I want to put one option of tetrahedron SABC with AB=c, BC=a, AC=b, SA=m, SB=n, SC=p. I tried
restart;
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [c, 0, 0];
C := [(-a^2 + b^2 + c^2)/(2*c), sqrt((a + b - c)*(a - b + c)*(-a + b + c)*(a + b + c))/(2*c), 0];
S := [x, y, z];
solve([distance(S, A) = m, distance(S, B) = n, distance(S, C) = p], [x, y, z]);

I got warning, solutions may have been lost. How can I solve that system of equations?

Just need some help using URL:-Get

Get("https://sdo.gsfc.nasa.gov/assets/img/browse/2023/05/05/20230505 _184918_512_0304.jpg")

I'm sure there are some tags to use but not sure how.  The site does show a script on best practices, but at the moment don't know how to apply them.  Can anyone offer some help?

i want to plot form 15 to 0 and 5 to 1.....but my plot shows only increasing order..how can i change it?

Download plot.mw

Is there a way to suppress dependencies of a all functions appearing in a worksheet without having to do suppress([each function])?

out_parameter_for_Sample(_)_and_rtables.mw
When I generate sample data using a random variable, a normal distribution and the Sample command, I want to see the sample and the values used to randomly evaluate the distribution which generates said sample. The Maple help sheets say you can so this with the out parameter in the Sample command. I try several different calls and hoped the rtable is filled on execution. As seen below, the execution fails. Am a specifying the rtable incorrectly? See attached Maple sheet.

Download out_parameter_for_Sample(_)_and_rtables.mw

I followed the code on the website https://de.maplesoft.com/support/help/maple/view.aspx?path=updates/Maple18/GraphTheory to convert a graph to LaTeX code. However, after compiling with pdflatex, I found that some edges of the graph are jagged.

restart:    
with(GraphTheory):
with(SpecialGraphs):
S:=SoccerBallGraph():
Latex(S,FileTools:-JoinPath([currentdir(), "soccer.tex"]),300,300,true)

soccer.pdf

I suspect it's because of the converted LaTeX code.

PS: The PDF conversion issue from last time still remains unsolved in Maple 2023; see

https://www.mapleprimes.com/questions/236142-How-To-Remove-The-Mosaic-Of-Vertices.

How to rectify this Error,in RK Method.Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 3, got 2.

I cound't plot p5,p6,p7.

If RK Method is suitable for this or not please tell the suitable numerical method code for this.Help me

IP-TEMP.mw

The example worksheet uses table to determine the covering relations in a POSET. This is old (Maple 11 and earlier code) that I have been trying to update into a package to explore calculations in an algebraic structure.  The example procedure seems to work well, but because of problems with similar procedures elsewhere, I have some concerns about the validity of using tables in this fashion. Specifically, this procedure initializes a table, then proceeds to modify the table entries, and then reformats the sequences into sets.  I have not been able to find documentation for modifying entries in tables after they have been defined. The documentation for tables only covers adding entries, removing entries, but not modifying entries.

Is modifying tables as my  procedure does an undocumented feature?

In addition, the documentation does not explain how to clear a table. It only describes how to clear a table entry. Older code sometimes purported to clear a table by assigning its name (with uneval quotes) to itself, but this does not seem to work.

exampletableoperations.mw

Hi to All! I have a big expression including 10 constant parameters (k_1, k_2, k_3, omega_1, omega_2, omega_3, a_3, b_2, c_0, c_2) to be solved for a_3, b_2, c_0, c_2. I wonder if there is any relation between the constants a_3, b_2, c_0, c_2 not depending on (k_1, k_2, k_3, omega_1, omega_2, omega_3) satisfying this big expression e.g. a_3=2, b_2=c_0/5, c_2 free. 

I also tried fsolve but I could not get an answer.

Thank you in advance.

Regards,

question1.mw

In accordance with this statement obtained by Чебышёв (1853), each of 

simplify(int(x^(1/2)*(x^2 + 1)^(-3/4), x), symbolic);
simplify(int((x^(1)*(1 - x^2))^(1/3), x), symnolic);
simplify(int(x^(-1)*(x^6 + 1)^(-1/6), x), symnolic);
simplify(int(x^(17/2)*(x^2 + 1)^(1/4), x), symnolic);

can be reduced to an integral of rational functions, which can be expressed in terms of elementary functions. But it appears that Maple 2023.0 is still unable to completely calculate them. For instance: 
 

Download Chebyshev_theorem_on_the_integration_of_binomial_differentials.mw

However, closed-form (and readable) solutions in elementary forms exist (cf. Regression reports for Computer Algebra Independent Integration Tests. Summer 2022 version (12000.org)); in fact, Mathematica returns: 

So, why can't Maple find these compact antiderivatives (expressed by elementary functions) directly here? In other words, is there a way to resolve them in Maple without applying some change of the variable to these indefinite integrals manually?

