How do I calculate and plot an Orthogonal Trajectory on Maple 2024?

Here's the equation of the contour lines:

x*y^2 - x^2 - y^2 = k

I need to make it pass through a precise point on my contour lines graph, and everything I do doesn't seem to work.

Given the ode   y''(x)*y'(x)=0, clearly it has solutions for y''=0 and y'=0.

These are y=c1+x*c2 and y=c1. But Maple gives 3 solutions

Download why_3_solutions_may_24_2024.mw

Where did the third solution come from? The 3 solutions are correct ofcourse, but why 3? There should only be two. 

FYI, I am using 

Physics:-Version()

The "Physics Updates" version in the MapleCloud is 1746. The 

   version installed in this computer is 1745 created 2024, May 

I have to check earlier Maple versions to see if same thing happens there.

I am stuck this command works seemlessly in Maple:

ThermophysicalData:-CoolProp:-Property(D, T = 20*Unit('degC'), P = 760*Unit('mmHg'), water)

but it does not work in Maple Flow. Does anyone knows why? Thank you so much for your help in the matter.

Hello :) 

I have a math problem, where I first need to use Linear regression to find the equation based on a set of data. I did that, no problem. 

However, in the next part of the problem I need to check if the residuals are under "normal distribution". Usually, I check if a dataset is normally distributed via "QQ-plot", and there will be no problems. But this time, because I need to check the residuals, I need to use the "residualQQplot(data,LinReg)" command to make it happen. But when I read the mean-value, mu, it says "-0," and nothing else? I know it should be "-3,2752*10^-15. 

The standard deviation is correct.

How do I fix this, so the residualQQplot shows me the right result? 

I have attached the worksheet here. worksheet_-_linear_reg_and_residuals_for_normal_distribution.mw

Thank you! 

I can't understand this behavior. Any idea why it happens?

Solve is able to solve equation   f(y)=x+A for y, but can't solve   f(y)=x for y.

This is unexpected for me. I do not see why it can solve it when RHS is x+A but not when RHS is just x.

I can trick it to solve  f(y)=x for y  by asking it to solve f(y)=x+A for y and then set A=0 in the solution. But one should not have to do this. Is this a bug or Am I missing something?

Download why_solve_when_adding_term_only_may_22_2024.mw

Hello.

I am very new to Maple. Many this are great, but I do not understand how maple deals with, especially, radiological units. In particular regarding joules [J] wich Maple seems to have alt least three types:

1) J - in relation to work

2) J(radiation) in relation to Gy (Gray) J/kg

3) J(dose_equivalent_index) in relation to Sv also J/kg

Why does Maple distinguish between these "joules"? As a phycisist they are all (well maby not entirely for Sv) equal to me. How can I make Maple treat them all at the "same joule"?

I have tried the following first:

with(Units[Standard]) and

with(Units[Natural])

Best,

Carsten

If I understand correctly, both of 

int(RETURN(is(y::positive)), y = 0 .. x) assuming 0 <= x, x < 1;
int(RETURN(coulditbe(y = 1)), y = 0 .. x) assuming 0 < x, x < 1;

should output . However, Maple simply returns  for the second one. 
Isn't this result incorrect? Or am I missing something?

I would like to remove isomorphs from some graphs. That is to filter out non-isomorphic graphs.

graph_list := [GraphTheory:-CompleteGraph(3), GraphTheory:-PathGraph(3),Graph({{a,b},{b,c},{c,a}})]:

# Create a table to store non-isomorphic graphs
non_isomorphic_graphs := table():

# Counter for indexing the table
counter := 1:

# Iterate over each graph and check if it is isomorphic to any of the stored graphs
for g in graph_list do
    is_isomorphic := false:
    for key in indices(non_isomorphic_graphs,'nolist') do
        if GraphTheory:-IsIsomorphic(g, non_isomorphic_graphs[key]) then
            is_isomorphic := true:
            break:
        end if:
    end do:
    if not is_isomorphic then
        non_isomorphic_graphs[counter] := g:
        counter := counter + 1:
    end if:
end do:
op(non_isomorphic_graphs)
DrawGraph~(non_isomorphic_graphs,  layoutoptions = [neutral_color = "pink", initial = spring])

