Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

Hi all,

I drew a undirected graph using Maple

restart;
with(GraphTheory);
with(SpecialGraphs);
with(RandomGraphs);
G := Graph(undirected, {[{1, 2}, 4], {1, 4}, {2, 3}, {2, 5}, {3, 4}});
DrawGraph(G, style = circle);

I want to import this graph to picturebox or panel on C#, please help me!

hi

if possible to convert matlab file in to maple fie program??convert_to_maple_program.txt

thanks

 

hi...how i can gain result for solve three equations,in which term '' Root of'' dont appear?

thanks

root.mw

restart; Q1 := aa*(y-x)

aa*(y-x)

(1)

Q2 := -ll*x*z+bb*x

-ll*x*z+bb*x

(2)

 

-ll*x*z+bb*x

(3)

Q3 := -cc*z+hh*x*x+kk*y*y

hh*x^2+kk*y^2-cc*z

(4)

SOLL := solve({Q1, Q2, Q3}, {x, y, z})

{x = 0, y = 0, z = 0}, {x = RootOf((hh*ll+kk*ll)*_Z^2-bb*cc), y = RootOf((hh*ll+kk*ll)*_Z^2-bb*cc), z = bb/ll}

(5)

``

 

Download root.mw

For people new to Maple, an easy way to learn how to code may be Tutor Syntax, that is the technique of generating code by selecting everything in a Tutor dialog Maple Command window and then copying it to a current session.

The code can then be edited to tailor it to user’s needs. A problem with this technique is the copied syntax contains many single quotes (‘ ‘). The single quotes, which are usually not needed if the program in current session is short and specific, increase the difficulty when editing copied syntax. The attached file (mby2.mw) shows a method which removes the single quotes by using the SubstitueAll command in the StringTools package. One drawback: any strings inside the original syntax (e.g., “#78000E”) must be removed before the syntax can be converted to a string.

Is there a better way to generate code from Tutor dialog so it can be edited (without single quotes) in user’s current session?

mby2.mw

hi.please help me for remove error'' 

Error, illegal use of an object as a name''

 

thanks

PLATE.mw

   

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Error, illegal use of an object as a name

