MaplePrimes Questions

Could anyone please tell me how to solve the following system of equations and inequalities numerically in Maple:

{x + y = 2 and y = 1 and x > 0} or {x^2 = 4 and x < 0 and y = 0}?

By now I have been using solve() function in similar cases, but did not manage to adopt it for the or logical connector. 

Solving the two cases separately obviously works here, but does not help in the example, for which I need this, 

Thank you in advance!

Hi! I'm trying to draw the basins of attraction for Newton's method with f(z) = z^3 - 1 in three colors, just like the pictures on the links below:

https://i.stack.imgur.com/0wHfa.jpg

or

http://dept.cs.williams.edu/~heeringa/classes/cs135/s15/labs/lab3/

Can this be done? Thanks in advance,

RM

The Abel integral equation of the form

g(x) =  Int( f(y) / (x-y)^alpha, y = 0 .. x ) assuming alpha>0, alpha<1;

is linear and has a well known explicit solution for f(x).  

It is a particular form of Volterra equation of the first kind. 

It occurs in many problems of physics with alpha = 1/2.

However intsolve gives an error message:

> eq := g(x) =  Int(f(y)/(x-y)^alpha, y = 0 .. x) assuming alpha>0, alpha<1

> intsolve(eq, f(x));
Error, (in intsolve) numeric exception: division by zero

Replacing (x-y)^alpha by sqrt(x-y) gives the same error message.

restart

with(Physics)

Setup(spacetime)

[spacetimeindices = greek]

(1)

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1142 and is the same as the version installed in this computer, created 2022, February 12, 11:16 hours Pacific Time.`

(2)

Define(t[mu])

{Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], t[mu], Physics:-LeviCivita[alpha, beta, mu, nu]}

(3)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(4)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(5)

NULL

SumOverRepeatedIndices(t[mu]*t[`~&mu;`])

t[mu]*t[`~&mu;`]

(6)

NULL

Download greek-index.mw

Dear all

I have a set of three element, I want to apply each step of the definition of monotone class generated by a set to obtain the element of the monotone class generated by a given set. 

The definition and condition of monotone class is added in maple worksheet. 

I hope find some steps ( using maple) that will be applied later to other problem.

Monotone_class.mw

thanks

windows 11 maple 2020 I can load other packages but cannot load the student packages

How to find the axis and focus of a parabola whose equation we know ? Thank you.

Session Save doesnt work:

DeepLearning:-Save("model.ckpt");  
Error, (in DeepLearning:-Save) format not supported

DeepLearning:-Save("model.h5");
Error, (in DeepLearning:-Save) format not supported

DeepLearning:-Save("model.keras");
Error, (in DeepLearning:-Save) format not supported
 

Which format is supported?

With two vectors a and b, we know that
Norm(CrossProduct(a, b)) = Norm(a)* Norm(b) * sin(a,b).
I tried with a := <1, 2, -2>; b := <2, 10, 11>; 

Note that a perpendicular to b and 

Norm(CrossProduct(a, b)) = Norm(a)* Norm(b)

I tried

restart;
with(VectorCalculus);
SetCoordinates(cartesian[x, y, z]);
a := <1, 2, -2>;
b := <2, 10, 11>;
Norm(a);
Norm(b);
v := CrossProduct(a, b);
Norm(v);


Are there two vectors a and b with integer coordinates and  not perpendicular,  so that Norm(a), Norm(b), Norm(CrossProduct(a, b)) are interger numbers satisfying
Norm(CrossProduct(a, b)) = Norm(a)* Norm(b) * sin(a,b).

Hello!

I am trying to isolate each variable in this equation.I get a weird answer when I solve for n in this equation. I do know it is possible to isolate n in this equation. You might have to use/apply the Lambert Series identies to isolate it. Any help/insight would be appreciated.

Attached is a picture of the equation.

For syntax highlighting etc of Maple programs

Why int gives this error? Is this a known problem?

Update

fyi, This is reported to Maplesoft.

Here is updated worksheet. The int() command does not generate the error the second time it used, but generates the error the very first time used. Hopefully will be fixed in 2022 Maple.
 

interface(version);

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

restart;

Example 1

 

expr:=(7*x - 3 + sqrt(x^2 + (x^3*(x - 1)^2)^(1/3) - x) + sqrt(-2*((-x^2 + x + (x^3*(x - 1)^2)^(1/3)/2)*sqrt(x^2 + (x^3*(x - 1)^2)^(1/3) - x) + x^2*(x - 1))/sqrt(x^2 + (x^3*(x - 1)^2)^(1/3) - x)))/(12*x*(x - 1));

(1/12)*(7*x-3+(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2)+(-2*((-x^2+x+(1/2)*(x^3*(x-1)^2)^(1/3))*(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2)+x^2*(x-1))/(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2))^(1/2))/(x*(x-1))

int(expr,x)

Error, (in IntegrationTools:-Indefinite:-AlgebraicFunction) invalid argument for sign, lcoeff or tcoeff

int(expr,x)

int((1/12)*(7*x-3+(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2)+(-2*((-x^2+x+(1/2)*(x^3*(x-1)^2)^(1/3))*(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2)+x^2*(x-1))/(x^2+(x^3*(x-1)^2)^(1/3)-x)^(1/2))^(1/2))/(x*(x-1)), x)


 

Download int_problem_feb_13_2022.mw

Dear all

I can I obtain the sigma-algebra generated by a given set. 

sigma_algebra.mw

thanks

I am attempting to use the pdsolve function in Maple to explicitly solve a PDE which is basically a perturbation of the Laplace equation.  Nothing happens when I enter pdsolve, however, is this because a boundary condition is also needed to produce a solution?  The BC which I have is that f(x, y, z) goes to zero as sqrt(x^2 + y^2 + z^2) goes to infinity but I am not sure how to enter such a BC in Maple.

PDE := diff(diff(f(x, y, z), x), x) + diff(diff(f(x, y, z), y), y) + diff(diff(f(x, y, z), z), z) - exp(-t*exp(sqrt(x^2 + y^2 + z^2)))*(diff(diff(f(x, y, z), x), x) + diff(diff(f(x, y, z), y), y) + diff(diff(f(x, y, z), z), z))/(1 + m/(2*sqrt(x^2 + y^2 + z^2)))^4 = 3/2*exp(sqrt(x^2 + y^2 + z^2) - t*exp(sqrt(x^2 + y^2 + z^2)))*(diff(f(x, y, z), x)*tx/sqrt(x^2 + y^2 + z^2) + diff(f(x, y, z), y)*ty/sqrt(x^2 + y^2 + z^2) + diff(f(x, y, z), z)*tz/sqrt(x^2 + y^2 + z^2))/(1 + m/(2*sqrt(x^2 + y^2 + z^2)))^4;

pdsolve(PDE);

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