I am reading the Maple Programming Guide chapter 3 "Maple Expressions". There are subsections on "Indexed Expressions" and "Member Selection".

The following is based on reading these sections.

Consider the following module definition

m := module() export e, f:=2; end module:

What is the difference between m[e] and m:-e or m[f] and m:-f?

The documentation says that both evaluate module m's export e but the difference is that the index selection form will evaluate e before resolving the export.

What does this mean exactly?

When I try out in a worksheet both m[f] and m:-f return 2 and m[e] and m:-e return the name e.

when i finding parameter i want just choose a case for example a_1=a_1  and any other case a_2=0,and remove other case how i can do in maple

Download choose_case.mw

dear maple user help me to correct this error . 

I want to solve the coupled pdes  plot the graphs but unable to get it. please help me. Here are the maple codes

restart:
L:=0.4:
d1:=0.3: d2:=0.3: 

h:=z->piecewise( z<=d1,   1,
                 z<=d1+L,   1-(delta/(2))*(1 + cos((2*(Pi)/L)*(z - d1 - L/2))), 
                 z<=d1+L+d2,  1 ):

a:=x4*S*Gr/(4*x1*x5)*sin(alpha):
b:=1/Da+(x3*M/(x1*(1+m^2))):
c:=(1/x1)*DP:
x1:=1/((1-phi1)^2.5*(1-phi2)^2.5):
x5:=khnf/kf:
x3:=shnf/sf:
x4:=(1-phi2)*((1-phi1)+phi1*(RBs1)/(RBf))+phi2*RBs2/RBf:
shnf:=sbf*((ss2+2*sbf-2*phi2*(sbf-ss2))/(ss2+2*sbf+phi2*(sbf-ss2))):
sbf:=sf*((ss1+2*sf-2*phi1*(sf-ss1))/(ss1+2*sf+phi1*(sf-ss1))):
ss2:=2.7*10^(-8):
ss1:=59.6*10^(6):
sf:=6.67*10^(-1):
khnf:=kbf*((ks2+2*kbf-2*phi2*(kbf-ks2))/(ks2+2*kbf+phi2*(kbf-ks2))):
kbf:=kf*((ks1+2*kf-2*phi1*(kf-ks1))/(ks1+2*kf+phi1*(kf-ks1))):
ks1:=401:
ks2:=76.5:
kf:=0.4972:
RBs1:=8933*16.7*10^(6):
RBs2:=6320*18*10^(6):
RBf:=1063*1.8*10^(6):
DP:=(1/192)*(18432*F-77*b^2*h(z)^8+308*b*h(z)^8*a+768*h(z)^6*a+12*b*h(z)^8)/(h(z)^4*(b*h(z)^2-6)):
conds:= w(h(z),0)=0, theta(h(z),0)=0, D[1](w)(r,0)=0, D[1](theta)(r,0)=0:
pdes:= diff(w(r, z), r, r)+(1/r)*(diff(w(r, z), r))-(1/Da+(x3/x1)*M)*w(r, z)-(1/x1)*(DP+theta*x4*sin(alpha))=0,
         diff(theta(r, z), r,r)+(1/r)*(diff(theta(r, z), r))+(S/x5)=0:
pars:= { F=1.5,Da=0.1,phi1=0.01,phi2=0.02,alpha=Pi/4,S=0.1,Gr=2,m=0.5}:
         
  PrVals:=[2, 5, 7,9]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {M=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( w(r,z), z=1, r=0..1, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);
Error, final value in for loop must be numeric or character
Error, unable to execute seq
 PrVals:=[2, 5, 7,9]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {M=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( theta(r,z), z=1, r=0..1, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);
Error, final value in for loop must be numeric or character
Error, unable to execute seq

 PrVals:=[2, 5, 7,9]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {M=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( DP,  z=0..1, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

Download simplify.mw

A little continuation of topics 1 and 2. This is a very similar cube from 2, 
 

but with a different equation:

f1 := (x1-sin(x1))^2+(x2-sin(x2))^2+(x3-sin(x3))^2-0.02513144866;
And other point coordinates (-.8283302152, -.8283302152, .8283302152) and (.8283302152, .8283302152, -.8283302152).

I'm a little busy with the Rule feature in Maple 
Just started with the limits and can't get 1 limit rule working in my FSimp procedure yet
As a limit example I saw this in Maple help 

with(Student:-Calculus1);
infolevel[Student[Calculus1]] := 1;

Rule[lhopital, ln(x)](Limit(x*ln(x), x = 0, right));
Creating problem #2

                  lim   (x ln(x)) =   lim   (-x)
                x -> 0+             x -> 0+     

A meaningless example of how one limit of a function is equal to another limit of a function, when I think there is no connection between the two functions. ( I don't see it ) 
You might as well calculate the limit value right away.

It gets more interesting when you analyze the function/expression : x*ln(x) and start rewriting it, to a [0/0] or [infinity/infinity] form in this case and from this it shows the need to start using lhopital rule.

