Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello everybody. Ive got some questions. 

As the title states: Draining a shaped container from the top, and the amount of Joule it takes to do it. That is what the questions are about. 

I did make the first one, and some attempts at the sphere questions b, and c. I left them out because i want to see what you guys come up with. I think ive got the right answers, but we will see if our answers compare. :) 

The Dutch text translated: Calculate in questions a, b, and c the amount of work (joule, J) it takes to drain a tank filled with water from the top with a pump. Each question has a discription of the shape of the tank. Take for gravity g=9.81m/s^2. For water take rho=1000kg/m^3.

a.
A coneshaped tank, the topangle is down, with a height of 2.0meters and a radius of 0.5meters. 

b.
A sphere with a radius of 1.0meters.

c.
The lower half of a sphere with a radius 2.0meters. 

Greetings,

The Function. 

"f(x):=(Pi*(x/(4))^(2)*x)/(3)*9.81"

proc (x) options operator, arrow, function_assign; (1/48)*Pi*x^2*x*9.81 end proc

(1)

1000*(int(f(x), x = 0 .. 2))

2568.251995

(2)

``

Download Question_for_maple_primes_8.mw

In the code above expression #1 contains the term D(Phi)(X): how can I replace the "abstract" function Phi by a "specific" one  phi = k*X(t) ?

restart:
alias(X = X(t)):
alias(Phi=Phi(X(t))):
kin := 1/2*M*diff(X, t)^2 + 1/2*m*diff(Phi, t)^2;  #1

# attempt to replace Phi by phi=k*X(t))
alias(phi=k*X(t)):
eval(kin, Phi=phi);                                #2 ... I expected phi would replace Phi

The attached file  How_to_eval.mw contains a more detailed explanation and a more general situation.

Thanks in advance

Dear all

I would like to compute the monomial polynomial in taylor series, I tried 
f:=cos(t);

fn:=n->subs(diff(f(x),x$n),x=0)/factorial(n);
but it is does not work 
anay help please

   Is there a way to export routines from a package. The reason I ask, I was answering a question here and I needed two routines I have, that I put together a couple of years ago in a package. I used showstat copied, pasted and edited. Worked, but not great and would utterly fail with anything complicated. e.g. In the two routines pasted  below SignedArea on line 3 c[1]  is c   [1] that caused a minor problem.  

restart

NULL

"RonanRoutines:-SignedArea := proc(a::{Vector, list}, b::{Vector, list}, c::{Vector, list, null} := null)  local M, A;     1   if c = null then     2       A := 1/2*a[1]*b[2]-1/2*a[2]*b[1]         else     3       A := 1/2*(b[2]-c[2])*a[1]+1/2*(-b[1]+c[1])*a[2]+1/2*c[2]*b[1]-1/2*c               [1]*b[2]         end if;     4   return A  end proc:"

NULLNULL

"RonanRoutines:-CrossingNumber := proc(A::list, B::list, C::list, E::list)  local s1, s2, s3, s4;     1   s1 := RonanRoutines:-SignedArea(A,B,C);     2   s2 := RonanRoutines:-SignedArea(A,B,E);     3   s3 := RonanRoutines:-SignedArea(C,E,B);     4   s4 := RonanRoutines:-SignedArea(C,E,A);     5   if s1 = 0 and s2 = 0 and s3 = 0 and s4 = 0 then     6       'undefined'         elif 0 <= signum(s1) and signum(s2) <= 0 then     7       if 0 <= signum(s3) and signum(s4) <= 0 then     8           -1             end if         elif signum(s1) <= 0 and 0 <= signum(s2) then     9       if signum(s3) <= 0 and 0 <= signum(s4) then    10           1             end if         else    11       0         end if  end proc:  "

NULL

Download Export_from_Package.mw

Hi,

Does anyone know how can I write this thing in a Maple script?
I have a problem with printing math expressions when there is an increment in the matrix power.

Please see attached.


 

with(plots); with(LinearAlgebra)

NULL

NULL

NULL

couples := [5, 0], [6, 0], [6, 3], [10, 3], [7, 5], [9, 5], [7, 7], [8, 7], [5.5, 9], [3, 7], [4, 7], [2, 5], [4, 5], [1, 3], [5, 3]

Points := Matrix([[5, 6, 6, 10, 7, 9, 7, 8, 5.5, 3, 4, 2, 4, 1, 5], [0, 0, 3, 3, 5, 5, 7, 7, 9, 7, 7, 5, 5, 3, 3]])

NULL

Homothety

 

W := Matrix(2, 2, {(1, 1) = (1/60)*k, (1, 2) = 0, (2, 1) = 0, (2, 2) = (1/60)*k})NULLNULL``NULLNULL