Trying to solve in Maple:

restart;
f := 15;
fk := 7;
zm := 350;
ym := 200;
eps := 1 - fk^2*exp(-((z - zm)/ym)^2)/f^2;
dz := diff(z(x, bn), bn);
db := diff(b(x, bn), bn);
eq1 := diff(z(x, bn), x) = cot(b(x, bn));
eq2 := diff(b(x, bn), x) = subs(z = z(x, bn), -1/(2*eps)*diff(eps, z));
eq3 := diff(dz, x) = -bd/sin(b(x, bn))^2;
eq4 := diff(bd, x) = subs(z = z(x, bn), dz/(2*eps)*(diff(eps, z)^2/eps - diff(eps, z $ 2)));
sys := eq1, eq2, eq3, eq4;
cond := z(0, bn) = 0, b(0, bn) = bn, zd(0, bn) = 0, bd(0, bn) = 1;
dsolve({cond, sys}, [z(x, bn), b(x, bn)], numeric);
Error, (in dsolve/numeric/process_input) dependent variables must be functions of a single unknown, the independent variable. Got [z(x, bn), b(x, bn)]

What does "Error, (in dsolve/numeric/process_input) dependent variables must be functions of a single unknown, the independent variable. Got [z(x, bn), b(x, bn)] " mean?

How can this system be solved?

So that computed results do not take up many lines in Euler transforms and in various tensor math, how can I present the sine and cosine functions in Maple with this compact form:

• sin(x(t)) = s(x) or sx
• cos(x(t)) = c(x) or cx

The input and computed output of symbolic calculations equations needs to be output in this compact notation. Derivatives with the compact notation are understood to be function of time.

Here is an example implimentation in Mathematica:

Matricies Rx and Ry are similarly defined and the dot product can be computed:

Here's example derivative:

Any help or pointers on this is appreciated. I'm new on Maple Primes and am not sure how to find out if this is already posted somewhere.

Thanks,

David

The issue arises from solving the following ODEs in Maple (where a is a suitable real parameter): 

ode__1 := a*(diff(y(x), x) + 1)^2 + (y(x) - x)^2*diff(y(x), x) = 0: # dsolve(ode__1);
ode__4 := a*(x*diff(y(x), x) + y(x))^2 - (y(x) + x)^2*diff(y(x), x) = 0: # dsolve(ode__4);

However, dsolve cannot give fully simplified solutions, so I have to compute these unevaluated integrals (i.e., expr₁) manually: (For the sake of completeness, I list some related ODEs below.) 
 

Download senseless_results_of_int.mw
 

Download senseless_results_of_int.mw

As you can see, the lengthy output of is nearly meaningless! (And if you want to simplify it, Maple will simply return: Error, (in simplify/recurse) indeterminate expression of the form 0/0.) So, how do I get the simplified results in Maple?
The integrals are: 

expr__1 := [Int(1/(z^2 + sqrt(z^4 + 4*a*z^2) + 4*a), z), Int(-1/(z^2 - sqrt(z^4 + 4*a*z^2) + 4*a), z)]: # (value(expr__1));
expr__4 := [Int((z^2 - 4*a*z + sqrt(-4*a*z^3 + z^4 - 8*a*z^2 + 4*z^3 - 4*a*z + 6*z^2 + 4*z + 1) + 2*z + 1)/(z*(-4*a*z + z^2 + 2*z + 1)), z), Int(-(z^2 - 4*a*z + 2*z + 1 - sqrt((-4*a*z + z^2 + 2*z + 1)*(z + 1)^2))/(z*(-4*a*z + z^2 + 2*z + 1)), z)]: # (value(expr__4)):

Note. By the way, Mma can solve the original ODEs directly and explicitly: 

In[1]:= DSolve[a*(y'[x]+1)^2+(y[x]-x)^2*y'[x]==0,y[x],x,IncludeSingularSolutions->Automatic]

                                   2                3                    2
                  a - x C[1] - C[1]             16 a  - 4 a x C[1] - C[1]
Out[1]= {{y[x] -> ------------------}, {y[x] -> --------------------------}}
                       x + C[1]                     4 a (4 a x + C[1])

In[2]:= DSolve[a*(x*y'[x]+y[x])^2-(y[x]+x)^2*y'[x]==0,y[x],x,IncludeSingularSolutions->Automatic]

                     2 a C[1]       2 a C[1]     2  2 a C[1]
                  a E         (-(a E        ) + a  E         + x)
Out[2]= {{y[x] -> -----------------------------------------------}, 
                                     2 a C[1]
                                  a E         - x
 
                2 a C[1]    2 a C[1]
               E         (-E         + 2 a x)
>    {y[x] -> --------------------------------}}
                    2 a C[1]              2
              2 a (E         - 2 a x + 2 a  x)

Unfortunately, Maple fails to do so.

(x^(3))^(1/3) doesn't simplify to x.  I am missing something.