What is the correct way, in code, to check if Maple result contains any one of its own global build in symbols such as _Z or _C or any such symbol it uses?

I need to bypass this result. Currently I check explicitly, but I am sure there is a better way. Here is an example

r:=discont(1/tan(x),x);

This returns 

Currently I do 

if has(r,_Z1)  or has(r,_Z2) or has(r,_Z3) then
etc...

same for _C1, _C2., etc...

But this method is not robust. The problem is that _Z1 is symbol. So I can't check for symbol type in the  result as result could possibly have one of my own symbols there depending on input.

Is there  better way to do this? I am only asking about output of discont here and not any other Maple function. I assume discont uses _Zn only but I am not sure. It could use different symbol? 

given 

r1:=   -1 <= x and x <= 0;
r2:=   0 <= x and x <= 1;

We see that the above can be simplified to one inequality

-1<= x and x<=1

The closest I found to do this is

r1:=-1 <= x and x <= 0;
r2:=0 <= x and x <= 1;
solve(r1 or r2,x);

which gives RealRange(-1, 1) but I'd like to get the form  -1<= x and x<=1 similar to:

I tried convert to piecewise and simplify and few other things. Is there a trick in Maple to simplify/combine/join inequalites like the above? i.e. convert RealRange(-1, 1) to -1<=x and x<=1 

everything is on the real line.

Maple 2023.2

> kernelopts(version)
   Maple 2023.2, X86 64 LINUX, Nov 24 2023, Build ID 1762575

I got results I did not expect using &^ and mod. So, I created a simple example.

powermod.mw

&^ ... mod does not seem to allow () to set order of execution where ^ ... mod does.

How does &^ ... mod arrive at the values that are different than ^ ... mod?

Tom Dean

how do i change the decimal separator, i cant find the setting anywhere. I already changed all the settings in windows related to this. It displays numbers the way i want it to, by separating decimals using a comma, since that's what I'm used to. My regional settings on windows are also correct, however I can't seem to get maple to use the same separation. It looks like 123.13 when i want it to be 123,13. I couldn't find a solution online so I made an account here in the hope of finding a solution. Thanks

I would like to simulate the evolution of the so-called B, C, K, W system and SKI combinator calculus in Maple.
The rewrite rules of them are simple: 

However, if I try to evaluate the following example given in the  article, 

Maple will only return an unchanged result: 

restart;
applyrule([cS(x::anything)(y::anything)(z::anything) = x(z)(y(z)), 
   cK(x::anything)(y::anything) = x, cI(x::anything) = x], 
  cS(cK(cS(cI)))(cS(cK(cK))(cI))(x)(y)); # Unable to reduce??? 
 = 
              cS(cK(cS(cI)))(cS(cK(cK))(cI))(x)(y)

I believe that this is not an outlier.
Here are two additional instances: 

> rls := [cS(x::anything)(y::anything)(z::anything) = x(z)(y(z)), cK(x::anything)(y::anything) = x]:
> map2(applyrule, rls, [cS(cS(cS)(cS))(cS)(cS(cS))(cK), cS(cS(cS))(cS)(cS)(cS)(cS(cS)(cK(cK)))]);
                       [cS(cS(cS)(cS))(cS)(cS(cS))(cK), cS(cS(cS))(cS)(cS)(cS)(cS(cS)(cK(cK)))]

>

So why can't `applyrule` apply rules as desired? Meanwhile, how to automatically and thoroughly (like :-eval['recurse'] or MmaTranslator:-Mma:-ReplaceRepeated) apply those transformation rules to 

1. , 
2. , and
3. ? 

I have read something like How to apply a recursive rule in an expression? - MaplePrimes, but they are not the same issue.

I have this overloaded function foo(). 

restart;

foo:= overload(  
        [
        proc(A::integer,$)option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);             
        end proc,

        proc(A::integer,B::integer,$)option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ]);

Which works OK. so I can now do 

foo(1)
foo(1,2)

But I wanted to indicate that the proc returns say ::integer , and this where I am stuck, I do not know where to add this ::integer

With non-overloaded proc's, this is the syntax

foo:=proc(A::integer,$)::integer;
     ......
end proc;

but I can't do this with the overloaded function. If I type

foo:= overload(  
        [
        proc(A::integer,$)option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);             
        end proc,

        proc(A::integer,B::integer,$)option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ])::integer;

Maple simply does not like it. typing foo(1) now it just echos the definition back.

And these give syntax errors

foo:= overload(  
        [
        proc(A::integer,$)::integer option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);    
        end proc,

        proc(A::integer,B::integer,$)::integer option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ]);

Tried many other variations and looked at help but see nothing to far.

Can one add ::type to indicate type proc returns with overloaded proc?

Maple 2023.2.1

I want to execute a function at least one time. So, I use do ... until ...

However, the function sometimes returns FAIL. So, I looked at help FAIL.

FAIL.mw

The while loop works. The until loop returns an error. evalb(testeq(...)=FAIL) seems overly complicated.

Tom Dean

I am starting a course on differential forms. They have introduced the wedge product by comparing it to the curl product. I can do it by hand. But I would like to do it in Maple. I tried to read the help page of with(difforms) but I cannot see how to do it. And to add to the complication, since my keyboard is in French, I don't know how to insert the circumflex accent right after &. Maybe I should just wait that more theory is done, but just for the principle, I would like to be able to do it. For example, the vectors are:

a=(1, 3,-2)

b=(5, 2, 8)

Thank you in advance for your help.

Mario

The attached integral is plotted quite quickly, but the search for the maximum and for the inverses of function values takes time. Can the search be accelerated or is the integrand simply too complicated?