"restart:Digits :=15: beta:=10:alpha:=100: xi:=.5: upsilon:=0.2841945289:n:=3: aa:=1:b:=1:N_x:=0.4:N_y:=0.4:N_xy:=0: hl2:=1:mu:=65.8e9:E:=169e9: delta0:=1:delta1:=1: mus:=3:D1:=2;h:=1: lambda:=0.1: D2:=5:A1:=-2:A2:=-2:A3:=-6:A4:=7:A5:=7:A6:=7:A7:=7:A8:=8:A9:=7:A10:=7:A11:=1: A12:=1:tau:=4.730040745:t:=0: g2:=sin(theta):g3:=cos(theta):g1:=cos(theta):a:=0.0:with(Student[Calculus1]): a1:=evalf((A1*ApproximateInt(g3^2,theta=a..1,method=simpson)  ) ) : a2:= evalf(A2*ApproximateInt(g3*((ⅆ)^2)/((ⅆtheta)^2)g3,theta=a..1,method=simpson)): a3:=evalf(A3*ApproximateInt(g3*g3,theta=a..1,method=simpson)) : a4:=evalf(A4*ApproximateInt(g3*g3,theta=a..1,method=simpson)) :a5:=evalf(A5*ApproximateInt(g3^2,theta=a..1,method=simpson)) : a6:=evalf(A6*ApproximateInt(((ⅆ)^2)/((ⅆtheta)^2)g3*g3,theta=a..1,method=simpson)) :a7:=evalf(A7*ApproximateInt(g3*g3,theta=a..1,method=simpson)): a8:=evalf(A8*ApproximateInt(g3^2,theta=a..1,method=simpson)):a9:=evalf(ApproximateInt(A9*(g3*g3 )     ,theta=a..1,method=simpson)) :a10:=evalf(A10*ApproximateInt(g3*g3,theta=a..1,method=simpson)):a11:=evalf(ApproximateInt(1,theta=a..1,method=simpson)):a12:=evalf(ApproximateInt(1*(1-1/2 (1)),theta=a..1,method=simpson)):dsys3 := { f3(x)*(a1)+ f3(x)*(a2)  +((ⅆ)^2)/((ⅆx)^2) f3(x)*(a3) +f3(x)*a4+ f3(x)*(a5) +((ⅆ)^2)/((ⅆx)^2) f3(x)*(a6) +f3(x)*a7= ((ⅆ)^2)/((ⅆx)^2) f3(x) *(a8)   + a9*(ⅆ)/(ⅆx) f3(x) +f3(x)*a10+ a11+a12  , f3(1) =0,f3(0) =0 , D^(1)(f3)(1) = 0, D^(1)(f3)(0)=0,D^(3)(f3)(1) = 0, D^(3)(f3)(0)=0}    :dsol5 := dsolve(dsys3, 'maxmesh'=2024, numeric,abserr=.0001, range=0..1, output=listprocedure):fy3:= eval(f3(x),dsol5):with(CurveFitting):fy33:=PolynomialInterpolation([[0,fy3(0)],[.1,fy3(0.1)],[.2,fy3(0.2)],[0.3,fy3(0.3)],[.4,fy3(0.4)],[.5,fy3(0.5)],[0.6,fy3(0.6)],[0.7,fy3(0.7)],[0.8,fy3(0.8)],[0.9,fy3(0.9)],[1,fy3(1)]],x): d1:=A1*ApproximateInt(((ⅆ)^6)/((ⅆx)^6)fy33*fy33,x=a..1,method=simpson)   :d2:= A2*ApproximateInt(((ⅆ)^4)/((ⅆx)^4)fy33*fy33 ,x=a..1,method=simpson)   :d3:=A3*ApproximateInt(((ⅆ)^2)/((ⅆx)^2)fy33*fy33,x=a..1,method=simpson): d4:= A4*ApproximateInt(fy33*fy33,x=a..1,method=simpson):d5:=A5*ApproximateInt(((ⅆ)^4)/((ⅆx)^4)fy33*fy33,x=a..1,method=simpson)  : d6:=A6*ApproximateInt(((ⅆ)^2)/((ⅆx)^2)fy33*fy33,x=a..1,method=simpson)    :d7:=A7*ApproximateInt(fy33*fy33,x=a..1,method=simpson)  :d8:=A8*ApproximateInt(((ⅆ)^2)/((ⅆx)^2)fy33*fy33,x=a..1,method=simpson)      :d9:=ApproximateInt(A9*(((ⅆ)^1)/((ⅆx)^1)fy33*fy33 )   ,x=a..1,method=simpson) :d10:=A10*ApproximateInt(fy33*fy33,x=a..1,method=simpson)    :d11:=evalf(ApproximateInt(1,theta=a..1,method=simpson)):d12:=evalf(ApproximateInt(1*(1-1/2 (1)),theta=a..1,method=simpson))  : d sys4 := { h3(theta)*(d1)+((ⅆ)^2)/((ⅆtheta)^2) h3(theta)*(d2)+((ⅆ)^4)/((ⅆtheta)^4) h3(theta)*(d3)+ ((ⅆ)^6)/((ⅆtheta)^6) h3(theta)*(d4)+h3(theta) *(d5)+ h3(theta) *(d6) +((ⅆ)^4)/((ⅆtheta)^4) h3(theta)*(d7)= h3(theta)*(d8)  +d9*(ⅆ)/(ⅆtheta) h3(theta)  +((ⅆ)^2)/((ⅆtheta)^2) h3(theta)*(d10)  +d11+d12   ,h3(1) = 0,h3(0) = 0 , D^(1)(h3)(1) = 0, D^(1)(h3)(0)=0,D^(3)(h3)(1) = 0, D^(3)(h3)(0)=0}  :dsol6 := dsolve(dsys4, 'maxmesh'=2024, abserr=.0001, range=0..1, numeric, output=listprocedure):g33:= eval(h3(theta),dsol6):with(CurveFitting):g3:=PolynomialInterpolation([[0,g33(0)],[.1,g33(0.1)],[.2,g33(0.2)],[0.3,g33(0.3)],[.4,g33(0.4)],[.5,g33(0.5)],[0.6,g33(0.6)],[0.7,g33(0.7)],[0.8,g33(0.8)],[0.9,g33(0.9)],[1,g33(1)]],theta):"

 

 

``

 

Download PLATE.mw

This is the second of three blog posts about working with data sets in Maple.

In my previous post, I discussed how to use Maple to access a large number of data sets from Quandl, an online data aggregator. In this post, I’ll focus on exploring built-in data sets in Maple.