A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. I noticed that Maple has a function called CanonicalGraph. Can this function achieve the effect I want? I can easily achieve this by combining the  canonical form and property of sets  in  Sage.

graph_list = [Graph([(0, "a"), ("a", 2), (2, 0)]),graphs.PathGraph(3), graphs.CompleteGraph(3)]
non_isomorphic_graphs_labels = {g.canonical_label().copy(immutable=True) for g in graph_list}

An underlying motivation：My collaborators and I designed generation rules (algorithms) for 1-planar 4-trees；see https://arxiv.org/abs/2404.15663. Since the generating process is based on 1-planar embeddings, it will ultimately require filtering non-isomorphic graphs among a list of embeddings. I would be especially delighted to see that someone implement our algorithm in the future. Currently, I am stuck on handling some labeling details. It is somewhat similar to generating Apollonian networks (planar 3-trees). However, since its simplicial vertices are only two, the growth rate will not be too fast as the number of vertices increases.

Can the display of an object o in Maple, i.e.
> o;
                                                      display of the object
be controlled in a standard Maple worksheet, e.g. with Typesetting or something similar?

Hello, 

I have come across a problem in Maple, when I try plotting af slope field from my differential equation. 

I have tried different ways of defining the ODE, but when I use it in the command of "linjeelementer" (Danish for line elements - It's a command that's part of a package called "With (Gym)" in Maple, it gives me the error: Error, (in DEtools/DEplot/CheckDE) - Derivatives must be given explicitly. 

I don't understand what derivatives I must "give explicitly"?

Translation of the relevant sentences if anyone needs it when looking at the screenshot:

"I need to draw a slope field for the differential equation along with the solution curve for the population growth in India after 1960.

I define the differential equation:
ODE := -0.000032229*y^2 + 0.065843*y - 15.103"

"I am drawing the slope field for the differential equation along with the solution curve for the population growth in India after 1960, i.e., the solution curve that passes through the point (0,449):I am drawing a slope field for the differential equation along with the solution curve for the population growth in India after 1960, i.e., the solution curve that passes through the point (0,449):
linjeelementer(ODE, y(t), t = 0 .. 350, y = 0 .. 2000)"

Hi,

I'm trying out the 2024 version of Maple and I'm getting the following warning message:

Warning, not a built-in function (`rtable_alias`)

which I didn´t get for the 2023 version. I have no clue where it is coming from since it happens even when I start a new worksheet:

I've also attached print outs of the same worksheets (from Maple help examples and from Maple Portal), one using Maple 2023 version and the other one using Maple 2024 version so youcould see the warning and some other problems.

I really appreciate if someone would have an idea of what is going on here. Thanks very much in advance.

interpolation_2023.pdf

interpolation_2024.pdf

optimization_2023.pdf

optimization_2024.pdf

This is perhaps a stupid question. It is quite easy to add a vector with minutes to 60 minutes. However, when I try to do this stating 1 hour instead of 60 minutes it does no longer do the calculation. Why is this? Thank you for any explanation.

QuestionMP.mw

In the example below, the second call to simplify is ineffective

eq := (a*x + b)/(c*x + d) = 1;

`simplify/nodenom`:= x -> (numer@(lhs - rhs) = 0)(x);                       
                      
`simplify/nodenom`(eq);
simplify(eq, nodenom);

Why is that?
Convert, for example, works

`convert/nodenom`:= x -> (numer@(lhs - rhs) = 0)(x);

`convert/nodenom`(eq);
               
convert(eq, nodenom);

Deal All,

I have a system of linear differential equations with unknown functions T[1](t) to T[n](t). In the attached example, I considered the value of n equal to 10, but depending on the problem, the value of n may be higher. Maple is not able to solve this problem analytically with the ‘dsolve’. 

Does anyone have an idea to analytically solve for such a set of linear differential equations?

Best wishes

Set_of_Linear_DEs.mw

I try to solve triple integraton in Maple with this code.

but it leaves the last integral dz in the answer and warns: unable to determine if a*h/(-b+a) is between 0 and h; try to use assumptions or use the AllSolutions option
What is the problem?
and i need to get V = Pi*h(a^2 + ab +b^2)/3

Regards