Maple 2015 Questions and Posts

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

The initial conditions are U[13.75]=0.7787 and U'[13.75]=0.344037

Hi everybody,

I use the Grid package to do intensive computations.

For some reason I'm ignorant about, the test case described in the Grid[Server][StartServer] 

 help page doesn't work with Maple 2015 (neither on Mac OS X, neither on Windows 7 ; here is the mw file run on MAC Os X)

Could someone explain me why (probably something I did not read with enough attention ... some license maybe) ?
Thanks in advance

GridServer.mw

Hello
I try to reproduce in Maple this document in pdf. In it you can see the code in MathCad to find the roots of a system of equations by the method of Draghilev.
After seeing some of the codes posted in the Maple forum where the development of the method is shown and reading the document in the Application Center, some questions arise.
When the deferential ecacuion system is divided, in this case stored in variale b [i], by b [i] / (b [1] ^ 2 + b [2] ^ 2) ^ 0.5; i = 1..n + 1
Why, as I could see in some systems, the first two differential equations are taken and in others it takes three?
And in what systems does it divide at all?

https://www.mapleprimes.com/view.aspx?sf=223821_question/Draghilev

 

In this case in my transfer of code from Mathcad to Maple I do not get the initial values of the system fsolve calculates indefinitely

sistema9.mw

 

Hello,

I'm trying to evaluate an integral (code snippet and screen-shot included below) assuming that certain parameters and integers. Using assume statements the integral evaluates to 0. However, if I evaluate the integral for a specific set of integers, the integral evaluates as non-zero.

Can anyone clarify why the two int statements return different values?

Thanks!

assume(K::integer);
assume(L::integer);
assume(M::integer);
int(sin(K*x)*sin(L*x)*cos(M*x), x = 0 .. Pi);
     returns: 0
int(sin(14*x)*sin(2*x)*cos(12*x), x = 0 .. Pi);
     returns: Pi/4

How do you way text below

Maple 2015 

if i use function cat() is not 

 

The attached worksheet performs two functions:

(1) It lets me print 4 × 6 Index Cards for the short entries in each table.

(2) It allows for easy storage and retrieval of syntax (code).

The worksheet has many tables, each separated by a Page Break.

Questions:

(a) Is there a way to sort all the different tables so they will be arranged in alphebetical order?

(b) When I select one table to print and open the Print Dialog, the "Selection" option is grayed out. (see graphic below).  (1) Is there a way to enable the selection option?  (2) Is there a way to determine what page I am on so I can use the "Pages from...to" option?  If I need to number the pages, will the page numbers reset to parallel a new alphabetic sort order.

Many thanks in advance.  See WC29_4_BY_6_NOTE_CARDS_UNSORTED.mw attached. And see image of Print Dialog below.

Les

Dears 

Hope you all are fine. I want to solve the following nonlinear system ODEs numerically

Eq1 := diff(F(eta), eta, eta, eta)-phi1*((diff(F(eta), eta))^2-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(F(eta), eta, eta)))+alpha*(1-phi)^2.5*((diff(F(eta), eta, eta))^2+2*(diff(F(eta), eta))*(diff(F(eta), eta, eta))-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(F(eta), eta, eta, eta, eta))+A*(2*(diff(F(eta), eta, eta, eta))+(1/2)*eta*(diff(F(eta), eta, eta, eta, eta))))-A*phi1*(diff(F(eta), eta)+(1/2)*eta*(diff(F(eta), eta, eta))) = 0; Eq2 := diff(G(eta), eta, eta, eta)-phi1*((diff(G(eta), eta))^2-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(G(eta), eta, eta)))+alpha*(1-phi)^2.5*((diff(G(eta), eta, eta))^2+2*(diff(G(eta), eta))*(diff(G(eta), eta, eta))-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(G(eta), eta, eta, eta, eta))+A*(2*(diff(G(eta), eta, eta, eta))+(1/2)*eta*(diff(G(eta), eta, eta, eta, eta))))-A*phi1*(diff(F(eta), eta)+(1/2)*eta*(diff(F(eta), eta, eta))) = 0;

assoicated with the following BCs

F(0)=0,D(F)(0)=1,G(0)=0,D(G)(0)=p, D(F)(L)=0, D( G(L)=0;

for phi1 := 1.2; alpha := 2; A := 1.5;phi:=0.1;

Please help me to find the solution

Special request to @acer@Carl Love @Preben Alsholm

can result ?