Download slow_maximize_and_fsolve.mw

I wanted to debug some code from worksheet A.  So added DEBUG(); command in the code where I want to start the GUI debugger from, and then run the command from the worksheet. All is working OK. the debugger GUI comes up and I can step in. 

Now I wanted to debug some other code from worksheet B. But without closing the currect debugger which is open and running.

It turned out this is not possible.  When running debugger from worksheet B, it uses the same debugger GUI that was up and running. I think it closed that session automtically also.

So basically using same Maple process, one can't open two debgging sessions at same time? Is there a way around this.

I run each worksheet using its own math engine. So each is separated from each other.

But this is first time I wanted to debug two things at same time, i.e. side by side, thinking I will be able to open two GUI debuggers at same time.

I know ofcourse I can open two separate Maple processes and then I will be able to do this. I think I am allowed to have two Maple's open at same time. Will try that next.

But it will be better if one is able to open two debuggers from same Maple at same time. I do not see why this should not be possible.

Any suggestions if there is a workaround? May be some hidden setting that allows this?

Maple 2023.2.1 on windows 10

Plots of physical quantities has significantly improved with Maple 2022. The updated useunits option makes unit conversion errors in plots very unlikely. A lot of time is saved when creating plots of physical quantities where values and units must be correct.

One final source of user errors remains: The manual entry of incorrect units in labels.

Below is a way to avoid such errors by computing labels with units for three prevalent axis labeling schemes.

Other desireable labels are given as a suggestion for future plot label enhancements where plot commands could provide formating functionality.

The rendering on this website adds double brakets ⟦ ⟧ wherever units are used. You have to open the document to see how Maple renders.

Simple plot example: Solar irradiance in space (1) (2) This plot has inconsistent axis labeling: •  The vertical axis has units but no name •  The horizontal axis has a name and units but they are not easily distinguishable. Misinterpretation is possible. Due to the close spacing the label could be read as a product of the dimension "time squared" (the time t times hours h is of the dimension time squared). Or the reader confounds name and units. (The use of italic fonts for names and roman fonts for units might not be noticeable and is a convention that is not used everywhere.)   The above labeling should be improved for communication, documentation or publication purposes.   A quick attempt using strings and the options useuints and labels. Axes are now consistent and can be interpreted unambiguously. Formatting can still be improved.   Unfortunately, using the options useunits (for unit conversion) and labels this way introduces a new source of user error when labels are entered with the wrong units.   A way to address this and to ensure unit error-free plotting of expressions of physical quantities is the following:   Step1: Define two lists, one for the units to display and the other for the names to display (3) Step2: Compute labels from the lists This step avoids the labeling error: No manual entry of units in labels required. (4)   Dimensionless labels  Double brackets Parenthesis The axis values equal physical quantities divided by their units. The algebraic equation , for example, is physically speaking correct. Most functions of Maple can process dimensionless expression of the kind  if G is given with appropriate physical units. This way of using physical quantities is consistent with ISO 80000.   Used in Maple to enter units in 2D-Math input mode Can be confounded with functional notation. Units are therefore often written as a whole word (e.g. seconds instead of s).     The time to produce the above three plots was about 10 Minutes. The most part was spent to get the typesetting of the second and third plot correct.   What takes significant more time (more a question of hours when Typesetting is used for the first time) are   Labels with or  formatting.   This formatting might be preferred but is unfortunately again not free from user errors. (I would probably use it if there was a simple and safe way). (5)       Remarks •  For two reasons, I have not given an example with the often used square brackets [ ] because:          Maple uses square brackets already for lists and indexing purposes,     and ISO 80000 uses square brackets as an operator that extracts the unit from a physical quantity (e.g.       ). •  Adding a unit to each value at axes ticks would definitely be a nice labeling feature for simple units. •  Programmatically analyzing the units defined in list  above and converting them in a generic way to a typesetting structure is not possible with a few high-level commands.   •  For inline quotients like in , an additional backslash must be entered in 2D-Math: \/   (6)      This will not prevent evaluation to a normal quotient but the input can be used to create an atomic variable (select with mouse -> 2-D Math -> Atomic Variable) (7)      This makes labeling much easier as compared to typesetting commands (compare to the above statements). (8) In any case it is a good idea to read ?plot,typesetting before experimenting with typesetting.

Axes_with_unit_labels.mw

My personal preference is for dimensionless labels.

Note:

The solution to avoid labeling errors works only for Maple 2022 and higher.

Some plot commands do not support plotting with units, or they do not fully support it yet.

The attached worksheet shows that Maple 2023 produces an incomplete plot of a function.  Maple 2021, however, produces the full graph.  I wonder if Maple 2023's behavior is due to a bad setting in my environment or a plotting bug in Maple.

Download cannot-plot.mw

As I am new to using the statistics package, I have some doubts about how to perform certain operations in Maple.

For example, let sigma be a variable containing any real number, finding the average is easy, just use the command A0:=Median(sigma) and if you want A (see image below) just take A1:=A0^2. However, the terms that make up <sigma^2> cause a certain difficulty, how to do this? In other words, calculate the B of the image?

sigma := [2, 4, 0, 6]

AMedia := (2 + 4 + 0 + 6)/4;
AMedia1 := AMedia^2;

A0 := Median(sigma)

A1 := A0^2

BMedia := (2^2 + 4^2 + 0^2 + 6^2)/4

sigma0 := sigma^2

sigma1 := Mean(sigma0)

.......................................................................................

hi every one.

in the attached maple file at line x=o in the plotted figure we have some inconsistency in starting the branches from x=0 and the branches do not start from the same value on this axis.

I can not find the problem because there are not any differences between phi 1 and phi 2! 

evalf(f1 - f2)= -5* 10 ^-49

h-x_nemodar-e.mw