MaplePrimes Questions

Hi.

I have a question, if it is possible please guide me. I tried for this problem but I failed.

I have a set of linear equations that I want to find the "minimum" "positive" "integer" solution to it. This system may contain free parameters in some cases that they should be set an integer in such a way that they yield our goal namely "Minimum positive solution".

I used isolve but it does not work for this case.

Indeed I especially want that maple use isolve it and then search that if there are "freevars" (in the solution: produced by maple when we use isolve code) or not, if yes then set number such that all solutions be the minimum positive integer set that we can have, indeed, the "freevars" should not set manually, but by the Maple. In the case that there is no "freevar", then maple should give me the minimum positive integer that we can have.

Note that the result must be a unique set of solutions.

For example, one of such systems that I am concerning is as follows which contains freevar in solution when we use isolve.

sys := [a[1] = 2*a[5], a[1] = a[4], 4*a[1]+2*a[3] = a[6]+2*a[7], 2*a[2]+2*a[3] = 2*a[6], a[2] = a[4]+a[5], 2*a[2]-a[1] = 2*a[4]]

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) = x (x^2 - 1)^5
The correct answer is F(x) = 1/12 (-1 + x^2)^6+ an arbitary Constant and if you expand F(x), you will get

F(x) = x^12/12 - x^10/2 + (5 x^8)/4 - (5 x^6)/3 + (5 x^4)/4 - x^2/2 + 1/12+ an arbitary Constant 

When I do the integration command in Maple2021 for f(x) = x (x^2 - 1)^5 , Maple2021 gives me the output in expanded form
F(x) = x^12/12 - x^10/2 + (5 x^8)/4 - (5 x^6)/3 + (5 x^4)/4 + x^2/2

Maple2021's output is missing the 1/12

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 

On my maple page i got also all the time typesetting info ?
Looked at the help page :NumberTheory,PrimeCounting

How to produce the graph of the prime counting function with the two approximations?

how can i sort this expresion by index of L

f(15) := expand(((673*L[13] - 485*L[14] - 176*L[15])*h^2 - 90*(L[13] - (13*L[14])/15 - (2*L[14])/15)*x*h)/(12*h^3));

thank you

Imagine you want to precisely refer to this help page

The only way I am aware of is typing the whole string

Task,building,spe……

that it can be pasted as Maple input (with a leading ?) or as search term in the help system.

Are there other methods (like creating a hyperlink by right click somewhere) to extract this information/string once you are in the help system on a specific page?

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