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These are questions asked by MDD

Hi all

Let us consider the set [f1=x-y, f2=-x^2+y^2, f3=x*y+x*z, f4=-x*y*z+z^3, f5=x*y^2+y*z^2-z^3] contain homogeneous polynomials in K[x,y,z]. It has the elements of degree 1,2, and 3. Now, we start from degree 1 so we have [x-y]. Now, we go to degree 2. Now, we shall multiply f1 by the variables and add to this set f2 and f3 i.e. we have now

[x-y], [x^2-x*y, x*y-y^2, x*z-y*z, -x^2+y^2, x*y+x*z]

 We have to continue to degree 3 and multiply f1 by all monomials in degree two in k[x,y,z] and multiply f2 and f3 by any variable and add them to f4 and f5 so we have finalyas a output:

[[x-y], [x^2-x*y, x*y-y^2, x*z-y*z, -x^2+y^2, x*y+x*z], [x^3-x^2*y, x^2*y-x*y^2, x^2*z-x*y*z, x*y^2-y^3, x*y*z-y^2*z, x*z^2-y*z^2, -x^3+x*y^2, -x^2*y+y^3, -x^2*z+y^2*z, x^2*y+x^2*z, x*y^2+x*y*z, x*y*z+x*z^2, -x*y*z+z^3, x*y^2+y*z^2-z^3]]. How can I do this automatically by a simple and efficient method in Maple?






randomzero := proc (ListVar) local A, G, i, lm, B, f, g; option trace; A := ListVar; G := NULL; for i to nops(A) do f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i); G := G, f end do; print(IsZeroDimensional(`<,>`(G))); RETURN([G]) end proc:

randomzero([x, y])

{--> enter randomzero, args = [x, y]


[x, y]










x^2-y-4, y^3-3*x




<-- exit randomzero (now at top level) = [x^2-y-4, y^3-3*x]}


[x^2-y-4, y^3-3*x]





I think there is a bug in the "randpoly" command. please see the attached file line 7 of my procedure "randomzero". Why x^2-y-4 is created while terms=1 is considered and the outputs must contain binomial?

Hi Dears

I need some random zero-dimensional binomial ideals (20 ideals or more) with two, three, or four ... generators with 4 variables atmost. Then I want to regenerate each of them such that some of their generators are not binomial and the obtained ideals are equal to the first corresponding original binomial ideals. How can do I this automatically?

As a simple example let I be an ideal generated by {x-1, y-1, z-1} which is zero-dim. We can obtain J=<x-z, x+z-2, y+z-2> that is equal to I.

Thank you in advance.


Is there any command to compute the Gauss-Jordan form and the Inverse of a Matrix simultaneously?

Thank you in advance


Hi every one

Let F= [x^2-z^2, x*y+y*z, x*z-y*z, y^2+y*z,w^2] be a special list of monomials and binomials. How to convert F into the following list:

FF=[x^2=z^2, x*y=-y*z, x*z=y*z, y^2=-y*z,w^2=0]. Please note that the left side of each equation of FF is greater than the right side w.r.t. lex ordering plex(x,y,z,w). 

Thank you in advance.

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