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Bug using Heaviside and PDF in statistics package...

Asked by: markweitzman 100
integration heaviside statistics
September 08 2019
1  2

Integrating a positive definite function (normal distribution) and a >= 0 function (Heaviside) should not return a negative value.

 

 

with(Statistics);
X := RandomVariable(Normal(1, sqrt(2.25)));
int(PDF(X, x)*Heaviside(x^7-5*x^4-3*x+1), x = -infinity .. infinity);
                         -0.08507120131

 

 

Bug.mw

How to Generate a Longest Path and Longest Cycle i...

Asked by: DJJerome1976 535
graph cycle path
September 08 2019
1  4

I'm doing some work with undirected and directed graphs, and I'm needing to find examples of longest paths and longest cycles.  How may this be done in Maple?

How to Solve a system of coupled ODEs in Maple ?...

Asked by: Mayo_Kun 5
ode dsolve numeric
September 08 2019
1  5

Hello,

I am trying to solve a set of coupled ODEs in the following code (ODE_Prob.mw). But I am getting an error.

Please, what does this error mean and what is the solution.

Thanks in advance. 
 

> 

restart; PDEtools[declare](f(eta), prime = eta, theta(eta), prime = eta); Digits := 16; inf := 9

f(eta)*`will now be displayed as`*f

  

`derivatives with respect to`*eta*`of functions of one variable will now be displayed with '`

  

theta(eta)*`will now be displayed as`*theta

 (1)
> 

equ1 := (2*n+1)*f(eta)*(diff(theta(eta), eta))/(2*(n+1)) = (diff(theta(eta), eta, eta))/Pr^(2/(n+1))

(2*n+1)*f(eta)*(diff(theta(eta), eta))/(2*n+2) = (diff(diff(theta(eta), eta), eta))/Pr^(2/(n+1))

 (2)
> 

equ2 := (1/2)*(diff(f(eta), eta))^2-(2*n+1)*f(eta)*(diff(f(eta), eta, eta))/(2*n+2) = -n*(diff(f(eta), eta, eta))^(n-1)*(diff(f(eta), eta, eta, eta))+theta(eta)

(1/2)*(diff(f(eta), eta))^2-(2*n+1)*f(eta)*(diff(diff(f(eta), eta), eta))/(2*n+2) = -n*(diff(diff(f(eta), eta), eta))^(n-1)*(diff(diff(diff(f(eta), eta), eta), eta))+theta(eta)

 (3)
> 

indets(equ1);

{Pr, eta, n, Pr^(2/(n+1)), diff(diff(theta(eta), eta), eta), diff(theta(eta), eta), f(eta), theta(eta)}

  

{eta, n, (diff(diff(f(eta), eta), eta))^(n-1), diff(diff(diff(f(eta), eta), eta), eta), diff(diff(f(eta), eta), eta), diff(f(eta), eta), f(eta), theta(eta)}

 (4)
> 

Bcs := f(0) = 0, (D(f))(0) = 0, (D(f))(inf) = 1, theta(0) = 1, theta(inf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(f))(9) = 1, theta(0) = 1, theta(9) = 0

  

1.301763965

  

1.4

 (5)
> 

equ1;

.7916666666666667*f(eta)*(diff(theta(eta), eta)) = .8027059130737796*(diff(diff(theta(eta), eta), eta))

  

(1/2)*(diff(f(eta), eta))^2-.7916666666666667*f(eta)*(diff(diff(f(eta), eta), eta)) = -1.4*(diff(diff(f(eta), eta), eta))^.4*(diff(diff(diff(f(eta), eta), eta), eta))+theta(eta)

 (6)
> 

SolP1 := dsolve({Bcs, equ1, equ2}, numeric); SolP1(0); SolP1(inf)

Error, (in dsolve/numeric/BVPSolve) unable to store '-.4744942626692375+1.460343180701223*I' when datatype=sfloat

  

SolP1(0)

  

SolP1(9)

 (7)
> 

p1 := plots:-odeplot(SolP1, [eta, f(eta)], 0 .. inf); p2 := plots:-odeplot(SolP1, [eta, theta(eta)], 0 .. inf); p3 := plots:-odeplot(SolP1, [eta, diff(f(eta), eta)], 0 .. inf); plots:-display(Array([p1, p2, p3]))

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

  

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

  

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

  

Error, (in plots:-display) element 1 of the rtable is not a valid plot structure

  
> 

``


 

Download ODE_Prob.mw

 

why odetest no longer verify solution after expand...

Asked by: nm 8552
simplify expand trigonometry
September 08 2019
0  2

Is this documented somewhere?  Why Maple do not return 0 from odetest after expanding the solution?

update: added additional tries to simplify it to zero as suggested but they do not give zero.

> 

ode:=2*x^(1/2)*diff(y(x),x) = (1-y(x)^2)^(1/2);
sol:=dsolve(ode);

2*x^(1/2)*(diff(y(x), x)) = (1-y(x)^2)^(1/2)

y(x) = sin(x^(1/2)+(1/2)*_C1)

> 

odetest(sol,ode);

0

> 

res:=odetest(expand(sol),ode);

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,symbolic)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

expand(res)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res))

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),symbolic)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),trig)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),size)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

 

 

Download odetest_q.mw

Please help me to fix this error....

Asked by: Palm MP 5
plot syntax
September 08 2019
1  3

I want to plot the graph of the function as seen below but I have the error. Please help me.


restart;

a := 5;
b := 2;
u := 3;
v := 4;
A := 1;
B := 2;

In := (n, delta) -> Pi*a*((delta + a)^(2 - 2*n) + (delta - a)^(2 - 2*n))/(delta*(1 - n));

Jn := (n, delta) -> 1/2*(((delta + a)^2 - b^2)^(1 - n) - ((a - delta)^2 - b^2)^(1 - n))/(a*delta);

E1 := delta -> -u*A*In(3, delta) + u*B*In(6, delta);

E2 := delta -> -8*Pi^2*a^2*b^2*u*v*A*(Jn(3, delta) + 2*b^2*Jn(4, delta)) + 8/5*Pi^2*a^2*b^2*u*v*B*(5*Jn(6, delta) + 80*b^2*Jn(7, delta) + 336*b^4*Jn(8, delta) + 512*b^6*Jn(9, delta) + 256*b^8*Jn(10, delta));

Et(delta):= delta -> E1(delta) + E2(delta);
 
plot(Et(delta), delta = 16 .. 28);
 

 

IntTutor says unable to solve this problem...

Asked by: ferago42 40
integration inttutor
September 07 2019
5  5

Hi, I ran the following command: 

int(x^2 * sqrt(1-x^2), x)

and I got a solution. Then I try IntTutor: 

IntTutor(x^2 * sqrt(1-x^2), x)

And a UI window popus, does nothing. When I click "All Steps" it says "Unable to solve this problem". How so, if int() just gave me an answer? Or am I using the commands wrong?

I'm trying to see the steps by step solution of the integral, so I can compare it with my attempts. Kinda like what http://integral-calculator.com/ does. Thanks in advance. 

How to generate random prime numbers ?...

Asked by: jalal 380
random prime
September 07 2019
1  10

Hi,

How to generate random prime numbers ?

For example, prime number between 3 and 30 ?

Thanks

Way I get this Error it's work perfect outside the...

Asked by: panke 140
programming linearalgebra
September 07 2019
1  4


 

> 

restart
> 

with(LinearAlgebra):
> 

G := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 0, (1, 4) = 0, (2, 1) = 2, (2, 2) = -1, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = -1})
> 

``
> 

TRJH(G)

Error, (in TRJH) invalid input: LinearAlgebra:-JordanForm expects value for keyword parameter output to be of type {list, identical(J), identical(Q)}, but received Q

  
> 

``


 

Download temp.mw

how to solve this equation ...

Asked by: shimaa sadk 45
solve
September 07 2019
0  3

 

Ask_maple.pdf

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Ask_maple.mw .
 

Download Ask_maple.mw

 

executing a powershell script from the maple inter...

Asked by: Adam Ledger 360
September 07 2019
0  4

I know that you can open the command prompt from within the maple interface, but how do i append instructions for it to execute a .ps1 script please thank you in advance 

passing function and applying argument...

Asked by: Stretto 235
proc curry
September 06 2019
2  3

F := proc(f,x)

    f(x); # invalid.

end proc;

 

f := (a,b,c)->a*b*c;

 

F(f,3);

    = 3*b*c;

 

How can I just apply 3 to one of the parameters in F without knowing how man(I really want to apply it to the first parameter but it doesn't matter all that much).

 

I really need to sorty of curry and uncurry a function. I might want to pass an function of arbitrary dimension but only apply a value to one parameter(usually the first).

 

while I could do somethign like

 

F(x->f(x,b,c))

 

this is kinda verbose and requires me to know the parameters of f at the call site, I don't think that is necessary.

Extending maple...

Asked by: Stretto 235
initialization
September 06 2019
0  5

Is there any way to extend maple by adding constants, functions, etc that are automatically loaded without having to add a with statement?

 

While I can use a template there are two issues, I don't really wanna see all the additions and I the template opens as the file and so the filename does not change. If one modifies the template and saves then it ruins the template. (it should open the template but not use the filename)

Seq is not calling!!!...

Asked by: kencom1 110
assignment indexed
September 06 2019
1  2

Anyone with the idea of seq such help please. I am tryong to collect all the series into one case but its only calling the last one.

The link is attached below. Thank you in advance

 

 seq.mw

How to prevent execution of equation in math/text ...

Asked by: Jonas F 151
2dmath editing non-executable-math
September 06 2019
3  10

Hello

 

As title says, when I enter equation in math mode and switch to text mode and hit "enter" to go to the next line then it gets executed, usually in former versions it didnt execute and was much faster for me to use the program this way.

How do I fix this? I don't want to use shift-F5 all the time to make the text unexecutable, I would like it to be like in the old version prior to 2019.

Now it does this which is really annoying, I dont want it to execute when changing line!

Best regards

Jonas

solve the differential equation...

Asked by: Dark Energy 90
ode differential-equations
September 06 2019
0  3

Hi guys

I want to solve the following differential equation but I can not. please help me in this way

diff(phi((8*R^(3/2)-W)*sqrt(2)/(24*sqrt(M))), W$2)=lambda*phi((8*R^(3/2)-W)*sqrt(2)/(24*sqrt(M)))

 

with the best regard

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