Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

In an old post, vv reported a bug in simpl/max, which has been "fixed" in Maple 2018. However, it seem that such repairs are not complete enough.
For example, suppose it is required to find the (squared) distance between the origin and a point on x3 - x + y2 = ⅓ which is closest to the origin. In other words, one needs to minimize x²+y² among the points on this curve, i.e., 

extrema(x^2 + y^2, {x^3 + y^2 - x = 1/3}, {x, y}, 's'); # in exact form

Unfortunately, an identical error message appears again: 

restart;

extrema(x^2+y^2, {x^3+y^2-x = -2/(3*sqrt(3))}, {x, y})

{4/3}

(1)

extrema(x^2+y^2, {x^3+y^2-x = 1/3}, {x, y})

Error, (in simpl/max) complex argument to max/min: 1/36*((36+12*I*3^(1/2))^(2/3)+12)^2/(36+12*I*3^(1/2))^(2/3)

 

`~`[`^`](extrema(sqrt(x^2+y^2), {x^3+y^2-x = 1/3}, {x, y}), 2)

{4/3, 4/27}

(2)

extrema(x^2+1/3-x^3+x, {x^3+y^2-x = 1/3}, {x, y})

{4/3, 4/27}

(3)

MTM[limit](extrema(x^2+y^2, {x^3+y^2-x = a}, {x, y}), 1/3)

{4/3, 4/27}

(4)

Download tryHarder.mws

How about changing the values of parameter ?

for a from -3 by 3/27 to 3 do
    try
        extrema(x^2 + y^2, {x^3 + y^2 - x = a}, {x, y}); 
    catch:
        print(a); 
    end;
od;
                               -1
                               --
                               3 

                               -2
                               --
                               9 

                               -1
                               --
                               9 

                               1
                               -
                               9

                               2
                               -
                               9

                               1
                               -
                               3

By the way, like extrema, Student[MultivariateCalculus]:-LagrangeMultipliers also executes the Lagrange Multiplier method, but strangely, 

Student[MultivariateCalculus][LagrangeMultipliers](y^2 + x^2, [x^3 + y^2 - x - 1/3], [x, y], output = plot):

does not cause any errors.

Dear Forum,

I get data from a mass-spectrometer and want to do some analysis on it . 

What I get looks like this : ( only a few lines, the files are very large )

t[s]; scanId; m/z; I[A]; pTot[mbar]
2.00;0;0; 0.000000e+000; 0.000000e+000
4.00;0;0; 0.000000e+000; 0.000000e+000
441.00;0;0; 0.000000e+000;1,29E+00
443.00;0;0; 0.000000e+000;1,29E+00
453.00;0;0; 0.000000e+000;1,26E+00
455.00;0;0; 0.000000e+000;1,24E+00
463.00;1; 0.390625;8,14E-05;1,23E+00
464.00;1; 0.40625;1,23E-04;1,43E+00
464.00;1; 0.421875;1,73E-04;1,43E+00
464.00;1; 0.4375;2,27E-04;1,43E+00
464.00;1; 0.453125;2,77E-04;1,43E+00

When I add some blanks, it looks like this :  

t[s];        scanId;   m/z;              I[A];               pTot[mbar]

464.00;  1;           0.421875;     1,73E-04;     1,43E+00

The columns are separated by semicolon

t[s]  and m/z are separated with a dot,  I[A]  and p come as exponentials with a comma.

When I try to import this  with

 BKK := Import("H:\\Maple\\Spielwiese\\BGSample.csv")

I get a DataFrame with two columns -correct-  because there are two commas. 

Is there a way to import such data without preprocessing into maple ?

I include the data file, had to change the suffix to .txt - the original is .csv

Thank you and kind regards, 

Klaus

BKK := Import("H:\\Maple\\Spielwiese\\BGSample.csv")

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

(1)

BKK[10, 1] = 27.NULL

NULL

Download howdoiimportthis.mw

I often want to export an expression from Maple to LaTeX. Often, the output will contain commands that my LaTeX compiler doesn't recongnize. This hinders my LaTeX document production efficiency greatly. I use MiKTeX and Texmaker to generate documents in LaTeX language. Naively I assumed that Maple sticks to core LaTeX packages when generating an output. I still don't know if that is the case. The main issue is that, I don't know which LaTeX packages some of the Maple outputs use, and so, I don't know which packages to load in my LaTeX document.