Data is being generated at an ever increasing rate. New data is generated every minute, adding to an expanding network of online information. Navigating through this information can be daunting. Simply preparing a tabular data set that collects information from several sources is often a difficult and time consuming effort. For example, even though the example in my previous post only required a couple of lines of Maple code to merge 540 different data sets from various sources, the effort to manually search for and select sources for data took significantly more time.

In an attempt to make the process of finding data easier, Maple’s built-in country data set collects information on country-specific variables including financial and economic data, as well as information on country codes, population, area, and more.

The built-in database for Country data can be accessed programmatically by creating a new DataSets Reference:

CountryData := DataSets:-Reference( "builtin", "country" );

This returns a Reference object, which can be further interrogated. There are several commands that are applicable to a DataSets Reference, including the following exports for the Reference object:

exports( CountryData, static );

The list of available countries in this data set is given using the following:

GetElementNames( CountryData );

The available data for each of these countries can be found using:

GetHeaders( CountryData );

There are many different data sets available for country data, 126 different variables to be exact. Similar to Maple’s DataFrame, the columns of information in the built-in data set can be accessed used the labelled name.

For example, the three-letter country codes for each country can be returned using:

CountryData[.., "3 Letter Country Code"];

The three-letter country code for Denmark is:

CountryData["Denmark", "3 Letter Country Code"];

Built-in data can also be queried in a similar manner to DataFrames. For example, to return the countries with a population density less than 3%:

pop_density := CountryData[ .., "Population Density" ]:
pop_density[ `Population Density` < 3 ];

At this time, Maple’s built-in country data collection contains 126 data sets for 185 countries. When I built the example from my first post, I knew exactly the data sets that I wanted to use and I built a script to collect these into a larger data container. Attempting a similar task using Maple’s built-in data left me with the difficult decision of choosing which data sets to use in my next example.

So rather than choose between these available options, I built a user interface that lets you quickly browse through all of Maple’s collection of built-in data.

Using a couple of tricks that I found in the pages for Programmatic Content Generation, I built the interface pictured above. (I’ll give more details on the method that I used to construct the interface in my next post.)

This interface allows you to select from a list of countries, and visualize up to three variables of the country data with a BubblePlot. Using the preassigned defaults, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product. The BubblePlot visualization also adds a third dimension of information by adjusting the bubble size according to the relative population compared with the other selected countries.

Now you may notice that the list of available data sets is longer than the list of available options in each of the selection boxes. In order to be able to generate BubblePlot animations, I made an arbitrary choice to filter out any of the built-in data sets that were not of type TimeSeries. This is something that could easily be changed in the code. The choice of a BubblePlot could also be updated to be any other type of Statistical visualization with some additional modifications.

You can download a copy of this application here: VisualizingCountryDataSets.mw

You can also interact with it via the MapleCloud: http://maplecloud.maplesoft.com/application.jsp?appId=5743882790764544

I’ll be following up this post with an in-depth post on how I authored the country selector interface using programmatic content generation.

I want to create a matrix (B) from entries of other matrices (A) with a helper-function (helper). The helper function is defined such that it returns a certain matrix depending on the index variables. This is necessary because the inner matrices are constructed with another function.

Since the helper-function returns matrices, the big matrix is of datatype=matrix. Unfortunately, creating the big matrix with the correct size and forcing the datatype=float, does not yield the desired result. However, the manual definition using the constructor with a list of matrices does create the desired matrix.

How do I resolve a matrix of matrices?

Note: I know that I could write a convert function that copies the entries to a corresponding matrix, though this seems to be unnecessary effort to me.

This might not be minimal but shows the issue. (Compare B and test)

MWE_matrix_of_matrices.mw

restart;
with(LinearAlgebra):

size_A := 2;
size_B := 3;

2

 

3

(1)

helper2 := proc(i::integer,j::integer);
  if i=j then
    a;
  elif i=j-1 or i=j+1 then
    b;
  else
    c;
  end if;
end proc:

helper3 := proc(i::integer,j::integer);
  if i=j then
    Matrix(size_A,size_A,helper2);
  elif i=j-1 or i=j+1 then
    -IdentityMatrix(size_A);
  else
    Matrix(size_A);
  end if;
end proc:

