MaplePrimes Questions

Often, in response to a question without code, the suggestion is made to upload a Maple file using the button with the green arrow .

This happens so often that I get the impression that new users don't recognize this as the best and most efficient way to get their question analyzed and answered. Or they just don't know how to do it.

So why not adding a hint to consider uploading code just before "Suggested Tags"?

The result of is said to be the Catalan constant, but unfortunately, Maple® only returns a lengthy output, so I have to apply the simplify command to get a shorter (and equivalent) form of it. However, I find that these do not work here: 

restart;

expr__1 := expand(value(student[Doubleint](sec(x+y)*sec(x-y)/(sec(x)*sec(y)), x = 0 .. (1/4)*Pi, y = 0 .. (1/4)*Pi)))

MmaTranslator:-Mma:-Chop(evalf(expr__1-Catalan))

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

 

0

(1)

simplify(expr__1, size = false)-Catalan; Physics:-Simplify(expr__1)-Catalan; simplify(expr__1-Catalan, size = false); Physics:-Simplify(expr__1-Catalan); verify(expr__1, Catalan, equal); is(expr__1 = Catalan); verify(expr__1-Catalan, 0, equal); is(expr__1-Catalan, 0)

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

 

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

 

((1/8)*I)*(-Pi^2+4*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+4*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2)))

 

((1/8)*I)*(-Pi^2+4*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+4*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2)))

 

FAIL

 

FAIL

 

FAIL

 

FAIL

(2)

expr__2 := expand(convert(expr__1, polylog, simplifier = NONE))

((1/2)*I)*polylog(2, (1/2)*2^(1/2)-((1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, -((1/2)*I)*2^(1/2)-(1/2)*2^(1/2))-((1/2)*I)*polylog(2, -(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

(3)

simplify(expr__2, size = false)-Catalan; Physics:-Simplify(expr__2)-Catalan; simplify(expr__2-Catalan, size = false); Physics:-Simplify(expr__2-Catalan); verify(expr__2, Catalan, equal); is(expr__2 = Catalan); verify(expr__2-Catalan, 0, equal); is(expr__2-Catalan, 0)

0

 

((1/2)*I)*polylog(2, (1/2-(1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2+(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2+(1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

 

0

 

-((1/8)*I)*(Pi^2+4*polylog(2, (-1/2+(1/2)*I)*2^(1/2))+4*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-4*polylog(2, (1/2+(1/2)*I)*2^(1/2))-4*polylog(2, (1/2-(1/2)*I)*2^(1/2)))

 

true

 

true

 

true

 

true

(4)

NULL

Download Unable_to_simplify_expressions_containing_dilog.mw

(By the way, Mathematica's Integrate cannot compute this double integral explicitly.)

Hi,

I am struggling with a task of creating a 2D contourplot of temperature values showing Iso-Lines (lines of equal temperatures in steps of 100°C).

I have a set of temperature values with corresponding x and y coordinates of a cross section. The data is given as an unsorted set of X-Y-Temperature data:

[[177.80000,0.,967.3266667],[169.80000,0.,963.5900000],[100.00000,0.,188.8933333],[176.92000,17.703000,967.3266667],[174.27000,35.230000,967.3200000],[169.90000,52.407000,967.3566667],[163.84000,69.064000,967.3366667],[156.15000,85.034000,967.3100000],[146.91000,100.16000,967.3366667],[136.20000,114.29000,967.3666667],...]

I can plot the data as a 3D pointplot and assign colors based on the temperature value:

plots:-pointplot3d(<ThermRes(2 .. (), 2) | ThermRes(2 .. (), 3) | ThermRes(2 .. (), TimeCol)>, colorscheme = ["zgradient", ["blue", "green", "yellow", "orange", "red"]], style = point, symbol = solidsphere, symbolsize = 20)

For better visualization, I would like to plot this data in a 2D contourplot showing coloured Iso-lines in 100°C steps, similar to the following scheme:

I know this is not directly possible from xyz datapoints. Therefore, I was trying to create an interpolation function using the Interpolation package. I have tried to find out if it is possible to get a working interpolation function for my data, but it seems like the x and y coordinates must be always in increasing order and there has to be a z value (temperature data point) for each pair of coordinates in matrix form, is that correct? Unfortunately, as you can see above, my x-y coordinate pairs are irregular and unsorted and I do not have a temperature value for every combination of x and y coordinate values.

Is there any way how to find an interpolation function for this kind of data that would enable a contourplot? Or any other ideas how to create a coloured 2D plot from this data with a legend showing the 100°C temperature color values?

