MaplePrimes Questions

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);

Good day everyone,

I am running a maple code for a pde and is given the error code "Error, (in pdsolve/numeric/process_IBCs) initial/boundary condition must be given in terms of the dependent variables of the problem only ([W]), got ((D@@2)[1](W))(0, tau) = 0". The link is attached below.

pde.mw

Thanks in advance.

Clifford http://math.tntech.edu/rafal/cliff12/index.html

I read really good reviews from fellow Maple users about Clifford Package( above link).

I couldn't access the link provided. What is the best way to install Clifford Package or get access to the link.

Thank You.

Hey everyone!

I have a complex function stored in a file (Comp-func.txt). The function is continues everywhere on the real axis (X-axis.txt). However, its log shows a jump somewhere close to x=-1.5. I would like to understand how Maple interprets this "jump" and how to avoid such numerical artifact.

thank you.

 Comp-func.txt

Jump-Log-Func.mw

X-axis.txt

Dear all

Can I compute using maple some Riemann Stieltjes integrals 

RSI.mw

Thanks 

This also looks like an applyrule bug.

restart;

kernelopts(version);

`Maple 2021.2, X86 64 LINUX, Nov 23 2021, Build ID 1576349`

double_angle_rule := [
        sin(x::name/2)*cos(x::name/2) = 1/2*sin(x),
        sin(x::name/2)^2 = 1/2*(1-cos(x)),
        cos(x::name/2)^2 = 1/2*(1+cos(x))
];

[sin((1/2)*x::name)*cos((1/2)*x::name) = (1/2)*sin(x), sin((1/2)*x::name)^2 = 1/2-(1/2)*cos(x), cos((1/2)*x::name)^2 = 1/2+(1/2)*cos(x)]

C := < cos(1/2*u)*sin(1/2*u), cos(1/2*u)^2 >;

Vector(2, {(1) = cos((1/2)*u)*sin((1/2)*u), (2) = cos((1/2)*u)^2})

This application fails. Why?

applyrule~(double_angle_rule, C);

Error, dimension bounds must be the same for all container objects in an elementwise operation

Download applyrule-bug2.mw

 

This looks like a bug to me but please correct me if it is not.

restart;

kernelopts(version);

`Maple 2021.2, X86 64 LINUX, Nov 23 2021, Build ID 1576349`

half_angle_rule := [
        sin(x::name) = 2*sin(x/2)*cos(x/2),
        cos(x::name) = 1 - 2*sin(x/2)^2
];

[sin(x::name) = 2*sin((1/2)*x)*cos((1/2)*x), cos(x::name) = 1-2*sin((1/2)*x)^2]

In this example, Maple applies the rule to the first element only.
It should apply to both.

A := < sin(u), sin(u) >;
applyrule~(half_angle_rule, A);

Vector(2, {(1) = sin(u), (2) = sin(u)})

Vector[column](%id = 36893628627946684772)

In this example, Maple applies the rule to the second element only.
It should apply to both.

B := < cos(u), cos(u) >;
applyrule~(half_angle_rule, B);

Vector(2, {(1) = cos(u), (2) = cos(u)})

Vector[column](%id = 36893628627946688132)

Download applyrule-bug1.mw

 

How to trace the 2 parabolas that pass through 4 cocyclical points. Thank you

Hello all. I'm using version 2021.2 to try to make some simple energy plots for my research. The math is pretty straightforward, but for some reason I cannot get the results to plot properly. My code is below:

restart;
A := 7.17;
B := 2.56*10^(-3);
C := 0.08*10^5;
_local(D);
1;
D := 0*10^(-6);
                           A := 7.17

                      B := 0.002560000000

                          C := 8000.00

                             D := 0

T_0 := 298; 

G0 := -71.398;

S0 := 45.106;

Hf := -57.95;

 

cp := A + B*T + C/T^2 + D(T)^2;             

                           

`&Delta;H` := int(cp, T = T_0 .. T);

`&Delta;S` := int(cp/T, T = T_0 .. T);
           
G := -S0*T - T*`&Delta;S` + Hf + `&Delta;H`;

plot(G, T = T_0 .. T_max);

Which yields the following error message:

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

I've looked through everything I can find on this issue, and I'm coming up empty. Anyone know what's happening here?

Dear colleagues.

I use gradplot for a displacement vector in x-direction only, as foolows

gradplot(u1(x), x = 0 .. a, y = 0 .. b, grid = [10, 10], arrows = SLIM, color = u1(x), T, caption = typeset("The displacement field"), fieldstrength = fixed, size = [0.3, 0.5])

I need to make color legend to show the minimum and maximum value and in between for the displacement.

Amr

I need to use convert of complex exponentials to trig, but only to convert exp(I*x) to cos/sin using Euler formula.

The problem is that, since this is done in code without looking at what is inside the exp(), Maple will also convert non complex exponentials as exp(x) to hyperpolic trig which I do not want.  An example will make this clear

For an example, given exp(3*I*x - x)  and applying convert/trig to this it gives 

             (cosh(x) - sinh(x))*(cos(3*x) + sin(3*x)*I)                       --(1)

But I only want to conver the exp(3*I*x) part of the of the above to obtain

          exp(-x) *  (cos(3*x) + sin(3*x)*I)                          ---(2)

I can break  exp(3*I*x - x) first using expand command and obtain  exp(-x) exp(3*I*x) and then parse this and filter out the complex exponentials (may be using select with has I) and then use convert on those terms only leaving the non-complex exponentials alone. But this gets messy for more complex exponentials.

Is there an easy way to tell Maple  to convert expression of the form exp(I*f(x) + g(x)) to trig but only to sin/cos, hence leaving the exp( g(x) ) as a factor? I looked at help but see nothing there so far.

Maple 2021.2

I try to know an equation of the tangent on the point [0.504244923, 0.3781836925] on the hyperbola7*x^2 - 7*y^2 - 12.0*x + 9.0*y + 2.25 - 2*x*y=0.How can I do that? Thank you.

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