## Substituting out Radicals and (a*x..........) typ...

I have some long expressions that would be more readable if common sections were substituted out. There are many sets of radicals often stacked inside each other.  The other one is (a*x..........) I see repeated in some other expressions. indets is good, but is there a way to use it to select  (a*x..........) types
At these eexpressions are returned from procdures would probably put them in an array/table with their substitution components.
I dont need to substitute everything. What I have done below is reasonable for reading and seeing the structure.

What would be a good approact here?

 > restart
 >
 (1)
 > vals:=[a=18,b=21,c=7,d=-29,e=-37,f=-56]
 (2)
 > vars[1]:=x:vars[2]:=y:
 > eqn:= 8*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1                 /2)+(-8*a*f+2*d^2)*c^2+(8*a^2*f-2*a*d^2+2*a*e^2+2*b^2*f-2*b*d*e)*c-2*a^2*e^2-2*                 a*b^2*f+2*a*b*d*e)^(1/2)*(a*c-1/4*b^2)/(4*a*c-b^2)^2*(vars[1]-(1/4*b*e-1/2*c*d)/(a*c-\                 1/4*b^2))-8*csgn((4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)*(Complex(1)*a+Complex(-1)*c-                 b))*(a*c-1/4*b^2)*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^                 (1/2)+(8*a*f-2*d^2)*c^2+(-8*a^2*f+2*a*d^2-2*a*e^2-2*b^2*f+2*b*d*e)*c+2*a^2*e^2+                 2*a*b^2*f-2*a*b*d*e)^(1/2)/(4*a*c-b^2)^2*(vars[2]-(-1/2*a*e+1/4*b*d)/(a*c-1/4*b^2))
 (3)
 > length(eqn)
 (4)
 > simplify(eval(eqn,vals))
 (5)
 > indets(eqn)
 (6)
 > Subs:=[((a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)^2)=A^2,          (-8*a*f + 2*d^2)*c^2 + (8*a^2*f - 2*a*d^2 + 2*a*e^2 + 2*b^2*f - 2*b*d*e)*c - 2*a^2*e^2 - 2*a*b^2*f + 2*a*b*d*e=B^2,            f*b^3 - b^2*d*e - (-(-4*c*f + e^2)*a - c*d^2)*b=C]:
 > eqn1:=simplify(eqn,Subs)
 (7)
 > Subsnumeric:=eval(Subs,vals)
 (8)
 > simplify(eval(eqn1,[(rhs=lhs)~(Subsnumeric)[],vals[] ]))
 (9)

## How do I calculate and plot an Orthogonal Trajecto...

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.

## why Maple gives extra solutions to this basic ode?...

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

 > interface(version);

 > ode:=diff(y(x),x\$2)*diff(y(x),x)=0;

 > dsolve(ode)

 > dsolve(diff(y(x),x\$2)=0)

 > dsolve(diff(y(x),x)=0)

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.

## Why does this command only works in Maple and not ...

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.

## How come does "residualQQplot" give me a strange ...

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!

## Maple gives solutions may have been lost unless tw...

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.

 > interface(version);

 > Physics:-Version();

 > restart;

 > sol:=int(1/sqrt(sin(y)),y); solve(sol=x,y)

Warning, solutions may have been lost

 > sol:=int(1/sqrt(sin(y)),y); solve(sol=x+b,y): {%}; #to eliminate duplicates

 >

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?

## Unit confusion due to "different" joules...

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

## Wrong `coulditbe`?...

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?

## Filter out non-isomorphic graphs by canonical labe...

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.

## How to Control the Display of an Object in a Maple...

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?

## Error in DEtools/DEplot/CheckDE - Derivatives must...

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)"

## warning (`rtable_alias`)...

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

## Why does maple not add minutes to hours?...

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

## Command extension: Why is simplify(...,ext) not wo...

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);```