The Rule feature has a Hint capability and gives as a hint, lhopital that this rule is applied 
Of course, you also have a series of standard limits, beyond the lhopital limits
The Rule feature for the limit is not yet step by step, because the need to start using a lhopital limit rule has not yet been demonstrated by the user

I'm interested in installing the package update from I M Anderson's site, the Differential Geometry Software Project. This corresponds to the 2022 update. There are many new features:
- Submanifold theory
- Differential operators and  Pseudo-Differential Operators
- Principal connections
- Integrable System Library
- Cartan normal connections
and more. 
It's unfortunate that this update isn't included in this version of Maple 2024

Hi all guys, how can I extract the coefficient of order 6 of expand(SUMY-T) as below? I use the coeff but no use and I search last posts in mapleprime but no fit for my case, and substitute the parematers of a,b,c....

Thank you!

Download location_truncation_error_of_y.mw

I am going through the documentation on ScientificConstants and trying things out in a worksheet.

My first question about this package is about the following

Download ScientificConstants.mw

I have multiple questions on how Units[TestDimensions] works from reading the Maple documentation. I will use this thread to ask them.

My first question regards the difference between Unit(expr) and units inserted using shortcut (CMD+SHIFT+U) on a mac?

Download Units_-_TestDimensions.mw

I read in the programming guide that to print the body of Maple library commands we set the Maple interface variable `verboseproc` to 2 then use the print command passing in the procedure we're interested in as argument.

Built-in kernel commands are compiled in machine code and not written in Maple language so we cannot view their definitions.

According to the guide, if we try to print such procedures we will see that the procedure has only an `option builtin` statement and no visible body.

If I try to view `Units:-TestDimensions`, as follows

```interface(verboseproc=1);
print(Units:-TestDimensions);

```

then what I see is

In this case there isn't the `option builtin` but neither is there a visible body.

Is this procedure built-in or is there a way to see the code?

Hi
i write my code for calculate this type of function but the result is so different from mine i  will post here i hope someone tell me where is problem

i have this

i want this

Download EX1.mw

Hello!
I am wondering if there is any way i can produce a cayley graph of a fixed radius for a finitely presented infinite group? That is if i take a FinPresInfGrp such as Z² is there any way i could create the cayley graph for the first 5 steps away from e?

I have tried increasing  _EnvMaxCosetsToddCoxeter however i imagine that this is a bit pointless!

Any help would be very much appriciated :)

Is there a way to reassign the arcsecant function "arcsec()" as "asec()" so that "arcsec" can be assigned to the arcsecond unit "Unit(arcsec)"?

Ideally, I would like all of the inverse trigonometric functions to use the shorter notation "asec()" instead of "arcsec()".  I usually do this as aliases, i.e. "alias(asin = arcsin) : alias(asec = arcsec) :" but this won't allow reusing "arcsec" for a unit instead.

Example error for Maple 2023:

alias(asec = arcsec) :
AddUnit(astronomical_unit, context = astronomy, default = true, prefix = SI, conversion = 149597870700*m) : # https://en.wikipedia.org/wiki/astronomical_unit
AddUnit(second, context = angle, spelling = arcsecond, plural = arcseconds, symbol = arcsec, prefix = SI_negative) :

AddUnit(parsec, context = astronomy, default = true, prefix = SI, conversion = AU/tan(arcsec)) ; # https://en.wikipedia.org/wiki/Parsec#Calculating_the_value_of_a_parsec

"Pi/648000" has to be used instead of "arcsec" here when defining the parsec since "arcsec" is already reserved for the arcsecant function, even with "alias(asec = arcsec) ;".

Correction: it looks like the parsec was redefined by the IAU in 2012 as exactly "648000*AU/Pi" without any tangents (or sines) in the definition (so the angle subtended by 1 AU at 1 PC is actually 0.999999999992" not 1").  Both "astronomical_unit" and "parsec" have the wrong values in Maple 2023 which need to be corrected manually.  But the conflict between arcseconds and arcsecants remains the same.

https://iau.org/static/resolutions/IAU2015_English.pdf

https://iopscience.iop.org/article/10.3847/0004-6256/152/2/41

I am reading the documentation on the `Units[Simple]` package.

There is a section that says

"In the Simple Units environment, in contrast to the Standard and Natural environments, unassigned variables are not automatically assumed to represent unit-free quantities. For example, 5m+x is a valid expression if x is unassigned, because x may represent a length. On the other hand (5m+x)(6s+x) is an invalid expression because the first factor implies that x represents a length and the second factor implies that x is a duration."

The way I understood this paragraph is that in Units:-Simple an unassigned variable is not assumed to represent a unit-free quantity, but in Units:-Standard it is assumed to represent a unit-free quantity.

Consider the expression 5m+x. This expression works in Units:-Simple but not in Units:-Standard.

Units:-Simple adds a quantity 5m to a quantity without units. But why can one add a quantity with units to a quantity without units?

Units:-Standard tries to add a quantity 5m to a quantity that is assumed to have units. What units are assumed?

Next, consider (5m+x)(6s+x).

This fails in both packages, as can be seen below (actually, for some reason, the embed below is not showing the expressions typed in for Units:-Standard, but can be seen if you download the worksheet I imagine).

So my question is, what exactly is the difference between considering unassigned variables to be unit-free vs not unit-free?

Download Units_Simple_vs_Standard.mw