Please help me?

Hi,

I am a little bit surprised by the result of the operation evalf[8](f(y)) in the piece of code that follows.
I was expected the answer to be 2.4494897, not 2.4494898.

Happily the sequence
res := f(y) ; evalf[8](res)
returns the expected result 2.4494897

I suspect the difference comes from some precedence of the operators (f and evalf) but I can't figure out what really happens

Could you enlight me please ?

Thanks in advance

 

restart:

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

Digits;

10

(2)

f := x -> sqrt(2.0)*x;

proc (x) options operator, arrow; sqrt(2.0)*x end proc

(3)

y := sqrt(3.0):

f(y);

2.449489743

(4)

evalf[9](f(y));  # right

2.44948974

(5)

evalf[8](f(y));  # ????

2.4494898

(6)

res := f(y);
evalf[8](res);  # right

2.449489743

 

2.4494897

(7)

 

 

 

with maple

How can in maple 2015? Help me?

hi everyone,

i have attached a maple worksheet which you can see the issue...azido_displacement.mw
i think tittle says by itself... thanks in advance for taking the time to review and aswer me.

 

theta__o := (1/4)*Pi

(1/4)*Pi

(1)

omega__o := 0

0

(2)

tau := 1

1

(3)

m := 2.28335

2.28335

(4)

g := 9.80665

9.80665

(5)

L := .35

.35

(6)

Iota := 0.9996799726e-1

0.9996799726e-1

(7)

with(DirectSearch)

[BoundedObjective, CompromiseProgramming, DataFit, ExponentialWeightedSum, GlobalOptima, GlobalSearch, Minimax, ModifiedTchebycheff, Search, SolveEquations, WeightedProduct, WeightedSum]

(8)

SolveEquations([omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau+(1/3)*alpha__3*tau = 0, theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau)*tau-(1/2)*alpha__2*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau)*tau+(1/2)*alpha__3*((1/3)*tau)^2 = (1/2)*Pi, int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. (1/3)*tau)+int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)-alpha__2*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)), t = 0 .. (1/3)*tau)+int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau)*tau-(1/2)*alpha__2*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau)*t+(1/2)*alpha__3*t^2)+alpha__3*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau)*tau-(1/2)*alpha__2*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau)*t+(1/2)*alpha__3*t^2)), t = 0 .. (1/3)*tau) = 0], initialpoint = [alpha__1 = 12.7751705882228, alpha__2 = 18.4817577058678, alpha__3 = 5.70658711764534])

[6.74607137501932*10^(-24), Vector(3, {(1) = HFloat(1.936228954946273e-13), (2) = HFloat(2.027322754116767e-12), (3) = 0.1612e-11}), [`#msub(mi("α",fontstyle = "normal"),mi("1"))` = 14.7208062595154, `#msub(mi("α",fontstyle = "normal"),mi("2"))` = 22.3730290484357, `#msub(mi("α",fontstyle = "normal"),mi("3"))` = 7.65222278892092], 139]

(9)

alpha__1 := 14.7208062595154

14.7208062595154

(10)

alpha__2 := 22.3730290484357

22.3730290484357

(11)

alpha__3 := 7.65222278892092

7.65222278892092

(12)

x__1 := int(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. t), t = 0 .. t2)

int(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. t), t = 0 .. t2)

(13)

x__2 := int(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. t), t = 0 .. (1/3)*tau)+t2*(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. (1/3)*tau))+int(int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)-alpha__2*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)), t = 0 .. t), t = 0 .. t2)

int(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. t), t = 0 .. 1/3)+t2*(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. 1/3))+int(int(-.4379530076*(22.39201428*cos(-1.603220734-4.906935420*t+11.18651452*t^2)-20.11649647)/sin(-1.603220734-4.906935420*t+11.18651452*t^2), t = 0 .. t), t = 0 .. t2)