Greetings, Oliver

Could you help me how to deal with this problem?

restart;

with(plots):with(plottools):with(DETools):

 

Sys:=diff(T(R),R)=((1-1/R)*(sqrt(1-(alpha/R)^2*(1-1/R))))^(-1),diff(Phi(R),R)=(alpha/R)^2*(sqrt(1-(alpha/R)^2*(1-1/R)))^(-1);

diff(T(R), R) = 1/((1-1/R)*(1-alpha^2*(1-1/R)/R^2)^(1/2)), diff(Phi(R), R) = alpha^2/(R^2*(1-alpha^2*(1-1/R)/R^2)^(1/2))

(1)

 

inits:=[[T(0)=0.5,Phi(0)=0],[T(0)=0.5,Phi(0)=Pi/4]];

[[T(0) = .5, Phi(0) = 0], [T(0) = .5, Phi(0) = (1/4)*Pi]]

(2)

K:=dsolve([Sys,op(op(1,inits))],[Phi(R),T(R)],numeric,parameters=[alpha],output=listprocedure);

Error, (in dsolve/numeric/make_proc) ode system is singular at the initial point

 

 

Download HW6.m

Hey Guys . is it possible to import a Simulink block into maplesim . can some one explain the process . i already found something called BlockImporter Add-in. but it's some old maple addins and it's not support Windows 10

The linearfit in Maple has the option to output the covariance matrix.  I do not see that option for nonlinear fitting.  Am I missing something?

what is wrong..in the past ..this equations was solved..now it doesnt' solved anymore...integral equations

total_PE.mw

hello sir..i'm new..and i want to know how to put command prompt ..between two command line .i read but i didn't find..

Essentially, this issue is only about how to make the graph look relatively more aesthetically pleasing.

It seems that the color of the arrowheads in a directed graph is consistent with the color of the edges, and their shape also seems to be unchangeable. I wonder if I missed something.

with(GraphTheory):
G := Digraph({[1, 2], [2, 3], [3, 4], [4, 1]});
DrawGraph(G, stylesheet=[vertexborder=false,vertexpadding=5,edgecolor = "Black",vertexcolor="MistyRose",edgethickness=2],size=[250,250]);

 

For example, I would like to draw it in the following style, where the arrowhead color of the directed edge "[1,2]" is red, and the arrowhead of the edge [3,4] is hollow.

Interestingly, the layer where the arrowhead is located seems to always be below the layer of the straight edge, making it impossible to cover it. I prefer the following style (adjusted using Inkscape).

 

 

 

 

 

 

 

 

 

 

Of course, it would be better if the two black arrowheads could be further apart. This can be easily achieved with other vector software. I wonder if it is easy to implement in Maple.

Linear combinations of random variables: why Maple does not "inherit" the distributional assumptions when adding up two random variables?

In the script I attach below, I first define a vector of two uncorrelated gaussian RVs [epsilon[1],epsilon[2]] and then a vector of two correlated gaussian RVs [nu[1],nu[2]]. Both epsilon[1] and epsilon[2] are also uncorrelated with nu[1] and nu[2].

Now I want to create a vector of two correlated gaussian RVs, S, where S[1]=nu[1]+epsilon[1] and S[2]=nu[2]+epsilon[2]. The means and the variances of [S[1],S[2]] are correct, but the covariance (off-diagonal element of the covariance matrix) is weird. How to do this in Maple?

Please check this script:

RVs_sum.mw

 

If I have a pde with multiple constants (for example a and b) in them such that some are fixed constants (say k) and some terms are undetermined constants , how do I put that in a PDE such that Maple knows to solve the equation not for arbritary k (in case no solution exists), but any k such that k is not a function of the differentiating variable.

hey guys...please watch my file and help me. when i call(Am)...it only shows last value. how can i get all (Am) value in like seq or table

restart

with(LinearAlgebra):

i := [seq(2*i-1, i = 1 .. 10)];

[1, 3, 5, 7, 9, 11, 13, 15, 17, 19]

(1)

for i in i do A[m] := (x/a)^(i+1)*(1-x/a)^2 end do;

x^2*(1-x/a)^2/a^2

 

x^4*(1-x/a)^2/a^4

 

x^6*(1-x/a)^2/a^6

 

x^8*(1-x/a)^2/a^8

 

x^10*(1-x/a)^2/a^10

 

x^12*(1-x/a)^2/a^12

 

x^14*(1-x/a)^2/a^14

 

x^16*(1-x/a)^2/a^16

 

x^18*(1-x/a)^2/a^18

 

x^20*(1-x/a)^2/a^20

(2)

``

Download 3.mw

when i call(Am)...it only shows last value. how can i get all (Am) value in like seq or table

i want to solve..this what is happening..i used maple not a long time ago.help me

restart; with(LinearAlgebra)

i := 1;

1

(1)

w := c[i]*(x/a)^(i+1)*(1-x/a)^2*(y/b)^(i+1)*(1-y/b)^2;

c[1]*x^2*(1-x/a)^2*y^2*(1-y/b)^2/(a^2*b^2)

(2)

(1/2)*(int(int([D__11*(diff(w, x, x))^2+2*D__12*(diff(w, x, x))*(diff(w, y, y))+4*D[66]*(diff(w, x, y))^2+D[22]*(diff(w, y, y))^2-2*q*w], x = 0 .. b), y = 0 .. a))

Error, (in int) wrong number (or type) of arguments: for an operator integrand a range without a variable of integration is expected, got x = 0 .. b

 

``

Download 2.mw

Given a list of equations say: eq1 := [diff(kk(r), r) = 0, ff(r)*1/2 = 0], how would i extract just the left hand side of each element ?
[diff(kk(r), r) , ff(r)*1/2 ]

Is there a way to compute the Riemann tensor for two different metrics in the physics package without each time setting up the metric. For example you just put the metric as an argument to do so in the differential geometry package.

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