Maple 2022 Questions and Posts

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

Here is a graph (g.txt) in Graphlet (gml) format that I threw up with another program. I want to import it by maple. 

I am expecting to do two things:

  • Import the graph correctly;
  • draw the graph according to the vertex position, vertex color, vertex shape and edge color etc. in the file.

This question may come from https://www.mapleprimes.com/questions/235457-How-To-Draw-A-Directed-but-Maybe-Not-Acyclic. My intention is to use this format to efficiently pass graphs and other attributes such as vertex positions, vertex colors, and edge colors. 

However maple doesn't seem to be able to handle them even it cannot handle  the above first point well.

Import ("G:\\test\\g.gml");
# or 
GraphTheory:-ImportGraph ("G:\\test\\g.gml",graphlet)

Error, (in Import) incorrect syntax in parse: unexpected number (near 12th character of parsed string)

Error, (in GraphTheory:-ImportGraph) incorrect syntax in parse: unexpected number (near 12th character of parsed string)

I'm not sure what type of the mistake is here.

 

Mathematica can do it nicely:

g=Import["G:\\test\\g.gml"]

List @@@ PropertyValue[g, VertexLabels]
GraphEmbedding[g]

 

{{8, "x8"}, {12, "b3"}, {14, "x14"}, {2, "b2"}, {13, "x13"}, {5, 
  "r3"}, {7, "r5"}, {9, "r6"}, {11, "x11"}, {6, "r4"}, {1, "b1"}, {15,
   "x15"}, {3, "r1"}, {4, "r2"}, {10, "x10"}}

{{1080, 1440}, {480, 320}, {660, 560}, {420, 160}, {1380, 880}, {1020,
   720}, {720, 880}, {660, 800}, {2160, 0}, {0, 0}, {1500, 
  480}, {1320, 800}, {1800, 240}, {900, 1120}, {1080, 1360}}

PropertyValue[g, VertexStyle]

 

Is there a way to write a function definition that involves multiple cases so that it looks nice with braces as one would write on paper. 
For example, the function $f(x)=|x|$ which is $f(x)=x$ if $x>0$ and $f(x)=-x$ if $x<0$.

First of all, I'd like to be able to write this out with braces in non-executable math in my worksheet. This would already be great.

Then, is it possible to actually define a function this way (ie, not just display the braces in non-executable, but actually run in executable math and have a defined function)?

Hello guys,

I created a palette, but when I click on an entry, the following occurs:

If the entry line, where the mouse cursor is, is empty, insertion takes place on this line.
If the input line has any expression and the mouse cursor is to the left of the expression, insertion takes place on the line above.

If the input line has any expression and the mouse cursor is to the right of the expression, insertion takes place on the line below.

Does anyone know how to fix this?

Sincerely,

Oliveira

How do I find the maximum value of k by putting dw/dk = 0? Also, how to find the range of k for which w is real? 

restart

w = -(1/2)*sqrt(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)

w = -(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

(1)

diff(w = -(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2), k)

0 = -(1/4)*(1920*c^6*gamma^2*k-1344*c^4*gamma^2*k^3+384*c^2*gamma^2*k^5-32*gamma^2*k^7+576*alpha*c^6*gamma-864*alpha*c^4*gamma*k^2-80*alpha*c^2*gamma*k^4+56*alpha*gamma*k^6-288*alpha^2*c^4*k-192*alpha^2*c^2*k^3-24*alpha^2*k^5+256*c^4*gamma*k-160*c^2*gamma*k^3+24*gamma*k^5+48*alpha*c^4-48*alpha*c^2*k^2-20*alpha*k^4+8*c^2*k-4*k^3)/(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

(2)

NULL

NULL

Download drelation.mw

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

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