Rotation on x axis

 

NULL

X := Matrix(2, 2, {(1, 1) = cos((1/90)*Pi*k), (1, 2) = sin((1/90)*Pi*k), (2, 1) = sin((1/90)*Pi*k), (2, 2) = -cos((1/90)*Pi*k)})````NULLNULL

Rotation of angle k

 

Y := Matrix(2, 2, {(1, 1) = cos((1/180)*Pi*k), (1, 2) = -sin((1/180)*Pi*k), (2, 1) = sin((1/180)*Pi*k), (2, 2) = cos((1/180)*Pi*k)})NULLNULLNULL

``

n := Multiply(Y, Multiply(X, Multiply(W, Points)))

_rtable[18446746437110297774]

(3.1)

NouvCouples := seq([n[1, i], n[2, i]], i = 1 .. 15)

Sapin := animate(polygonplot, [[NouvCouples], color = "ForestGreen"], k = 0 .. 180)

 

 

NULL

Neige

 

PointsNeige := seq([-30+i, 30-(1/2)*j*sin(i+j)], i = 0 .. 60); neige := animate(pointplot, [[PointsNeige], color = black], j = 0 .. 60, view = [-30 .. 30, 0 .. 30])

 

NULL

display([Sapin, neige], scaling = constrained)

 

NULL

NULL


 

Download Homework.mw

 

Hi, i need some help for a homework.

Here is the statement

You must first animate a series of linear transformations on the polygon formed by the following couples: [5, 0], [6., 0], [6, 3], [10, 3], [7, 5], [9, 5], [7, 7], [8, 7], [5.5, 9], [3, 7], [4, 7], [2, 5], [4, 5], [1, 3], [5, 3] It will be necessary to make, at the same time, a rotation around a line making an angle k with the axis of x, a rotation of an angle k and a scaling of variable ratio (but equal to 3 at the end animation). The k animation parameter should range from 0 to 180. I suggest you use the color green for your polygon. Then you will need to create a second animation by entering these command lines: SnowPoints: = seq ([- 30 + i, 30 - j / 2 * sin (i + j)], i = 0 .. 60): snow: = animate (pointplot, [[PointsNeige], color = black], j = 0 .. 60, view = [-30 .. 30, 0 .. 30]) : Finally, you will have to roll both animations at the same time.

The GIF shows the results that I should get according to my teacher

Thanks for the help !

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

tahnk you for your help

Can Maple solve an ode by asymptotic expansions methods? series methods (power series or Frobenius series) work only on ordinary expansion point or removable singularity point. For non removable singularity (essential), Maple's dsolve with series method can't solve these. Also, if the RHS of the ode is not analytic at the expansion point, series method do not work. 

The asympt command only applies to algebraic expressions.

Does Maple have something similar to Mathematica's AsymptoticDSolveValue  ?

Here is an example. This is an ode with RHS not analytic (has no Taylor series) at x=0

ode:=diff(y(x),x)+y(x)=1/x;
dsolve(ode,y(x),'series',x=0)

No solution.  While in Mathematica

ode = y'[x] + y[x] == 1/x
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]

 

Here is another example of ode where the coefficient of y(x) is not analytic at x=0

ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
dsolve(ode,y(x),'series',x=0)

No solution. In Mathematica

ode = y'[x] + Sqrt[x] y[x] == 0
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]

Does there exist a package in Maple that can do this? Will this functionality be added in Maple in the future if currently there is no support? ( I searched and could not find anything so far).

One possible workaround I found is to solve the ODE using normal methods (non-series), then apply the asympt command on the solution. But one needs to remove the constant of integration first, Here is the above example done this way

ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
sol:=dsolve(ode);
Order:=8;
sol:=eval(sol,_C1=1);
asympt(eval(rhs(sol),x=1/y),y);
eval(%,y=1/x)

Mutliplying the above back by the constant _C1 gives same answer as Mathematica's.

Is the above how one is supposed to do it in Maple? It worked on the above simple example, but need to see if it will work for other examples. it will be better if this was more directly supported. i.e. if asympt will work directly on ode's (or a new command or a new option to dsolve similar to 'series' but call 'asympt').

Greetings!

For factorization and computing times purposes, I'd like Maple to not perform this automatic conversion.

whattype(a*b) gives whattype(a*b)

while whattype(a*a) gives whattype(a*a)

Alternatively, a way to factorize 6*x^2+a*x-10 into (a+6*x)*x-10 could do the trick.

Here's a list of the functions I've already tried:

  • factor
  • collect (so coeff too)
  • combine/expand

Any ideas?

Thank you!

Hi. I can't seem to get my Explore plot to work. Maple gives me a cryptic error message (IMHO).

