## How do I select only certain elements from a set a...

I have the set {1, 2, 3, 4, 6, 8, 12, 17, 19, 20} and i need to select all the elements between 5 and 15 and create another set with just those elements. So, I want to obtain the set {6,8,12}. How might that be done using the select( ) command? Other suggestions welcome.

## What shall I do if the function is two variable li...

For a single variable function, I can expand the function

series(x/(1−x−x^2),x,4);

and get the expansion upto order 4 term.

What shall I do if the function is two variable like f(x,y)=xy/(y−x*sqrt(y)−x^2) and intended to keep terms upto order 5, or moreseries.mw

 (1)

 (2)

say.

My attempt failed as (x^7 + x^5 + x^3 + x)*y etc contains O(8) terms x^7.y

## overload vs. using optional arguments?...

I have some of my main functions defined to take input in different formats. Some have required  parameters and also optional parameters. Similar to how say dsolve can take one ode, or a list of ode's or set of ode's and also other additional arguments.

Currently I use something like  ode::{`=`,set(`=`),list(`=`)} in the signature of the proc to indicate this input can be any of these types. There are also optional aguments.

So inside the proc, it does lots and lots of if this then do such else do such type of logic in order to determine which case/combination of input it is called with.

I am thinking of rewriting all of the API to use overload. Yes, it means I will have lots of copies of the same proc, each to handle specific case of the signature. But it also mean it will be now much simpler inside each of the overloaded proc's to determine which case of call it is processing.

I'd like to ask, is there anything to be aware of before making this change? does it affect performance much? It seems to me it will make the logic and the program simpler.  Here is a very simple example to illustrate.

Which you think is better? I like the overload version more. But I am worried that I will end up with too many versions of the API since I need one for each possible combination and may be this will slow Maple down?

The following is the worksheet also.

 > restart;
 > interface(warnlevel=4); kernelopts('assertlevel'=2): foo:=overload( [    proc(A::`=`) option overload;        print("single equation");    end,       proc(A::set(`=`)) option overload;        if nops(A)=1 then           print("single eq in a set");        else           print("more than one eq in a set");        fi;    end,    proc(A::list(`=`)) option overload;        if nops(A)=1 then           print("single eq in a list");        else           print("more than one eq in a list");        fi;    end ]):

 > foo(x=1); foo([x=1]); foo([x=1,y=2]); foo({x=1}); foo({x=1,y=2})

 > restart;
 > interface(warnlevel=4); kernelopts('assertlevel'=2): foo:=proc(A::{`=`,set(`=`), list(`=`)})     if type(A,`=`) then         print("single equation");     elif type(A,set) then           if nops(A)=1 then              print("single eq in a set");           else              print("more than one eq in a set");           fi;     else #must be list        if nops(A)=1 then           print("single eq in a list");        else           print("more than one eq in a list");        fi;     fi; end proc:

 > foo(x=1); foo([x=1]); foo([x=1,y=2]); foo({x=1}); foo({x=1,y=2})

 >

## Van der Waals equation expressed in a cubic form...

Consider the following code:

```van_der_Waals := (p + a / V[m]^2) * (V[m] - b) = R * T:
expand(van_der_Waals);```

The objective of the exercise is express the equation in a cubic form. Obvious solution is to take the output of the code above and multiplie both sides by V[m]^2. However, I would like to know if there exists a different aproach to get the same result.

## Period in a decimal number...

How can I write a decimal number with period in maple? For example, in the following code;

```restart;
number := 3.123123123123:
convert(number, rational);```

I got 1040 / 333. However if number := 3.123123 then output is 76123 / 24374, so, in order to solve the exercise assign to the variable number a value of 3.123123123123123123123123123... How can I do it in abreviate form?

## Simplify expressions...

simplify is a procedure in Maple that have as parameter an assumption ¿Have the assumption a default value? For example, if we consider the following code:

```restart;
f:= (x^3 - 27) / (x^2 - 3 * x):
print(f = simplify(f));```

The output of that code assume that denominator is not zero, so I think the procedure have a default value for assume parameter.

## Is It Possible to Manipulate The Output From A Map...

I am working with expressions resulting from maple calculations that are 3-4 lines long, but I have to make a term-by-term comparison between one calculation and another. I would like to interweave the results of the two calculation so that one is above the other allowing direct comparison. It would also be nice to break up the expressions into pieces.  Unfortunately, I have gone as far as I can using maple directly.  The only solution I have come up with is to convert the expressions into Tex, copy them to a Tex editor and manipulate the expressions.  Unfortunately, Tex markup makes it difficult interpret the terms.

Has anyone come up with another method to manually manipulate the output from maple calculations.

## How to plot piecewise function?...

eval.mw This is the maple worksheet The regions are u<=-1, -1<=u<=1,u>=1

## How to plot sequencially points created in a loop ...

I want to plot a number created in a loop to monitor how it varies while keeping all previous ones on the figure. This is simply done in Matlab by hold on command, but I dont know how it is possible in Maple?

for i to 22 do
plot([i], [i^.5], style = point) :
end do

Note I want to monitor points during the loop running not after it finishes.

## how to arrange the following ...

how to write

-a2/3 + a3 - (2*a4)/3 - (2*a5)/3

into the form

-(-3*a3 + a2 + 2*a4 + 2*a5)/2

## How to collect the coefficient of epsilon^(1/2) fr...

test.mw

How to collect the coefficient of epsilon^(1/2) from A.

Actually, I want to write A as A=c1*epsilon^(1/2) +c2*epsilon+c3*epsilon^(3/2)

How to do that? My collect command failed to do this.

A:=-epsilon^(3/2)*a2^3/4 - (5*epsilon^(3/2)*a4^3)/3 - (5*epsilon^(3/2)*a5^3)/3 + a3*sqrt(epsilon) - sqrt(epsilon)*a2/3 - (2*sqrt(epsilon)*a4)/3 - (2*sqrt(epsilon)*a5)/3 - (5*epsilon^(3/2)*a2)/36 + (5*epsilon^(3/2)*a4)/9 + (5*epsilon^(3/2)*a5)/9 + epsilon/12 + (4*epsilon^(3/2)*a2*a4*a5)/3 - (7*epsilon^(3/2)*a2*a3*a4)/12 - (7*epsilon^(3/2)*a2*a3*a5)/12 + 5*epsilon^(3/2)*a3*a4*a5 - (3*epsilon^(3/2)*a2^2*a4)/4 - (3*epsilon^(3/2)*a2^2*a5)/4 + (2*epsilon^(3/2)*a2*a4^2)/3 + (2*epsilon^(3/2)*a2*a5^2)/3 - 5*epsilon^(3/2)*a4^2*a5 - 5*epsilon^(3/2)*a4*a5^2 + epsilon^(3/2)*a2^2*a3/12 + (5*epsilon^(3/2)*a3*a4^2)/2 + (5*epsilon^(3/2)*a3*a5^2)/2

to_maple.pdf

## Degrees package and working with RPMs...

Hello im an amateur using maple for my hidraulics machines course at engineering school. Does anyone know how to use the degrees package on maple 2021, i called it out by using the short form. with(Degrees): and then try to use sind but it doesnt recognice the command.

Also when using RPMs the units that should be giving me m/s appear as m2/m*s(radious). I know that the software recognice it as angular speed but is there anyway to eliminate the (radious) so i can work with the speed as lineal?

## How to solve system with one discrete variable?...

We have the system with one discrete variable along x-axis (i.e. 'i' is discrete in the attached file) and other variable 't' is continuous. But maple return error.

CD.mw