As a concrete example, I show how I convert an expression to LaTeX language and how that particular output contains commands: \iup and \idn which are not recongnized by my LaTeX compiler since I don't know which package these commands come from. I google search for commands \iup and \idn came up empty. How do I figure out what package these commands come from

Latex_export_problems_1.mw

I am a little not clear why Maple's odeadvisor gives [_2nd_order, _reducible, _mu_xy] as an ode type for a second order ode which is already exact as is.

When the ode is exact, then no integrating factor mu is needed (or rather mu=1). But Maple says the ode is "reducible" using an integrating factor mu(x,y)

restart;
ode:=x*diff(diff(y(x),x),x)+(y(x)-1)*diff(y(x),x)=0;
DEtools:-intfactor(ode);
DEtools:-odeadvisor(ode)

 

THis ode is Kamke's 6.78, it is alslo mentioned in this paper in table 1 at page 18

I am just little confused, about the terminology. I thought reducible means the ode reguire an integrating factor of the form mu(x,y) or my(x,y') or mu(y,y') when it is not exact in order to make it to an exact ode so it can be now solved.

Why would odeavisor then says an ode which is already exact is also reducible using mu(x,y)?

Mathematica's Dimensions returns a list of the allowed levels, which has been implemented in Maple as . But 

MmaTranslator:-Mma:-Dimensions(<<1 | 2>, <1 | 0>>);

returns [6], and 

MmaTranslator:-Mma:-Dimensions([[1, 2], [1, 0]]);

returns [2, 2, 4]. What happened here?

It should be [2, 2].

restart;

MmaTranslator:-Mma:-Dimensions(linalg[matrix]([[1, 2], [1, 0]]));

[0]

(1)

MmaTranslator:-Mma:-Dimensions(< 1 , 2 ; 1 , 0 >);

[6]

(2)

MmaTranslator:-Mma:-Dimensions(convert(`{{1, 2}, {1, 0}}`, FromMma));

[2, 2, 4]

(3)

MmaTranslator:-FromMma(`Dimensions[{{1, 2}, {1, 0}}]`, evaluate);

[2, 2]

(4)

NULL

Download Mma[Dimensions].mws

Hello guys,
Can anyone recommend good books on advanced programming and other Maple topics? The books I have only have the basics.
Regards,
Oliveira

Execute the following codes in Maple input (1-D math) in the Standard interface. 

(cat("A".."C"),cat("d".."f"))||'$"G".."I",$"j".."l"'; 

Then an error occurred. But if one copy them into 2-D math (instead of Convert To>2-D Math Input) and execute them directly, everything goes without any error messages.

It says that mixed 1-D and 2-D math inside one command is not supported and not recommended stylistically. However, I just want to understand the reason why an error is raised here. 

restart;

kernelopts(version);

`Maple 2022.2, X86 64 WINDOWS, Oct 23 2022, Build ID 1657361`

(1)

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

(2)

(cat("A".."C"),cat("d".."f"))||'$"G".."I",$"j".."l"';

Error, `||` unexpected

 

cat("A" .. "C"), cat("d" .. "f") || '`$`("G" .. "I"), `$`("j" .. "l")'

"AG", "AH", "AI", "Aj", "Ak", "Al", "BG", "BH", "BI", "Bj", "Bk", "Bl", "CG", "CH", "CI", "Cj", "Ck", "Cl", "dG", "dH", "dI", "dj", "dk", "dl", "eG", "eH", "eI", "ej", "ek", "el", "fG", "fH", "fI", "fj", "fk", "fl"

(3)

NULL

Download unexpectedConcatenation.mws

hello dear maple, in the following code (code attached at the bottom )

I'm curious to know if it's possible to show the product of two matrices  in an unevaluated form, so for instance something like this instead of this 

UnEval_Mat.mw

Thanks in advance

hello maple world, in the following code (code attached at the bottom) i wish to select the terms which have the term so i used the "select" command for this task

but as u can see from the results it also selects other terms which is wrong. so what is the mistake here

thanks in advance

Physic_select.mw

Hey guys. i recently faced a problem where i needed to substitute the "physics's overloaded product operator" , namely with normal matrice product (`.`), so maple can do the matrice product calculation after my non-commutative physics operator(yellow symbols in the following code) has been replaced with real matrices (for instance, this substitution:)

now in order to substitute  with `.` I have utilized the maple `use` command. but the problem is, it doesn't do the substitution when I utilized `use` command as follows (code file is attached at the bottom) :

so what's the mistake here?

thanks in advance

Physic_subs.mw

Let's say we have a velocity vector v := c _i + d _j, where _i and _j are the i hat and j hat Cartesian basis vectors as present in the Physics[Vectors] package.

