I have two functions, and .

Based the plot, I can see that they intersect around x equals 0, 1, around 4.5 and 10.

So I tried to find the numerical solution by solving  for x assuming x is real.

I'm stuck here because the aswer involves RootOf and _Z and I don't know what to do next.

This is what I've tried so far:
 

Download intersect_curve.mw

I know there's an answer to this because I can get the expected answer from Wolfram Alpha (see here).

How can I accomplish this in Maple? 

Hello everyone,

I would like to know if it is possible to directly enter LateX expressions into the plot command. My goal is to be able to create a plot where the font style (in for example the title) can switch between LateX math and LateX regular. See the following example.

The LateX input used for the tilte was <Verl{\"a}ufe von $e(t)$ und $\dot{\varepsilon}_\mathrm{p}(t)$>

In Matlab one can use the command <"interpreter","Latex"> which allows direct LateX input. I am basically looking for an equvialent Maple command.

If no such command exists, I would be grateful for any idea on how to create a title like the one above with other methods.

Thanks to everyone in advance.

What is your choice for creating a good table?

For example;

f:=(x,t)->x*t;
g:=(x,t)->x^2*t;

How to create a table as follows? (Appearance similar to the following is not required. I am open to all options)

Hi, I am doing a project about three body problem. I am solving a DE system with 12 DEs and plotting it with phase portrait. It is all good if I am only using vars in scene. like this:

pp1 := phaseportrait([eq1(t), eq2(t), eq3(t), eq4(t), eq5(t), eq6(t), eq7(t), eq8(t), eq9(t), eq10(t), eq11(t), eq12(t)], [x1(t), y1(t), vx1(t), vy1(t), x2(t), y2(t), vx2(t), vy2(t), x3(t), y3(t), vx3(t), vy3(t)], t = 0 .. 8.75*10^7, [[x1(0) = X1, y1(0) = Y1, vx1(0) = VX1, vy1(0) = VY1, x2(0) = X2, y2(0) = Y2, vx2(0) = VX2, vy2(0) = VY2, x3(0) = X3, y3(0) = Y3, vx3(0) = VX3, vy3(0) = VY3]], scene = [x1(t), y1(t)], stepsize = 1000, x1 = 0 .. 10^6, y1 = 0 .. 6*10^6, color = [red], scaling = constrained):

But I cannot plot any combinations of my variables. I have orthogonalized all the velocity, and I can plot [t,vx(t)] or [t, vy(t)]. But I cannot plot [t, (vx(t)^2+vy(t)^2)^1/2]:

vel1 := phaseportrait([eq1(t), eq2(t), eq3(t), eq4(t), eq5(t), eq6(t), eq7(t), eq8(t), eq9(t), eq10(t), eq11(t), eq12(t)], [x1(t), y1(t), vx1(t), vy1(t), x2(t), y2(t), vx2(t), vy2(t), x3(t), y3(t), vx3(t), vy3(t)], t = 0 .. 3.5*10^7, [[x1(0) = X1, y1(0) = Y1, vx1(0) = VX1, vy1(0) = VY1, x2(0) = X2, y2(0) = Y2, vx2(0) = VX2, vy2(0) = VY2, x3(0) = X3, y3(0) = Y3, vx3(0) = VX3, vy3(0) = VY3]], scene = [t, (vx3(t)^2 + vy3(t)^2)^(1/2)], stepsize = 1000, linecolor = [purple], scaling = constrained);
Error, (in DEtools/phaseportrait) Invalid scene; must be list of vars: scene = [t, (vx3(t)^2+vy3(t)^2)^(1/2)]
 

Is there a way to let me plot the v(t) ?

why setting interface(warnlevel=0); makes dsolve change the form of the final solution to an ODE?

Is this to be expected? Help on warnlevel 0 says to just suppress all warnings. 

In this example, both solutions are equivalent. One is just simpler than the other.

But now I am worried if this setting could affect dsolve in other ways not yet anticipated.
 

Download warnlevel_difference.mw

btw, the same thing happens with warnlevel 2. i.e. answers look different.

But with warnlevel 3 and 4, now dsolve gives the same answer. 

SInce it seems default is warnlevel 3, it seems internally, dsolve takes different path depending on warnlevel setting? 

Edit

Here is a movie. I am using windows 10.

Edit: Here is another video. Tried now with fresh start of Maple. i.e. closed Maple and started it again.  Using worksheet. No other worksheet was open. This is what I found. Initially it gives the longer solution. After couple of tries, it then changed to the simpler one

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

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.

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