A := Matrix(size_A, size_A, helper2);
B := Matrix(size_B, size_B, helper3);
B := Matrix(size_B,size_B, helper3, datatype = float);
B := Matrix(size_B*size_A, size_B*size_A,[Matrix(size_B,size_B,helper3)], datatype = float)

A := Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a})

 

B := Matrix(3, 3, {(1, 1) = Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a}), (1, 2) = Matrix(2, 2, {(1, 1) = -1, (1, 2) = 0, (2, 1) = 0, (2, 2) = -1}), (1, 3) = Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0}), (2, 1) = Matrix(2, 2, {(1, 1) = -1, (1, 2) = 0, (2, 1) = 0, (2, 2) = -1}), (2, 2) = Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a}), (2, 3) = Matrix(2, 2, {(1, 1) = -1, (1, 2) = 0, (2, 1) = 0, (2, 2) = -1}), (3, 1) = Matrix(2, 2, {(1, 1) = 0, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0}), (3, 2) = Matrix(2, 2, {(1, 1) = -1, (1, 2) = 0, (2, 1) = 0, (2, 2) = -1}), (3, 3) = Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a})})

 

Error, (in Matrix) unable to store 'Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a})' when datatype=float[8]

 

Error, (in Matrix) unable to store 'Matrix(2, 2, {(1, 1) = a, (1, 2) = b, (2, 1) = b, (2, 2) = a})' when datatype=float[8]

 

test := Matrix(4, 4, [
                [Matrix([[1,2],[0,9]]), Matrix([[3,6],[0,9]])],
                [Matrix([[3,4],[7,8]]), Matrix([[7,6],[5,5]])]
               ]); # is converted to a matrix of floats

test := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 3, (1, 4) = 6, (2, 1) = 0, (2, 2) = 9, (2, 3) = 0, (2, 4) = 9, (3, 1) = 3, (3, 2) = 4, (3, 3) = 7, (3, 4) = 6, (4, 1) = 7, (4, 2) = 8, (4, 3) = 5, (4, 4) = 5})

(2)


rather than last time saved file result?

When I open maple script file, it display the result which file created.

however, not the latest result 

it need to move cursor to the end of script and press enter again.

hi

how i can solve nonlinear differential equations with shooting method in maple?ω in equation is unknown...

thanks

eq.mw

dsys3 := {-0.326905829596411e-2*g(x)-(diff(g(x), x, x))-(diff(s(x), x))*(diff(s(x), x, x))-(4/3)*omega^2*g(x), -s(x)*omega^2-(-0.573628192993074e-1*sin(0.571756792348295e-1*x)-0.163452914798206e-2*cos(0.571756792348295e-1*x))*(diff(s(x), x))-(1.00327307112014*cos(0.571756792348295e-1*x)-0.285878396174148e-1*sin(0.571756792348295e-1*x)-1)*(diff(s(x), x, x))+0.220893539279189e-4*(diff(s(x), x, x, x, x))-(9/8)*(diff(s(x), x, x))*(diff(s(x), x))^2-(3/4)*(diff(s(x), x, x))*(diff(g(x), x))-(3/4)*(diff(s(x), x))*(diff(g(x), x, x)), (D(g))(1)+(1/2)*(D(s))(1)^2 = 0, g(0) = 0, s(0) = 0, (D(s))(0) = 0, ((D@@2)(s))(1) = 0, ((D@@3)(s))(1) = 0}

{-0.326905829596411e-2*g(x)-(diff(diff(g(x), x), x))-(diff(s(x), x))*(diff(diff(s(x), x), x))-(4/3)*omega^2*g(x), -s(x)*omega^2-(-0.573628192993074e-1*sin(0.571756792348295e-1*x)-0.163452914798206e-2*cos(0.571756792348295e-1*x))*(diff(s(x), x))-(1.00327307112014*cos(0.571756792348295e-1*x)-0.285878396174148e-1*sin(0.571756792348295e-1*x)-1)*(diff(diff(s(x), x), x))+0.220893539279189e-4*(diff(diff(diff(diff(s(x), x), x), x), x))-(9/8)*(diff(diff(s(x), x), x))*(diff(s(x), x))^2-(3/4)*(diff(diff(s(x), x), x))*(diff(g(x), x))-(3/4)*(diff(s(x), x))*(diff(diff(g(x), x), x)), (D(g))(1)+(1/2)*(D(s))(1)^2 = 0, g(0) = 0, s(0) = 0, (D(s))(0) = 0, ((D@@2)(s))(1) = 0, ((D@@3)(s))(1) = 0}

