MDD

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These are questions asked by MDD

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?

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?

 

restart

with(PolynomialIdeals):

``

``

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]

 

"G:="

 

x^2-y-4

 

x^2-y-4

 

y^3-3*x

 

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

 

true

 

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

 

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

(1)

``

Download bug.mw

Hi

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?

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