Is there some basis containing polynomials of the form x[1]^p*x[2]^q+x[2]^p*x[3]^q+x[3]^p*x[1]^q, (p,q posint)?
Are there known relationships between these?

Note: these are not the symmetric polynomials.

Kitonum had provided us the basis for a solution to this question.  I created a proc to make it versatile. 
The problem was how to force Maple to display the RHS of :

Here is the proc(I've condensed the variables)

extract := proc(a, expr) 
  local f:
  f := a: 
  ``(f)*expand(expr/f); 
end proc:

eq := 1/cao - 1/caa:
extract(1/cao, eq);
                     

 Now suppose we had an trigonometric expresssion and we extract cos(x) out of it

expr := cos(x) - sin(x)/(x^2*y) + 3*x*y
                       
bb := extract(cos(x), expr)
                       

ok, that's good, now we would like to keep the order but simplify the middle term sin/cos to tan.  The best way about it is to use algsubs and manually substitute the relation with the option exact.  I don't Maple can achieve this without the manual help.

algsubs(sin(x)/cos(x) = tan(x), bb, exact)
                   

Now we're at the mercy of Maple here.  Maple always likes to throw negative terms out front.  The premise of Maple is to show it as it would appear on paper.  I mentioned exact and it shouldn't have changed the order but it did.  So maybe if we use sort we can right it. 

sort(%)
             

Ok, good but now Maple has thrown the single term multiplier at the end. 

Can anyone get maple to put the cos(x) term out front?

help under object it says  (in Maple 2021)

The above has not been true for almost a year. Since in Maple 2021 one can do o:-m() 

person_class :=module()
  option object;
  export m:=proc(_self,$)
      print("you called me");
  end proc;
end module;

o:=Object(person_class);
o:-m()

            person_class := Object<<1758956556512>>
                  o := Object<<1758955674784>>
                        "you called me"

I hope this gets updated in Version 2022,  with examples also. The notation o:-method() is hidden in help and could not even find it, but it is meantioned in some pdf file which I lost track of at this moment. 

On another help page titled Overview of Object Methods it briefly mentions alternative call but the link that is supposed to explain it does not work. (clicking on it, produces nothing. Stays on same page). I guess no one tried this link before shipping Maple. 

Is this link somewhere to access directly in the help page?

How can factorise a polynomial with complex roots, without showing their numerical values of the roots, but only their symbolical value.

For example I have:

factor(x^4 - x^2 + x - 1)

and it shows me the following factorisation: (x-1)(x^3+x^2+1) but I want to also factorise x^3+x^2+1 but the roots should be displayed symbolically without numerical values of these roots. Then how to implement this task?

In the book I am reading it's stated to use factor(x^4-x^2+x-1, I), but it doesn't seem to be working.

Hello everybody.

I have a short question. I have an expression related to the calculation of the Gaussian curvature

-24.*y^6*(y-1.)^7*(y+1.)^7*(4.+6.*y^8-22.*y^6+30.*y^4-18.*y^2)/(4.*y^18-28.*y^16+84.*y^14+4.-136.*y^12+116.*y^10-24.*y^8-52.*y^6+56.*y^4-24.*y^2)^2

that is diverged for y=1 as (y-1)^(-2). 

At the same time substitution of something like y:=1.00001 gives the value almost zero. 

What is the trick?

How do I write this in Maple?

Find points P and Q on the parabola y = 1 − x^2 so that the triangle ABC formed by the x-axis and the tangent lines at P and Q is an equilateral triangle.

Thank you!

How do I write this in maple?

Find the maximum value of l f"(x)l on the indicated interval. f(x)= sqrt1+x^2  [0,2]

Thank you!

How do I write this in maple?

The figure shows a circle with radius 1 inscribed in the parabola y = x^2 . Find the center of the circle.

Thank you!

When performing a RootOf command on a polynomial how would you then extract the polynomial itself from the result?

I.e. If i were to set A:= RootOf(x^2-1) Maple would then return A = RootOf(_Z^2-1), so what command performed on A is needed to give me just _Z^2-1 (or even better x^2-1)?

Sorry if this is horribly worded  :(

I want to arrange this equation in term of powers of x and then plot the  real and imagenery part of x vs y. How can I do this with Maple?
1-alpha*((1/x^2)+(1/(x-y)^2)+(1/(x+ay)^2))=0;

1.mw     (alpha and a are constant, for example alpha=1 and a=0.3)

Does anyone by any chance know why I might be getting this error?

I'm working with polynomials that have coefficients with many digits (16).

Thank you in advance,

Hello Dear Community

I was by pure coinsidence integrating a simple expression, f(x) =
The correct answer is F(x) = + an arbitary Constant and if you expand F(x), you will get

F(x) = + an arbitary Constant 

When I do the integration command in Maple2021 for f(x) =  , Maple2021 gives me the output in expanded form
F(x) = 

Maple2021's output is missing the 

I have uploaded my Maple-document regarding this issue to this link something_wrong.mw

Please do check this out and come back with a feedback since I find it disturbing that Maple2021 is giving an incomplete output for an integrating expression that is easy to solve in hand.

~~ Best regards

Please find the attached Maple file.

test_temp.mw

Dear all
My goal, is expand a given function using chebyshev polynomails. Everything is well written, but unfortynattely, the coeffients an, are not computed exactly, but the result return only integral form and there is evalaution of this integral.

How, can I expand my function f , using sum ( a_n chebyshev Tn), for x in [0,1] and we get explicitely the results. 

Question_integral_chebyshev.mw

Thank you for any help