(1)

``

 

Download eq.mw

hi.how i can determind  eignvalue of matrix in the form parametric?

thanks1.mw

T := Matrix(5, 5, {(1, 1) = -b*beta*k/(c*u)-d, (1, 2) = 0, (1, 3) = -beta*lambda*c*u/(b*beta*k+c*d*u), (1, 4) = 0, (1, 5) = 0, (2, 1) = b*beta*k/(c*u), (2, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P-a, (2, 3) = beta*lambda*c*u/(b*beta*k+c*d*u), (2, 4) = -s*b/c, (2, 5) = r*(s-p)/s, (3, 1) = 0, (3, 2) = k, (3, 3) = -u, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (4, 3) = 0, (4, 4) = -s*b/c-b, (4, 5) = r*(s+c)/s, (5, 1) = 0, (5, 2) = s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (5, 3) = 0, (5, 4) = s*b/c, (5, 5) = -r})

Matrix(5, 5, {(1, 1) = -b*beta*k/(c*u)-d, (1, 2) = 0, (1, 3) = -beta*lambda*c*u/(b*beta*k+c*d*u), (1, 4) = 0, (1, 5) = 0, (2, 1) = b*beta*k/(c*u), (2, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P-a, (2, 3) = beta*lambda*c*u/(b*beta*k+c*d*u), (2, 4) = -s*b/c, (2, 5) = r*(s-p)/s, (3, 1) = 0, (3, 2) = k, (3, 3) = -u, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = -s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (4, 3) = 0, (4, 4) = -s*b/c-b, (4, 5) = r*(s+c)/s, (5, 1) = 0, (5, 2) = s*(lambda*c*k*beta/(b*beta*k+c*d*u)-a)/P, (5, 3) = 0, (5, 4) = s*b/c, (5, 5) = -r})

(1)

``

 

Download 1.mw

 

I defined a procedure, OrderB(0,b,c), that essentially determines the order of a group that is defined by 2 parameters (the first parameter is always zero), so the output is an integer and the procedure is defined for every integer value of both parameters. I wanted to structure the outputs into a matrix with columns that represent one parameter and rows that represent the other. However, whenever I try to apply a method of defining the matrix, Maple returns the values of the procedure and then gives me an empty matrix.

>f:=proc (i, j) -> OrderB(0, i, j+3);
>Matrix(3, f);
                               1
                               4
                               1
                               1
                               4
                               1
                               1
                               4
                               1
               [NULL,NULL...]


I tried a second method where I defined a set s such that:

s:={(0,0)=OrderB(0,0,0) , (0,1)=OrderB(0,0,1).....}

but upon execution, maple returns:

1
4
1
....
s:={(0,0)=( ), (0,1)=( )...}

Please Help. I don't know what I'm mising in the code that is keeping Maple from putting the outputs of my procedure into the matrix.

Been working on a diffy q project, new to maple here. Any help is appreciated. Keep getting a similar error.

 

"Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem"

I thought I gave it initial values?

link to screenshot of the error bellow:

http://i.imgur.com/YVE1x7e.jpg

how to convert system of differential equations to differential form for evalDG?

 

[a(t)*(diff(c(t), t))+b(t), a(t)*(diff(b(t), t))+c(t)*(diff(b(t), t)), a(t)*(diff(c(t), t))+a(t)*(diff(b(t), t))+b(t)];

when i try eliminate dt which is the denominator

eliminate([a(t)*dc(t) + b(t)*dt,a(t)*db(t)+dt*c(t)*db(t),a(t)*dc(t)+a(t)*db(t)+b(t)*dt],dt);

[{dt = -a(t)/c(t)}, {a(t)*(c(t)*dc(t)-b(t)), a(t)*(db(t)*c(t)+c(t)*dc(t)-b(t))}]

 

i got two solutions, which one is correct?

a(t)*(c(t)*dc(t)-b(t)), a(t)*(db(t)*c(t)+c(t)*dc(t)-b(t))

does it mean that two have to use together to form a differential form?

 

update1

with(DifferentialGeometry):
DGsetup([a,b,c], M);
X := evalDG({a*(c*D_c-b), a*(D_b*c+c*D_c-b(t))});
Flow(X,t);
Flow(X, t, ode = true);

got error when run with above result

 

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