Maple Questions and Posts

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Please I have an issue with the attached plot code. Can you kindly help to correct it? 

restart:
interface(rtablesize=infinity):
B:=<<0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.49,"0","0.05","0.1","0.15","0.2","0.25","0.3","0.35","0.4","0.45","0.49">|
	<14.73,14.4,14,13.4,12.67,11.67,10.4,8.67,6,3,0,"14.73","14.4","14","13.4","12.67","11.67","10.4","8.67","6","3","0">|
     <-0.007072,0.013309,0.033707,0.054125,0.074571,0.095056,0.115597,0.136218,0.156956,0.177867,0.199036,0.22059,0.242719,0.265702,0.289932,0.31592,0.344214,0.375124,0.408175,0.441761,0.473484,0.501857>|
	<1.34E+01,1.33E+01,1.33E+01,1.32E+01,1.31E+01,1.31E+01,1.30E+01,1.29E+01,1.28E+01,1.26E+01,1.25E+01,1.22E+01,1.19E+01,1.14E+01,1.08E+01,9.86E+00,8.58E+00,6.90E+00,4.90E+00,2.81E+00,1.00E+00,-2.86E-01>>:

B:
 
 plot([B[..,[1, 2]],B[1..1,[1, 2]], B[.., [3, 4]],B[1..1,[3, 4]], B[..,[5, 6]],B[1..1,[5, 6]],B[.., [7, 8]],B[1..1,[7, 8]],
 	  B[..,[9, 10]],B[1..1,[9, 10]], B[.., [11, 12]],B[1..1,[11, 12]],B[..,[13, 14]],B[1..1,[13, 14]],B[.., [15, 16]],B[1..1,[15, 16]],
 	  B[..,[17, 18]],B[1..1,[17, 18]], B[.., [19, 20]],B[1..1,[19, 20]],B[..,[21, 22]],B[1..1,[21, 22]]],
 	  legend = ["","Experimental","","Simulation"],
 	  style = ["line","line","line","line","line","line","line","line","line","line","line","line","line","line","line","line",
 	 		"line","line","line","line","line","line"],
 	  color=[blue,red], labels=[`V (V)`, `Jsc (mA/cm^2)`]);
 



Download Graph_Example.mw

Hey there,

 

I'm trying to evaluate some parameter of a function when x and y are 0.

 

Here's the code:

> Y1 := proc (x) options operator, arrow; int(`Y1"`(x), x)+C1 end proc;

 

> solve({Y1(0) = 0}, {C1});

But unfortunately I get the following error:

Error, (in int) integration range or variable must be specified in the second argument, got 0

 

I know that the value of C1 is gonna be 0, but I want the program to say me this...

 

Please, some help.
 

i have a nonlinear equation,W, which have two unknowns: x and b 
i want to solve W for b, and the x domain is : -4e-6<x<4e-6. can anyone help? tnx in advance


 

restart; with(DirectSearch)

E := (-7.29511346879067*10^9*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(2.02316788462733*10^17*b+4.107030812*10^12)*phi(x)+1.74615339888993*10^17*b

(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b

(1)

dsolve(E, phi(x))

ivp := {E, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

{(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

(2)

N := dsolve(ivp, phi(x))

A := simplify(rhs(dsolve(ivp, phi(x))))

W := evalf(subs(phi(x) = simplify(rhs(dsolve(ivp, phi(x)))), (2.74505742817409*10^8+3.18054074382591*10^8*phi(x))^2-(1.63833629390402*(2.74505742817409*10^8+3.18054074382591*10^8*phi(x)))*(diff(phi(x), x, x))+3*(6.98727355657655*10^7+32282.4885498329*(diff(phi(x), x)))^2+2.68414581287153*(diff(phi(x), x, x))^2 = 0.9e17))

 

``

``

 

 

 


 

Download MZ2.mw

I found a condition for p, q that N=pq can be factored in plynominal time using Maple 2020.
Is fllowing Hypothesis and Proof is right?

Hypothesis

       N=pq  p and q are large prime respectively.
         R=q/p  q > p  R is very close to an small integer or a simple rational number.
       
        N=pq can be factorized in time polynomial

Proof
        point[p, q] is on y=N/x
        y=N/x  and y=Rx cross at point[p, q]
        N is n digit
        upper  2 digits N2  round off the 3rd digit
        upper  3 digits N3  round off the 4th digit
        upper  4 digits N4  round off the 5th digit
        
        y=N2/x and y=Rx cross at point[p2,q2]
        y=N3/x and y=Rx cross at point[p3,q3]
        y=N4/x and y=Rx cross at point[p4, p4]

        But we only know N.

        Let line up candidates point[p2,q2] , point[p3,q3] and point[p4, p4]


       N2 < 99  i=1..10 j=1..10
       R2=i/j
       f2=N2/R2 - j^2
       dn2=abs(N2-R2*j^2)   

      N4 < 9999  i=1..99 j=1.. sqrt(N4)
      R4=i/j
      f4=N4/R4 - j^2
      dn4=abs(N4-R4*j^2)

     Point[j, i] that have  small f2 and dn2 can be nominated as candidate for point[p2, q2]
     Point[j, i] that have  small f3 and dn3 can be nominated as candidate for point[p3, q3]
     Point[j, i] that have  small f4 and dn4 can be nominated as candidate for point[p4, q4]

    Find cross point[px, qx] of y=R2x and y=N/x , y=R3x, y=N/x and y=R4x, y=N/x
    Find the nearest prime pn for px and the nearest prime qn for qx
   
   pn*qn=N  bingo!

   Number of candidates are finit.
   You can factorized N=pq in time polynomial.
                                   
                                                                       Q.E.D. ?