When we integrate this velocity vector relative to t, the result in maple is the position vector (c _i + d _j)t.

I guess that is correct.

My question is: is there am in-built way to specify an initial position vector for the integration? Ie, can I specify constants in the integration?

Right now I am just doing 

s0 := sx _i + sy _j

s:= int(v, t) + s0

I've been trying to figure out what i_  means in Maple. In what follows is some experimentation and then my questions.

Just a few initial experiments without loading any packages.

i_

i_

(1)

i_ = i_NULL

_i

_i

(2)

_i = _iNULL

D(_i)

D(_i)

(3)

f := proc (t) options operator, arrow; _i end proc

proc (t) options operator, arrow; _i end proc

(4)

D(f)

0

(5)

f := proc (t) options operator, arrow; t*_i end proc

proc (t) options operator, arrow; t*_i end proc

(6)

D(f)

proc (t) options operator, arrow; _i end proc

(7)

D(t*_i)

D(t)*_i+t*D(_i)

(8)

Impression: _i is treated like an algebraic basis vector when the result of a function; but not in an expression.

NULL

with(Physics)

_i

_i

(9)

_i = _iNULL

D(_i)

D(_i)

(10)

f := proc (t) options operator, arrow; t*_i end proc

proc (t) options operator, arrow; Physics:-`*`(t, _i) end proc

(11)

D(f)

proc (t) options operator, arrow; _i end proc

(12)

Nothing really seemed to change with the Physics package being used. However, if we use the following package

with(Physics[Vectors])

_i

_i

(13)

i_

i_

(14)

_i = _iNULL

i_ = i_NULL

In the middle of v__0 := v__x0*_i = v__x0*_i text. Doesn't work as expected.

In the middle of v__0 = v__x0*_i = v__x0*_i = v__x0*_i text.

 

NULL

My question is: is the symbol _i somehow special by default? Where can I find it in the documentation?

Note the second-to-last line in the Maple document pasted above: "Doesn't work as expected". The difference between this line and the next one is simply the presence of a := instead of an =. The assignment makes the vector notation differ. Is this difference a bug or some feature I am unaware of?

Here is yet another behavior that seems kinda weird to me. Given the function f defined above, D(f) gives us the expected result but D(f(x)) does not. Yet, int(f) gives an error, and we have to use int(f(x))

EDIT: a little more research indicates there is a difference between the operator and the function diff. 

Download PhysicsVectors.mw

Reading another question today I discovered that I can use syntax like

a := 2 _i + 3 _j

b:= _i - _j

a+b  

Maple computes the sum by vector component. This is very useful, and it prompted me to start reading the Multivariate Calculus Study Guide. I am still going through it but haven't seen this particular notation yet. When I check the type of above I get a result that sort of looks like `+` but actually it seems to be tilted to the right (so I guess it is italicized and represents some symbol).

What is this type?

I don't find much searching online, and I did see this page that says 

"Any symbol beginning with an underscore (_) is effectively reserved for use only by library code. It is not available to users. Failure to observe this rule can lead to unexpected results."

Edit: After a bit more looking, looks like my example code is using notation available from the Physics package, which I am now reading a bit about (but it is not clear to my why this package is used since I am not importing it explicitly).

I noticed something that seems to be new to my usage of Maple.

As I am typing in an expression in a Maple Worksheet (Document Mode), it seems Maple goes into "Evaluating" for a split second on every new keystroke.

For context, I have my own worksheet open and also the Maple Study Guide open for Multivariate Calculus. But just now I closed it and restarted Maple. A brand new worksheet has this same behavior. 

Did I just miss this before or is it normal for Maple to show "Evaluating" for a split second on every keystroke (instead of just "Ready")?

I just wrote up a bug report (aka "Software Change Request") but got a "We are currently experiencing technical difficulties" error so the report is not being sent.

I will just post here about the bug in case anyone knows what it is.

I am going through the Multivariate Calculus Study Guide. I went to section 1.1, and was going through the examples. At the end of an example is a link "Next Example", but when I click this I get an error and have to go back to section 1.1 Table of Contents. Kind of annoying. Also, I notice that Maple simply crashes seemingly randomly when going through this study guide. Very annoying.

Here is a screenshot of the write-up to the bug report service that isn't working, for the record

I was wondering if this is something wrong with my Maple installation or if other people experience it too.

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