This is an excersise in one of Mathematica's tutorials. The problem is to find from all persumtations of [1,2,3,4] those lists which has 2 in them before 3.

But the idea is that 2 can be anywhere before the 3, with possibly zero or more numbers between.

Will show how to do this in that other software, and ask if there is a way using Maple pattern matching or better way to do this in Maple better than what I did.

L=Permutations[{1,2,3,4}]
Cases[L,{___,2,___,3,___}]

gives

{{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 4, 2, 3}, {2, 1, 3, 4}, 
{2, 1, 4,  3}, {2, 3, 1, 4}, {2, 3, 4, 1}, {2, 4, 1, 3}, 
{2, 4, 3, 1}, {4, 1,  2, 3}, {4, 2, 1, 3}, {4, 2, 3, 1}}

We see in all of the above, 2 is before 3.

In that other software, the ___ means there is zero or more things.  I could not find how to do this in Maple's pattern matching. So had to use has and then find the index of 2 and 3 in each list and check if the index of 2 is smaller than the index of 3. Which is kinda awakard and not as elegent as using a pattern, but it gives same result.

L:=combinat:-permute([1,2,3,4]);
map(X->`if`(has(X,2) and has(X,3) and ListTools:-Search(2,X)<ListTools:-Search(3,X),X,NULL) ,L);

Gives

[[1, 2, 3, 4], [1, 2, 4, 3], [1, 4, 2, 3], [2, 1, 3, 4], 
[2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], 
[2, 4, 3, 1], [4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]]

Can you suggest a way using either patmatch or applyrules in Maple to do the same?  

Could this be done easier than what I did using evalindents without the need for pattern?

I find patterns easier to work with myself.

ps. converting each list to string, and then using regular expression or string matching, is not what I am looking for. 

ps. the check in Maple code of has(X,2) and has(X,3) is not really needed here, since we know each list will have 2 and 3 in them. But I kept these to make it more general for other type of problems where these extra checks might be needed.

applyrule is useful but seems limited. I can't do operation such as expand in the RHS of the rule.

For example, I wanted to applyrule that says to take sin(x::anything) and change it to cos(expand(x)), but it does not expand x. 

It seems because in the RHS of the rule, at the instance applyrule sees expand, x remains a symbol and not evaluated. So there is nothing to expand. It gets evaluated at later time, but by then too late for expand to do anything, it is gone. Just a guess.

But is there a trick to allow one to do more things in RHS of applyrule, such as expand or simplify? This would make applyrule much more useful. Otherwise, as it is, applyrule is of limited use. 

I know I can use evalindets ofcourse for this. 

Download apply_rule.mw

Using other software, there is no such problem using other operations on RHS of a rule

You see, expand worked on RHS of rule. 

I'd like to do same thing using applyrule in Maple. Is there a trick to allow this?

Maple 2024.1

I was trying to odetest one of my solutions to this ode when I got this internal Maple error I have not seen before.

Is this a legitimate error? my solution could be wrong ofcourse but strange to get internal error in this case.

Does this happen on earlier versions of Maple?

Download internal_error_PDEtools_NumerDenom_sept_4_2024.mw

Here is another ode solution by Maple, I am not able to get zero from odetest. 

If someone could come up with a trick or method to verify this, that will be great. I tried all sort of assumptions and not able to get zero. Even coulditbe() could not give zero. 

It is a Chini ode and also homogeneous, `class G`.

Solving using either method, odetest do not returns zero.  There are no initial conditions. I am sure the solutions are correct, but odetest need some help or may be this requires different method to verify not using odetest?

Worksheet below.

Download challenge_odetest_sept_1_2024.mw

What is the correct syntax in Maple to do integration of variables on 

So that the new integration variable is y using the mapping    u=y*x^(1/3) so that the result is 

The problems seems is that there is no option to tell Maple what the new integration variable is. So it does not know it should be y or x?

I looked at help and all my tries failed. Below is worksheet and also examples from another software as reference. The other software has argument to tell change of variable what is the new integration variable should be. But in Maple, there is no such option.,  Does this mean in Maple change of integration variables only works when the right hand side of the transformation has only one symbol and not two or more? i.e. this works   u=y, but not u=y*x

Download change_of_variables_integration_august_31_2024.mw

I searched help and see nothing specific to change of variable for integration, so I assumed the above is the command to use. Am I using the wrong command for integration change of variables in Maple?

For reference, I need to duplicate this in Maple: