Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

hi, learners of maple like me, i was handling a project,but i came across this problem,and i began to doubt the accuracy of maple-plot,,,

very simply expression,result3,changing with the parameter f,

i first plot the f from 100 to 5000,

than i need to watch closer,

so i change the define domain of parameter f, plot f from 100 to 1000,  

and the result of plot definitely  differs from the previous one. 

low vally in the first figure (f in the scale of 100-1000),disappears! that's insane...

 

you can see below,

anyone see it, can you give me some clue? i really do not understand this. why ,why why,,

result3 := 3.269235506947450*10^11*sqrt(-1/(0.975698207102e-3*cos(0.19042716640833e-1*f)^2*cos(0.9521358320417e-2*f)^4-0.975698207102e-3*cos(0.19042716640833e-1*f)^2*cos(0.9521358320417e-2*f)^2+5.099915851388520*10^(-8)*cos(0.9521358320417e-2*f)^4-5.099915851388520*10^(-8)*cos(0.9521358320417e-2*f)^2+1.311634114532540*10^12*sin(0.19042716640833e-1*f)*sin(0.9521358320417e-2*f)*cos(0.9521358320417e-2*f)*cos(0.19042716640833e-1*f)+4.405792916762340*10^26*cos(0.19042716640833e-1*f)^2-4.406861706842330*10^26))

326923550694.745*(-1/(0.975698207102e-3*cos(0.19042716640833e-1*f)^2*cos(0.9521358320417e-2*f)^4-0.975698207102e-3*cos(0.19042716640833e-1*f)^2*cos(0.9521358320417e-2*f)^2+0.509991585138852e-7*cos(0.9521358320417e-2*f)^4-0.509991585138852e-7*cos(0.9521358320417e-2*f)^2+1311634114532.54*sin(0.19042716640833e-1*f)*sin(0.9521358320417e-2*f)*cos(0.9521358320417e-2*f)*cos(0.19042716640833e-1*f)+0.440579291676234e27*cos(0.19042716640833e-1*f)^2-0.440686170684233e27))^(1/2)

(1)

plot(result3, f = 100 .. 5000);

 

 

plot(result3, f = 100 .. 1000);

 

 

 

``


 

Download test.mw

 

 

 

I have a workbook that derives the Cobb-Douglas factor demand functions:

The final formulas (10) and (11) are not in the same format as the formulas in my textbook (by Hal Varian). In fact my last formulas betray no obvious symmetry while Varian's forms do.

Download cobb-douglas.mw

Here is a picture of them scraped from the text.

 

Is it possible to instruct Maple to obtain these forms?

Maple 17 is very exciting so I am hopeful ....

P.

 

The following construction of a simple vector of matrices (just a test example)

Vector(2,(a) -> Matrix(2,2,(b,c) -> m||a||b||c));

works in Maple 17, but not in Maple 2017 where the error message "Error, (in Vector[column]) number of elements on right side must match subselection on left side" is produced. Why that?

Update: If no output is prompted, i.e., if the above line is terminated with colon instead of semicolon, then no error is raised. What?!

I am thinking about buying maple 2017 however there are only 4 different categories to choose from when you want to buy: student, commercial, academic and government. I dont belong to any of them! Also the price difference is huge! I am on disability benefits and the academic license cost more or less the same amount that I get in disability benifts each month to cover my food, rent and medicines which is approximatly 1 100 usd. The price for a student licens is completely realistic and is a price that I am willing to pay but I am not a student and I dont feel comfortable claiming that I am even though everyone is a student as long as they live. When you stop learning you life is more or less over anyway. If I am forced to pay around 1 000 usd then I am not going to buy maple 2017. Then I am just going to continue using MathPapa free algbra calculator https://www.mathpapa.com/ because to be honest I dont really need maple that much in my research today but there are a couple of reaons why I want to buy. 1) I would like to support maplesoft because I think you have the best and most userfriendly mathematical software on the market. 2) I want to hedge my bets. My needs might change in the future. 3) I want to be able to run my large number of old worksheets and see if I can improve them. 4) I want to see what changes and improvments have been made to maple 2017 compared to let say 5 years ago and to assess if these changes provide any value to me. 

A question was raised recently on Stewart Gough platforms.  I decided to tidy up some old code to show platform position and leg lengths for any given displacement.
 

restart

``

Hexapod Setup Data

 

RotZ := proc (delta) options operator, arrow; Matrix(1 .. 3, 1 .. 3, {(1, 1) = cos(delta), (1, 2) = -sin(delta), (1, 3) = 0, (2, 1) = sin(delta), (2, 2) = cos(delta), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}, datatype = anything, storage = rectangular, order = Fortran_order, subtype = Matrix) end proc

a[1] := Vector(3, [.5, 3.0, 0]); a[2] := evalf(RotZ(20*((1/180)*Pi)).a[1]); a[3] := evalf(RotZ(100*((1/180)*Pi)).a[2]); a[4] := evalf(RotZ(20*((1/180)*Pi)).a[3]); a[5] := evalf(RotZ(100*((1/180)*Pi)).a[4]); a[6] := evalf(RotZ(20*((1/180)*Pi)).a[5])

b[1] := evalf(.7*RotZ(-40*((1/180)*Pi)).a[1]); b[2] := evalf(RotZ(100*Pi*(1/180)).b[1]); b[3] := evalf(RotZ(20*Pi*(1/180)).b[2]); b[4] := evalf(RotZ(100*Pi*(1/180)).b[3]); b[5] := evalf(RotZ(20*Pi*(1/180)).b[4]); b[6] := evalf(RotZ(100*Pi*(1/180)).b[5])

Zeroposn := Vector(3, [0, 0, 3])

Tx := Vector(3, [1, 0, 0]); Ty := Vector(3, [0, 1, 0]); Tz := Vector(3, [0, 0, 1])

``

``

NULL

Procedures

 

PlatPosn := proc (x := 0, y := 0, z := 0, alpha := 0, beta := 0, delta := 0) local i, v, Rot, L1, L2, L3, L4, L5, L6; global txn, tyn, tzn, ctrp; description "Calculates the platform position in the Global Coordinates, Unit normals and Leg Lengths"; v := Vector(3, [x, y, z]); ctrp := Zeroposn+v; Rot := Matrix(1 .. 3, 1 .. 3, {(1, 1) = cos(delta)*cos(beta), (1, 2) = -sin(delta)*cos(alpha)+cos(delta)*sin(beta)*sin(alpha), (1, 3) = sin(delta)*sin(alpha)+cos(delta)*sin(beta)*cos(alpha), (2, 1) = sin(delta)*cos(beta), (2, 2) = cos(delta)*cos(alpha)+sin(delta)*sin(beta)*sin(alpha), (2, 3) = -cos(delta)*sin(alpha)+sin(delta)*sin(beta)*cos(alpha), (3, 1) = -sin(beta), (3, 2) = cos(beta)*sin(alpha), (3, 3) = cos(beta)*cos(alpha)}, datatype = anything, storage = rectangular, order = Fortran_order, subtype = Matrix); for i to 6 do bn || i := Zeroposn+v+Rot.b[i] end do; txn := Rot.Tx; tyn := Rot.Ty; tzn := Rot.Tz; print(" Platform centre Global", ctrp); print(" Platform corner Co-ords Global", bn1, bn2, bn3, bn4, bn5, bn6); print("Platform Triad Vectors  ", "X green ", txn, "Y blue", tyn, "Z red ", tzn); L1 := sqrt((bn1-a[1])^%T.(bn1-a[1])); L2 := sqrt((bn2-a[2])^%T.(bn2-a[2])); L3 := sqrt((bn3-a[3])^%T.(bn3-a[3])); L4 := sqrt((bn4-a[4])^%T.(bn4-a[4])); L5 := sqrt((bn5-a[5])^%T.(bn5-a[5])); L6 := sqrt((bn6-a[6])^%T.(bn6-a[6])); print("Leg Lengths"); print("L1= ", L1); print("L2= ", L2); print("L3= ", L3); print("L4= ", L4); print("L5= ", L5); print("L6= ", L6) end proc

``

PlatPlot := proc () local Base, Platformdisplacement, picL1, picL2, picL3, picL4, picL5, picL6; global tx0, ty0, tz0; description "Displays the Hexapod"; Base := plots:-polygonplot3d(Matrix([a[1], a[2], a[3], a[4], a[5], a[6]], datatype = float), color = black, transparency = .5); Platformdisplacement := plots:-polygonplot3d(Matrix([seq(bn || i, i = 1 .. 6)]), color = cyan, transparency = .5); picL1 := plots:-arrow(a[1], bn || 1-a[1], colour = green); picL2 := plots:-arrow(a[2], bn || 2-a[2], colour = blue); picL3 := plots:-arrow(a[3], bn || 3-a[3], colour = blue); picL4 := plots:-arrow(a[4], bn || 4-a[4], colour = blue); picL5 := plots:-arrow(a[5], bn || 5-a[5], colour = blue); picL6 := plots:-arrow(a[6], bn || 6-a[6], colour = orange); tx0 := plots:-arrow(ctrp, txn, colour = green); ty0 := plots:-arrow(ctrp, tyn, colour = blue); tz0 := plots:-arrow(ctrp, tzn, colour = red); plots:-display(Base, picL1, picL2, picL3, picL4, picL5, picL6, Platformdisplacement, tx0, ty0, tz0, axes = box, labels = [X, Y, Z], scaling = constrained) end proc

``

NULL

``

``

PlatPosn()

"L6= ", 3.586394355

(1)

PlatPlot()

 

NULL

PlatPosn(.52, -.89, .7, .2, .67, .3)

"L6= ", 3.055217994

(2)

PlatPlot()

 

NULL

NULL

 

NULL

print('tzn' = LinearAlgebra:-CrossProduct(txn, tyn), `= `, tzn)

tzn = Vector[column](%id = 18446744074564617750), `= `, Vector[column](%id = 18446744074328082542)

(3)

``

``NULL

NULL

Rotation Matrices

NULL

``

 

RotZ := Matrix(3, 3, {(1, 1) = cos(delta), (1, 2) = -sin(delta), (1, 3) = 0, (2, 1) = sin(delta), (2, 2) = cos(delta), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1})

RotY := Matrix(3, 3, {(1, 1) = cos(beta), (1, 2) = 0, (1, 3) = sin(beta), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(beta), (3, 2) = 0, (3, 3) = cos(beta)})

RotX := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(alpha), (2, 3) = -sin(alpha), (3, 1) = 0, (3, 2) = sin(alpha), (3, 3) = cos(alpha)})

NULL

ROT := RotZ.RotY.RotX

Matrix(%id = 18446744074564619310)

(4)

``

``

``


 

Download Reverse_Kinematics_Stewart_Gough_Platform.mw

With this application the components of the acceleration can be calculated. The components of the acceleration in scalar and vector of the tangent and the normal. In addition to the curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanics, civilians and more.

In Spanish.

Kinematics_Curvilinear v18.mw

Kinematics_Curvilinear_updated_v2017.mw

Cinemática_en_Coordenadas_Polares_Cilindricas.mw

Kinematics_Curvilinear_updated_v2018.mw

Cinemática_de_una_partícula_nueva_sintaxis.mw

Lenin Araujo Castillo

Ambassador of Maple

 

 

Maple does not evaluate

>Re( (2-I*X)^4) ),  assuming((X, realcons)

or

>assume(X, realcons);

> Re( (2-I*X)^4) );

Why do these simple expression return unevealuated?

 

Hi,

I want to apply a rule to simplify an expression. The applyrule command works, when used directly in the worksheet. When I try to use the command within a procedure, Maple throws an error I cannot decipher:

Error, (in PatternMatching:-AlgStruct:-InsertPattern) first operand of `::' must be a name

 

Here is a full demonstration worksheet:

restart:

anexp:=abs(x)^2;

abs(x)^2

(1)

simplify(anexp);

abs(x)^2

(2)

rmabssq := proc(inexp)
description "removes the abs^2 construct in an expression":
local ruleabssqared1,ruleabssqared2,outexp:
    ruleabssqared1:= abs(''a''::algebraic)^2= ''a''^2:
    ruleabssqared2:= abs('expand'(-''a'')::algebraic)^2= ''a'':
    outexp:= applyrule([ruleabssqared1,ruleabssqared2],inexp):
    return outexp:
end proc;
 

proc (inexp) local ruleabssqared1, ruleabssqared2, outexp; description "removes the abs^2 construct in an expression"; ruleabssqared1 := abs(''a''::algebraic)^2 = ''a''^2; ruleabssqared2 := abs((('expand')(-''a''))::algebraic)^2 = ''a''; outexp := applyrule([ruleabssqared1, ruleabssqared2], inexp); return outexp end proc

(3)

## does not work :(
rmabssq(anexp);

Error, (in PatternMatching:-AlgStruct:-InsertPattern) first operand of `::' must be a name

 

## works!
ruleabssqared1:= abs(''a''::algebraic)^2= ''a''^2:
ruleabssqared2:= abs('expand'(-''a'')::algebraic)^2= ''a'':
newexp:= applyrule([ruleabssqared1,ruleabssqared2],anexp);

x^2

(4)

 


 

Download applyrule_4.mw

Thanks for your help

[[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]];
  [[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]]
data1 := [[1000, 20], [2000, 21], [3000, 32], [4000, 23], [5000, 23]]; 'data1';
                             data1
a*x^3+b*x^2+c*x+d;
                        3      2          
                     a x  + b x  + c x + d
x;
                               x
Equn1 := CurveFitting[LeastSquares]([[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]], x, curve = a*x^3+b*x^2+c*x+d);
plot(Equn1,x= 1000..5000)


 

Least Squares Approximation

 

 

Calculate a least squares approximation using specified data points.

 

 

Theoretical Curves for the Two-Stroke Engines and Four-Stroke Engines Brake Power Vs Brake Efficiency

List of Data Points:

[[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]]

[[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]]

(1)

data1 := [[1000, 20], [2000, 21], [3000, 32], [4000, 23], [5000, 23]]; 'data1'

data1

(2)

Fitting Curve:

a*x^3+b*x^2+c*x+d

a*x^3+b*x^2+c*x+d

(3)

Independent Variable:

x

x

(4)

Least Squares Curve:

Equn1 := CurveFitting[LeastSquares]([[1000, 20], [2000, 25], [3000, 24], [4000, 23], [5000, 24]], x, curve = a*x^3+b*x^2+c*x+d)

plot(Equn1,x= 1000..5000)

 

 

 

 

NULL

Equn1

31/5+(83/4200)*x-(23/3500000)*x^2+(1/1500000000)*x^3

(5)

 

 

Least Squares Fit of Data by a Specified Curve

List of Data Points:

[[3, -1], [5, 3], [6, -7], [7, 5], [9, -2]]

[[3, -1], [5, 3], [6, -7], [7, 5], [9, -2]]

(6)

Fitting Curve:

a*x^2+b*x+c

a*x^2+b*x+c

(7)

Independent Variable:

x

x

(8)

Least Squares Curve:

CurveFitting[LeastSquares]([[3, -1], [5, 3], [6, -7], [7, 5], [9, -2]], x, curve = a*x^2+b*x+c)

-901/210+(213/140)*x-(11/84)*x^2

(9)
 

 

a*x^2+b*x+c

a*x^2+b*x+c

(10)

plot(sin(x), x = 0 .. 4*Pi)

 

``


 

Download LeastSquareApproximation_2nd_and_3rd_Order.mw

The above command plots one curve alright. I want four such curves to go in the same figure using command like

plot(Equn1,Equn2,Equn3,Equn4,view(x=1000..5000)

I am not getting by the above command what I want. Can any one help. A shortcut method is required for me to repeat many times.

Thanks for help.

Ramakrishnav V
 

First at all, congratulation for the new update Maple 2017!!.                                        I'm a personal developer about renewable energy hybrid systems models. It is possible get data about irradiance or wind speed from the new world maps?. It will be very interesting!!!                                                                                   Thanks!!!!

Maple 2017 has launched!

Maple 2017 is the result of hard work by an enthusiastic team of developers and mathematicians.

As ever, we’re guided by you, our users. Many of the new features are of a result of your feedback, while others are passion projects that we feel you will find value in.

Here’s a few of my favourite enhancements. There’s far more that’s new - see What’s New in Maple 2017 to learn more.

 

MapleCloud Package Manager

Since it was first introduced in Maple 14, the MapleCloud has made thousands of Maple documents and interactive applications available through a web interface.

Maple 2017 completely refreshes the MapleCloud experience. Allied with a new, crisp, interface, you can now download and install user-created packages.

Simply open the MapleCloud interface from within Maple, and a mouse click later, you see a list of user-created packages, continuously updated via the Internet. Two clicks later, you’ve downloaded and installed a package.

This completely bypasses the traditional process of searching for and downloading a package, copying to the right folder, and then modifying libname in Maple. That was a laborious process, and, unless I was motivated, stopped me from installing packages.

The MapleCloud hosts a growing number of packages.

Many regular visitors to MaplePrimes are already familiar with Sergey Moiseev’s DirectSearch package for optimization, equation solving and curve fitting.

My fellow product manager, @DSkoog has written a package for grouping data into similar clusters (called ClusterAnalysis on the Package Manager)

Here’s a sample from a package I hacked together for downloading maps images using the Google Maps API (it’s called Google Maps and Geocoding on the Package Manager).

You’ll also find user-developed packages for exploring AES-based encryption, orthogonal series expansions, building Maple shell scripts and more.

Simply by making the process of finding and installing packages trivially easy, we’ve opened up a new world of functionality to users.

Maple 2017 also offers a simple method for package authors to upload workbook-based packages to the MapleCloud.

We’re engaging with many package authors to add to the growing list of packages on the MapleCloud. We’d be interested in seeing your packages, too!

 

Advanced Math

We’re committed to continually improving the core symbolic math routines. Here area few examples of what to expect in Maple 2017.

Resulting from enhancements to the Risch algorithm, Maple 2017 now computes symbolic integrals that were previously intractable

Groeber:-Basis uses a new implementation of the FGLM algorithm. The example below runs about 200 times faster in Maple 2017.

gcdex now uses a sparse primitive polynomial remainder sequence together.  For sparse structured problems the new routine is orders of magnitude faster. The example below was previously intractable.

The asympt and limit commands can now handle asymptotic cases of the incomplete Γ function where both arguments tend to infinity and their quotient remains finite.

Among several improvements in mathematical functions, you can now calculate and manipulate the four multi-parameter Appell functions.

 

Appel functions are of increasing importance in quantum mechanics, molecular physics, and general relativity.

pdsolve has seen many enhancements. For example, you can tell Maple that a dependent variable is bounded. This has the potential of simplifying the form of a solution.

 

Plot Builder

Plotting is probably the most common application of Maple, and for many years, you’ve been able to create these plots without using commands, if you want to.  Now, the re-designed interactive Plot Builder makes this process easier and better.

When invoked by a context menu or command on an expression or function, a panel slides out from the right-hand side of the interface.

 

Generating and customizing plots takes a single mouse click. You alter plot types, change formatting options on the fly and more.

To help you better learn Maple syntax, you can also display the actual plot command.

Password Protected Content

You can distribute password-protected executable content. This feature uses the workbook file format introduced with Maple 2016.

You can lock down any worksheet in a Workbook. But from any other worksheet, you can send (author-specified) parameters into the locked worksheet, and extract (author-specified) results.

 

Plot Annotations

You can now get information to pop up when you hover over a point or a curve on a plot.

In this application, you see the location and magnitude of an earthquake when you hover over a point

Here’s a ternary diagram of the color of gold-silver-copper alloys. If you let your mouse hover over the points, you see the composition of the points

Plot annotations may seem like a small feature, but they add an extra layer of depth to your visualizations. I’ve started using them all the time!

 

Engineering Portal

In my experience, if you ask an engineer how they prefer to learn, the vast majority of them will say “show me an example”. The significantly updated Maple Portal for Engineers does just that, incorporating many more examples and sample applications.  In fact, it has a whole new Application Gallery containing dozens of applications that solve concrete problems from different branches of engineering while illustrating important Maple techniques.

Designed as a starting point for engineers using Maple, the Portal also includes information on math and programming, interface features for managing your projects, data analysis and visualization tools, working with physical and scientific data, and a variety of specialized topics.

 

Geographic Data

You can now generate and customize world maps. This for example, is a choropleth of European fertility rates (lighter colors indicate lower fertility rates)

You can plot great circles that show the shortest path between two locations, show varying levels of detail on the map, and even experiment with map projections.

A new geographic database contains over one million locations, cross-referenced with their longitude, latitude, political designation and population.

The database is tightly linked to the mapping tools. Here, we ask Maple to plot the location of country capitals with a population of greater than 8 million and a longitude lower than 30.

 

There’s much more to Maple 2017. It’s a deep, rich release that has something for everyone.

Visit What’s New in Maple 2017 to learn more.

When Maple 2017?. Are there anybody about the new features of this version?. I,m waiting for a special project.

hello dear,

I was intersted in finding Weyl scalars for a given metric, would be really helpful if anyone can give me an example of how to find a Weyl Scalar for a given metric or set of null tetrads using Debever formalism in Tensor package(more specifically, how to define h in debever formalism for a given set of null tetrad or for a given metric).

Regards,
Suresh

Just starting some work on numerical engineering solutions by going through a workbook, which includes a Maple Document on CD (with one index.mw and several .mws files).

As I don't have acces to a Maple system, I downloaded Maple Player. However - Maple Player will only accept .mw and .mwz files(at least that shows up on 'FILE>OPEN'); so trying to open an .mws file results in - NOTHING. In your forum I found some information that .mwz is a nonpublic Maple format !?...... Now I don't see a way to work with PLAYER. Isn't PLAYER meant for exactly that scenario - sharing MAPLE worksheets ?

So - what to do ?

Thanks for some hint,

GW.G

 

 

 

 

Hi,

Can anyone please suggest a way to set the zoom factor for a 3D plot from the plot commands or using DocumentTools or in some other way that doesn't involve the interactive tools?

What I'm trying to achieve is the following:

I'm developing MapleCloud worksheets for a course I'm teaching and want to give my students several 3D plots to interact with through their web browser.  When I make the plots, Maple determines the scaling so that boxed axes with labels will fit in the area of the plot component.  However, I'm making plots with axes=none that look better at a higher zoom factor (the corners of the unseen boxed axes would be out of the plot area but all the plot components still fit) and I'm keen to create the plots that look like this if possible.

My ideal solution would be for there to be a zoomfactor option for the plots[display] command or to be able to use some code like SetProperty("Plot0",zoomfactor,1.25) but I haven't been able to find a way to achieve this.  The closest I found was setting the viewpoint option, but that locked the view, preventing rotation, and I want to just set the initial view.  Is there some other method I haven't found?

Thank you for your help,

Alex

 

 

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