MaplePrimes Questions

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?

How do I write this out in maple?

Sketch the graph of y =x^2+7x+3/x^2 , locate all maximum and minimum values, intervals of increase and decrease, and inflection points.

Thank you!

How do I write this in maple?

Find the point on the parabola x + y 2 = 0 that is closest to the point (0, -3).

Thank you!

Graph the curve with equation y(y2 −1)(y − 2)= x(x −1)(x − 2)
At how many points does the curve have horizontal tangents?

Estimate the x-coordinates of these points.

Find the equations of the tangent lines at the points (0,1) and (0,2)

Find the exact x-coordinates of the points of these points.
Create even more fanciful curves by modifying the equation.

PLEASE WRITE STEP BY STEP IN MAPLE

How to get rid of the boundary

display(ellipse([0, 0], 2, 1, filled=true, color = red),size=[1000,500],axes=none);

or how to make the boundary the same color as the filled region?

 

I am trying to adapt the code with Direct Search 2 for my needs but do not quite understand the syntaxis :( . I have system with 8 first order but nonlinear odes and 20 parameters but for starters I fix most of them (to estimate time consumption for full calculations etc). The part of the code where it ``breaks'' looks as follows:

#argument
X0:=Vector([24, 36, 48, 60, 72, 84], datatype = float):
#value
Y0:=Vector([13.8e+9, 12.13333333e+9, 10.7e+9, 10.5e+9, 9.8e+9, 10.1e+9], datatype = float):

#so this is the data - time in X0 and corresponding observables (at that time instances) at Y0


par_sol:=dsolve(dsys, numeric, range=0..85,  parameters=[eta_L, L0]);

#parametric numerical solution with eta_L parameter of the model and L0 initial condition to fit

ffit2 := proc(etaLValue, L0Value, tValue) global old_eta, old_L0; local res;
if not [etaLValue, L0Value,tValue]::list(numeric) then
      return 'procname'(args); end if;
if old_eta<>etaLValue and old_L0<>L0Value then
      (old_eta,old_L0) := etaLValue,L0Value;
      par_sol('parameters'=[eta_L=etaLValue,L0=L0Value]);
   end if;
   res:=rhs(par_sol(tValue)[4]); end proc;


# this is just adapted copy of your function

 

par_sol(parameters=[eta_L=0.004, L0=1.1e10]);

par_sol(84)[4];ffit2(0.004, 1.1e10, 84);

#their output coincide OK; same for another trio of parameters

DS2:=CodeTools:-Usage(
        DirectSearch:-DataFit(ffit2,X0,Y0,t,
                              [ eta_L=0.001 .. 0.1, L0=1.5e10 .. 1.7e10
 #                               
                              ] )
);

#and here it breaks:

Warning, initial point [L0Value = .9, tValue = .9] does not satisfy the inequality constraints; trying to find a feasible initial point
Error, (in DirectSearch:-Search) cannot find feasible initial point; specify a new one


But tValue is a time variable - I integrate over it, it is not a parameter to fit - I evaluate ffit2 at it. So basically ffit2 return exactly the model value which need to be fited with data in Y0 at times specified in X0. I thought it is easier than the other problems I saw in examples with Direct Search 2 and still I can't get through syntax neither with it not with NonlinearFit of core Maple...

I would appreciate if you could point me what I am doing wrong. Just in case I also attach full version of the file.01test.mw

Thank you in advance!

Hello. I want to organize some parameter
F=fsolve(1+x^2=j).

If j=-5, for example, an empty value 'F=' will be returned. How can I write the expression

If F=(void), then action 1, else action 2 end if

The fact is that I just don't know how to write the result (void), that is, the result of 'F ='

Thanks

Hi

I was wondering how one uses maple to solve for variables that comprise the limits of an integral?

X and R are between 0 and 1.

Any thoughts would be greatly appreciated, thanks in advance...!

Download Solvingforlimitsofintegrals.mw

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