Rectangle_within_circle_gen.mw

I want to simplify the following expression to 2a-2bk+k(n+6). But the following command is invalid.

algsubs(n2+n1=n+6,a+(n1-b)*k+a+(n2-b)*k);

 

However, the above expression can be simplified when k is fixed to a number, such as k=2.

algsubs(n2+n1=n+6,a+(n1-b)*2+a+(n2-b)*2);

I wonder what went wrong.

It seems to be recognized only if n1+ n2 is combined.

algsubs(n1+n2=n+6,simplify(a+(n1-b)*k+a+(n2-b)*k))

We’ve been busy! We have just released the 2021.2 updates for Maple, Maple Flow, and MapleSim. Here’s a quick overview. These updates are freely available to all customers who have the 2021 version of these products.

Maple

The Maple update includes a variety of corrections and improvements to the math engine and interface. It is available through Tools>Check for Updates in Maple, and is also available from the Maple 2021 download page, where you can also find more details.

In particular, this update includes fixes to the bug in the combine command when working with double summations, and the problems when performing context menu operations on values with units while in Document mode, both of which were reported on MaplePrimes. As always, we appreciate the feedback!

Maple Flow

The Maple Flow 2021.2 update offers a richer range of formatting features for creating professional-looking engineering documents, which have been requested by customers. Highlights include sections, controlling the display of commands, annotating images, and disabling automatic evaluation while making a series of changes.  This update is available from the Maple Flow 2021.2 download page, which also contains more details.

MapleSim

Lots of good stuff here that makes it easier to build and analyze models, including productivity features that speed up the creation of models that use hydraulics, support for the latest CAD file formats in the MapleSim CAD toolbox, the ability to model drift conditions with the MapleSim Tire Library, tools for simulating 3-D winding effects with the MapleSim Ropes and Pulleys Library, and a new MapleSim Web Handling Library add-on (which, I am sad to say, has nothing to do with Spiderman). See What’s New in MapleSim for details, and the MapleSim 2021.2 download page for instruction on how to obtain your update.

Error occurred running sample test.java (at new EngineCallBackDefault()):

# A fatal error has been detected by the Java Runtime Environment:
#
#  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x00007ffd66e7345a, pid=1740, tid=7716
#
# JRE version: Java(TM) SE Runtime Environment (11.0.1+13) (build 11.0.1+13-LTS)
# Java VM: Java HotSpot(TM) 64-Bit Server VM (11.0.1+13-LTS, mixed mode, tiered, compressed oops, g1 gc, windows-amd64)
# Problematic frame:
# C  [maplec.dll+0x345a]
#
# No core dump will be written. Minidumps are not enabled by default on client versions of Windows
#
# If you would like to submit a bug report, please visit:
#   http://bugreport.java.com/bugreport/crash.jsp
# The crash happened outside the Java Virtual Machine in native code.

Hello 

Imagine you have an irregular polygon as follows:

restart; with(plottools):with(plots):

display(polygon([[0,0],[200,0],[200,300],[250,400],[500,300],[500,500],[0,500]]),color=yellow,linestyle=solid,thickness=2);

with vertices that can be easily defined, and that you have an arbitrary point P(x,y) with coordinates of (x) and (y). I want Maple to check whether the point P(x,y) is inside or outside the polygon. In Matlab, the command (inpolygon) can be used for such a task. Is there a similar readily available command in Maple. 

Thank you very much for your help and support. 

 I can't seem to figure out how to use arctan on a complex number in Maple.  I expect arctan(a+jb) assuming a and b are real to return atan(b/a).  Instead, returns arctan(a+Ib).  How do I do this?

restart

````

assum := R1::real, C1::real, omega::real, vab::real

R1::real, C1::real, omega::real, vab::real

(1)

Pab := expand(rationalize(vab/(R1-I/(omega*C1))))``

vab*omega^2*C1^2*R1/(C1^2*R1^2*omega^2+1)+I*vab*omega*C1/(C1^2*R1^2*omega^2+1)

(2)

Pabmag := `assuming`([abs(Pab)], [assum])

(vab^2*omega^4*C1^4*R1^2/(C1^2*R1^2*omega^2+1)^2+vab^2*omega^2*C1^2/(C1^2*R1^2*omega^2+1)^2)^(1/2)

(3)

Pabang := `assuming`([arctan(Pab)], [assum])

arctan(vab*omega^2*C1^2*R1/(C1^2*R1^2*omega^2+1)+I*vab*omega*C1/(C1^2*R1^2*omega^2+1))

(4)

``

test out how to use arctan....

`assuming`([arctan(a+I*b)], [a::real, b::real])

arctan(a+I*b)

(5)

``

Download complex_power_RC.mw

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