(14)

x__3 := int(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. t), t = 0 .. (1/3)*tau)+(1/3)*tau*(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. (1/3)*tau))+int(int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)-alpha__2*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)), t = 0 .. t), t = 0 .. (1/3)*tau)+t2*(int((m*g*cos(omega__o*t+theta__o+(1/2)*alpha__1*t^2)+alpha__1*(L*m+Iota))/(m*sin(omega__o*t+theta__o+(1/2)*alpha__1*t^2)), t = 0 .. (1/3)*tau)+int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)-alpha__2*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau)*t-(1/2)*alpha__2*t^2)), t = 0 .. (1/3)*tau))+int(int((m*g*cos(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau)*tau-(1/2)*alpha__2*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau)*t+(1/2)*alpha__3*t^2)+alpha__3*(L*m+Iota))/(m*sin(theta__o+(1/3)*omega__o*tau+(1/2)*alpha__1*((1/3)*tau)^2+(1/3)*(omega__o+(1/3)*alpha__1*tau)*tau-(1/2)*alpha__2*((1/3)*tau)^2+(omega__o+(1/3)*alpha__1*tau-(1/3)*alpha__2*tau)*t+(1/2)*alpha__3*t^2)), t = 0 .. t), t = 0 .. t2)

int(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. t), t = 0 .. 1/3)+(1/3)*(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. 1/3))+int(int(-.4379530076*(22.39201428*cos(-1.603220734-4.906935420*t+11.18651452*t^2)-20.11649647)/sin(-1.603220734-4.906935420*t+11.18651452*t^2), t = 0 .. t), t = 0 .. 1/3)+t2*(int(.4379530076*(22.39201428*cos((1/4)*Pi+7.360403130*t^2)+13.23607306)/sin((1/4)*Pi+7.360403130*t^2), t = 0 .. 1/3)+int(-.4379530076*(22.39201428*cos(-1.603220734-4.906935420*t+11.18651452*t^2)-20.11649647)/sin(-1.603220734-4.906935420*t+11.18651452*t^2), t = 0 .. 1/3))+int(int(.4379530076*(22.39201428*cos(1.995919816-2.550740930*t+3.826111394*t^2)+6.880423404)/sin(1.995919816-2.550740930*t+3.826111394*t^2), t = 0 .. t), t = 0 .. t2)

(15)

plot([x__1, x__2, x__3], t2 = 0 .. (1/3)*tau)

 

``


 

Download azido_displacement.mw

 

Could someone help me with the following.  The syntax produces an unfinished graph with a warning.

> with(plots);
> z := polar(1.05, (1/10)*Pi);
                             
> display(polarplot(1, color = grey, axis[radial] = [color = "Blue"]), complexplot(seq(evalc(z))^n,
n = 1 .. 21));

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

the graphic looks like this

The graphic should look like this

Thanks, any help appreciated.

Les

 

Hellow dears!!!

Hope everyone is fine with everything. I want the animation of the numerical solution of ODE i,e., f4 for delta=[0,1.5]. Please see the attachment and fix my problem. I Shall be very thankful to you.

Graph.mw

Special request to  acer 13834@Carl Love ,Preben Alsholm 10271

Irrational numbers: numbers that cannot be represented as a ratio of integers. The decimal form of a rational number is non-repeating and non-terminating.

Change to:

Irrational numbers: numbers that cannot be represented as a ratio of integers. The decimal form of an irrational number is non-repeating and non-terminating. 

or change to

Irrational numbers can be represented by decimal fractions in which the digits go on forever without ever repeating a pattern.  See Downing, Douglas. Dictionary of Mathematics Terms. 2nd ed. Hauppauge, NY: Barron's Ed. Series, Inc., 1995, p. 176).

It is a truth universally acknowledged, that a single man in possession of an algorithm for calculating a Groebner basis, must be in want of an algorthim for calculating a reduced Groebner basis.

It seems odd that i can't find something in the Groebner package - if there isn't something there, I assume that there is a well known piece of code for doing this!

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