Maple 2022 Questions and Posts

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

Hello there, 

Is there any chance to ask if there is a way to simplify the numeric outcome from an operation?

Here is what I've been trying:

restart;

with(LinearAlgebra):

interface(imaginaryunit=j):

Amat := Matrix(2, 2, [[-0.1428571428*K__D, -0.1081971238], [376.9911185, 0]]);

Matrix(2, 2, {(1, 1) = -.1428571428*`#msub(mi("K"),mi("D",fontstyle = "normal"))`, (1, 2) = -.1081971238, (2, 1) = 376.9911185, (2, 2) = 0})

(1)

Eigenvalues(Amat);

Vector(2, {(1) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`+0.2000000000e-9*sqrt(0.1275510203e18*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-0.1019733868e22), (2) = -0.7142857140e-1*`#msub(mi("K"),mi("D",fontstyle = "normal"))`-0.2000000000e-9*sqrt(0.1275510203e18*`#msub(mi("K"),mi("D",fontstyle = "normal"))`^2-0.1019733868e22)})

(2)

Desired := sqrt((2.000000000*10^(-10))^2 * (1.275510203*10^17*K__D^2 - 1.019733868*10^21));

(0.5102040812e-2*K__D^2-40.78935472)^(1/2)

(3)

 


I tried to simplify the Eigen values, to make them in the formality of the 'Desired' numerical expression, but no success yet. 

Thank you, 

Download Q20230110_m1.mw

restart

with(DEtools); with(LinearAlgebra)

diff(u(x, t), t) = [Matrix([[0, (1/2)*mu*k^2], [2*A^2-(1/2)*mu*k^2, 0]])]*u(x, t)

diff(u(x, t), t) = [Matrix(%id = 36893489823894642308)]*u(x, t)

(1)

"where u(x,t)=[u1 u2]^(T) is a vector. The solution of differential equation (1) is u=v*exp(w*t)."

where*w^2 = -(1/4)*mu^2*k^4+mu*k^2*A^2

"How can we solve differntial equation*(1) on Maple"?""

NULL

Download dsol.mw

Hello guys
Could someone help me create a simple palette to contain, for example, three functions that I use constantly?

           conve1(a), conve2(a) and conve3(a).

I tried through the help documentation, but I couldn't.

Sincerely,
Oliveira

Hello,

I use Maple 2022 on a MacBook Pro. In most of the plots I create I use symbol=solidcircle and symbolsize=12.

Is there a way to make those (and perhaps oher) settings user default so I don't need them in every plot command?

Thanks.

Jose

After studying the plottools:-transform command, I intend to visualize the following regions with constrained parameters in 
 

(plottools[transform](proc (u, v) options operator, arrow; [u^3-v^2, u^2-v^3] end proc))(plots[inequal](`or`(u^2+4*v^2 <= 4, `and`(u^2+v^2 < 4, 4*v >= (u+2)^2+2*v^2)), nolines))

 

(plottools[transform](proc (s, t) options operator, arrow; [s^2*sqrt(t)*cos(t), s^2*sin(t)] end proc))(plots[inequal](`and`(`and`(s >= 1, 5*s <= 5+t), t < 5), s = 1 .. 2, t = 0 .. 5))

 

 

But Mma gives 

The first instance (with default settings) is the same, but as for the second instance, which graph is correct? 

restart;
with(plottools):
with(plots):
transform((u, v) -> [u^3 - v^2, u^2 - v^3])(inequal(Or(u^2 + 4*v^2 <= 4, And(u^2 + v^2 < 4, (u + 2)^2 + 2*(v - 1)^2 <= 2)), nolines));
transform((s, t) -> [s^2*sqrt(t)*cos(t), s^2*sin(t)])(inequal(`and`(1 <= s, 5*s <= 5 + t, t < 5), s = 1 .. 2, t = 0 .. 5));


Download TransformedRegion.mws

The range is wrong. For details, see below, please.
 

restart;

assume(x, RealRange(0, 1))

plot([sqrt(x*(2 - x)/3), 1 - sqrt((1 - x^2)/3)], legend = InertForm:-Display~([sqrt(x*(2 - x) %/ 3), 1 - sqrt((1 %- x^2) %/ 3)], 'inert' = false));

 

smartplot([sqrt(x*(2 - x)/3), 1 - sqrt((1 - x^2)/3)]);

 

smartplot([''piecewise'(And(0 <= x, x <= 1), sqrt(x*(2 - x)/3))', ''piecewise'(And(0 <= x, x <= 1), 1 - sqrt((1 - x^2)/3))']);

 

smartplot(['piecewise(And(0 <= x, x <= 1), sqrt(x*(2 - x)/3))', 'piecewise(And(0 <= x, x <= 1), 1 - sqrt((1 - x^2)/3))']);

 

smartplot([''piecewise''(And(0 <= x, x <= 1), sqrt(x*(2 - x)/3)), ''piecewise''(And(0 <= x, x <= 1), 1 - sqrt((1 - x^2)/3))]);

 

x := 'x'NULL


 

Download SmartPlots.mw

The help page claims that smartplot(..) will call 2-D plot procedures ultimately, but why is the smartplots command incompatible with the use of assume?

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

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