MDD

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These are questions asked by MDD

 

Let m, n be two monomials with parametric coefficients. How to decide that two monomials are distinct in the variables?

For example, if m= (a-1)x^2y and b= (a-b)z^2 (where a,b are parameters and x,y,z are variables) then m and n are distinct. Is there any command? 

Thank you in advance.

Dear all,

How can I decide that the product a*n appears on the list [1-a*n*xy, x+y]? I used from the following function but the result is false.

I am looking forward to hearing from you.

Sincerely yours

 Dear ...

Let us consider $F$ be a parametric polynomial set. How can decide that $F$ contains a constant or parameters, automatically? For example, if $F=/{a*x^3-1, b*y+x, -1, c/}$ where $a, b$ and $c$ are parameters and $x$ and $y$ are variables then the output of procedure is true since of $F$ contains $c$ and also $-1$ and the outputs for $G=\{\a*x^3-1, b*y+x, x+y}$ is false. Is there any command or simple procedure for this conclusion?

I am looking forward to hearing from you

Sincerely yours.

Is there any Maple command to detect whether the degree of a polynomial w.r.t. all variables is less or equal 1?

For example, if $f=ax+by-1$ when $x$ and $y$ are variables then the output is true and if $g=a*x^2+b*y-c$ then it returns false. 

Let us consider L be the following list of 6 lists of polynomials which all of their polynomials are linear combination of B=[x^2,x*y,z^2,1]. 

L:=[[a*x^2+b*x*y-1, -(a*b-b)*x*y/a-z^2+(a-1)/a, -a*c*z^2/(b*(a-1))+(b+c)/b], [a*x^2+b*x*y-1, -(a*b-b)*x*y/a-z^2+(a-1)/a, 1],

[a*x^2+b*x*y-1, -z^2+(a-1)/a, c*x*y+1], [b*x*y-1, -x^2-z^2, (b+c)/b], [-1, -x^2-z^2, c*x*y], [-1, -x^2-z^2]].

Now, I need the matrix coefficients of any member of L (please note that any matrix has 4 columns according to the list B) . Is there any command for this?

Thank you in advanced.

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