[4], (a-1)*x[1]+x[2]+(a+1)*x[3]+(C^2-1)*x[4], (a+b)*x[1]+(c-3)*x[2]+(-b-1)*x[3]+2*x[4]] from the following list:

[(a-1)*x[1]+x[2]+(a+1)*x[3]+(C^2-1)*x[4], 2*x[1]+2*x[2]-b*x[3]+(c+1)*x[4], (a+2)*x[1]+3*x[2]-x[3]+(a-2)*x[4], (a+b)*x[1]+(c-3)*x[2]+(-b-1)*x[3]+2*x[4]]. 

Could you please guide me?

Thanks.

Hi Dear

Is it possible to know the algorithm and method behind a specific Maple command? 

Thank you in advance.

Hi every one

I need a command or simple procedure to convert an ODE into a linear polynomial.

For example, let us consider the ode in the attached file. I want to return the poly in this file. draft1.mw

Could you please help me?