Yo

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These are replies submitted by Yo

@tomleslie 
@Kitonum
Thank you.

What  about when we have symbpmic coefficients ? 
In the case of " alpha*x[1]^3+beta*x[1]*x[2]^2 " for example, Maple consider that terms of degree 4 instead of degree 3.
Do you have some suggestions please ? 

@Kitonum  That's great!
I learned a lot from your answer.
Thank you.

@Carl Love That's also working, thanks a lot 🙏 

@Kitonum 
Thank you,  the double "seq" function  was the solution of my problem. Thanks again.

@mmcdara 

That makes sense, thank you for your remark and your proposal.

Best regards,

 

@tomleslie 

Effectively, by using unapply, my problem is solved.
Thank you for your suggestion and your help.

best regards,

@acer Thank you.

@Kitonum Thank you.

@nm Thank you.

@vv Thank you.

@Carl Love Thank you.

@vv Thank you, that’s what i want.

    What you mean by " ^+ " in you expression please, because for me it returns "Error, invalid power".
 

@vv Thank you.

What i want in other words is:

# If B is 8*8 (p*p) upper triangular matrix:
B:=Matrix(8, 8, [[1, -7, 0, 0, 0, 0, 0, 0], [-3, 21, 0, 0, 0, 0, 0, 0], [-1, 8, 1, -7, 0, 0, 0, 0], [2, -17, -3, 21, 0, 0, 0, 0], [1, -8, -1, 8, 1, -7, 0, 0], [-2, 9, 2, -17, -3, 21, 0, 0], [-1/3, 16/3, 1, -8, -1, 8, 1, -7], [4/3, -3, -2, 9, 2, -17, -3, 21]]);

# Then, instead of the two following Null vectors returned by NullSpace(B): 
  {
Vector[column](8, [0, 0, 0, 0, -7, -1, 1, 0]),
Vector[column](8, [0, 0, 0, 0, 49, 7, 0, 1])
  }.

# I need, Null Vectors of B of the followinf form: 
  {
Vector[column](8, [0, 0, 0, 0, 0, 0, X]),
Vector[column](8, [0, 0, 0, 0, X, Y])
  }.
# where,  X:=Vector[column](2, [x1, x2]),    and    Y=Vector[column](2, [y1, y2]).   

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