In addition, using "https://www.mapleprimes.com/questions/228532-Strange-Factorization"

Rang from p - half digits of p to p + half degits of p and /or range q - half digits of q to q + half degits of q  N=pq can be factored in plynominal time.

Hello everybody,

I am a Maple 2020 user and I want to ask, if it is possible to change the fonts in Plots (Axes, Lables, Legend...) to the standard font that is used by LateX (Computer Modern)

This would improve the look of a plot used in a LateX document.

 

Thank you in advance.

I know Maple supports Kovacic algorithm for second order linear ODE with rational function coefficients, which gives Liouvillian solutions if one exists. (one of the earliest implementation of this algorithm was on Maple in 1984 by Carolyn J. Smith at University of Waterloo.)

There is  now a new algorithm that finds hypergeometric solutions, which could be used, when Kovacic can not find Liouvillian solution.   By doing tracing, I am not sure if Maple implements this new algorithm or not.

The new algorithm is described in "Algorithms for Solving Linear Differential Equations with Rational Function Coefficients" by Erdal Imamoglu Department of Mathematics Florida State University. Here is power point description of it

https://www.math.fsu.edu/~hoeij/2017/erdal_imamoglu_slides.pdf

I tried one example they give, which is 

ode:=x*(1+x)*(8*x-1)*diff(y(x),x$2)+(24*x^2+14*x-1)*diff(y(x),x)+(2+8*x)*y(x)=0;

There is no Kovacic solution, but Maple finds solution in terms of Heun special functions and unresolved integral

 

The above link gives this solution in terms of 2F1. This is on slide 5 in the above PDF link

sol:=1/(1-2*x)*hypergeom([1/3,2/3], [1], 27*x^2/(1-2*x)^3)

Which odetest verifies:

My question is: Does Maple implement the above algorithm? Are there plans to do so if not? And is it possible to convert the solution obtained by Maple, to the one using hypergeom, since it looks much simpler. (pdf does not show the constants of integrations c1, and c2, in this example for some reason)

This seem a powerfull algorithm due to this

 

 

Hi, everyone!

I'm trying to do some computations with (truncated) multivariable power series, which I'd like to put into Hironaka standard basis form.  This is almost the same as a Groebner basis, except that the "leading" terms have smallest degree instead of largest.  This requires slight changes to the algorithms in order to make sure they terminate.  Does anyone know if this has been implemented in Maple or have a good way to fake it?  Here's what I've thought of:

  • Using the Groebner package with grlex_min instead of grlex.  The documentation warns that this may not terminate, and sure enough, it doesn't.  (At least not before my computer runs out of memory.)
  • Replacing the truncated power series with their palindromes, using the Groebner package, and then switching back, making sure all the degrees are correctly accounted for.  This should work, but it's going to be a major pain.
  • Reimplementing the Groebner routines.  I'd really rather not, but I'd love to know if anyone else has.

Anybody have any other ideas or suggestions?

Thanks!

----Josh

Dear community,

I am new to maple and was trying to get a solution for simple Hagen Poiseuille Flow. Hagen Poiseuille Flow  has governing equation as :

ode2 := -v+mu((diff(r*(diff(ur), r)), r))/r) = 0

here 'v' is a constant (pressure gradient) and the equation is in cylindrical coordinates

the problem has two boundary conditions as u(R) = 0 and u(0) = 'finite'.

I am struck at the second condition as there seems to be no option to say maple that the solution should be finite at a point.

Can anyone help me in this regard?

 

 

Alternatively, I can give second boundary condition as (D(u))(0) = 0. However, this gives a solution as follows:

dsolve({ode2, u(R) = 0, (D(u))(0) = 0}, u(r)):

u(r) = (1/4)*RootOf(-mu(_Z)+v)*r^2-(1/4)*RootOf(-mu(_Z)+v)*R^2

 

This doesn't look very easy, and I don't know what to do with this. 

The solution for the above differential equation is simple and can be obtained on paper. Please help.

 

Thank you.

 

 

Hello. I am trying to solve this system of equations but I can't get Maple to show all solutions.

I have solve the system by hand and there are two more solutions (x=x, y=1) and (x=x, y=-1).

 

Thanks for any help !

 

For example, the line:

> for x from 1 by 0.2 to 2 do print (fsolve (x*y = 1)) end do;

returns a list of 6 values of y. Is there any way of transferring this list into a spreadshhet program, such as SigmaPlot or Excel, as a column other than cutting-and-pasting? A simple cut-and-paste (I've tried) leaves empty cells in-between entries. An alternative is to right-click with the mouse and choose "Conversions" => "Make into List" or "Make into Set", which results in:

> R1 := {.8333333333, .5555555556, .6250000000, 1., .7142857143, .5000000000};

> R0 := [1., .8333333333, .7142857143, .6250000000, .5555555556, .5000000000];


These can be saved into a text file that can be opened in Excel and only needs to be transposed (the results are pasted as a row). Although the solution above would be fine for a small number of values, it would be cumbersome for a larger number of values.

 

 

Hi, could someone tell me what this comma inside the arctan means?

Screenshot: https://photos.app.goo.gl/ZHyfdqcxWDgvgMZL7

i want to compute and draw  lattice points from a given lattice basis.

for example 2d cartesian coordinate system;

thank 

 

 

Hi,

How to display combinations without repetition of a set ( order does not matter)

Thanks

CAP13Combinatoire.mw

My points are all numerical values. Why gives me such error?
 

 


``


 

Download temp.mw

Hi 
I need to represent the contourplot of sum a function as

contourplot(sum(BesselJ(n,r),n=0..5),r=-10..10).
can anyone know what the problem is ?

Thanks

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