MaplePrimes Questions

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The prime notation as used default on my keyboard is not the same as used in Maple.
 

NULL

restart;

with(student):

interface(typesetting = extended);

extended

(1)

Typesetting:-Settings(typesetprime = true);

true

(2)

diff(y(x), x)

diff(y(x), x)

(3)

y*`\`   `and  diff(y(x), x)are not working on my keyboard as prime?

 prime symbols (not showed)  not as (3)

 ========================================

restart

kernelopts(version)

`Maple 2021.1, X86 64 LINUX, May 19 2021, Build ID 1539851`

(4)

interface(typesetting = extended)

diff(y(x), x)

diff(y(x), x)

(5)

Typesetting:-Settings(typesetprime = true)

diff(y(x), x)

diff(y(x), x)

(6)

"y^((3))"

diff(diff(diff(y(x), x), x), x)

(7)

PDEtools:-declare(y(x))

y(x)*`will now be displayed as`*y

(8)

diff(y(x), x)

diff(y(x), x)

(9)

"y^((3))"

diff(diff(diff(y(x), x), x), x)

(10)

PDEtools:-declare(f(x, y))

f(x, y)*`will now be displayed as`*f

(11)

diff(f(x, y), y, x, y)

diff(diff(diff(f(x, y), x), y), y)

(12)

=================================================

Application Differential equation :  

int((10000*k/(100*k*P(t) - 1) - 100/P(t))*diff(P(t), t), t = 0 .. t) = t;

int((10000*k/(100*k*P(t)-1)-100/P(t))*(diff(P(t), t)), t = 0 .. t) = t

(13)

P(t)=solve(%,P(t));

Error, (in solve) cannot solve expressions with diff(P(t), t) for P(t)

 

This error .. see  Applications to Differential Equations

Applications to Differential Equations

   

 

NULL


 

Download vraag_over_dv_in_harald_pleym_-error_.mw

 

Also a error in old studymaterial : how to be fixed ? ...or obselote now this calculation and must be replaced for a modern calculation in Maple ?

 

question8.mw

In the exercise uploaded I have to plot asymptotes of a function. I know this is possible using definitions of all kind of asymptotes and ploting in a figure. However I would like to know if exists some parameter for plot method that automatically show asymptotes.

question7.mw

NULL

***e2.106

 

Plot this couple of parametric equations, identify the geometric figure known as the folium of Descartes , and relate properties of the figure to numerical coefficients in the equations.

  x = 3*t/(t^3+1), y = 3*t^2/(t^3+1)   

NULL

restart: with(plots):

 

 

 

See how the plot of the folium of Descartes can be built with the following code:

d1 :=

Error, invalid terms in product: -10 .. 10

Error, invalid terms in product: -10 .. 10

Error, (in plots:-pointplot) points cannot be converted to floating-point values

NULL

NULL

Download question7.mw

For this question I need that who help me focus in second block of code in the document. Basically, what I am trying is to get a plot of folium of Dercastes using parametric equation to plot ordered pairs. In order to success, is needed to exclude t=-1. In the block is showed what I tried. I concluded that my approach in solving that part of exercise is wrong. What could be a well approach?

I have to do this  diff(f(x), x) = f(1/x), f(0) = 0 , but it gives me the error on solution := dsolve(equations) :Error, (in dsolve) found the indeterminate function f with different arguments {f(x), f(1/x)} and I know what to do, please help me

Thought always that the round d is reserved for function of two variables x,y , but  that seems to be not the case here ?

restart;

Comparing Different Answers

 

Een antwoord ergens gegeven is

Int(sqrt(x^2+1), x) = (1/2)*x*sqrt(x^2+1)+(1/2)*ln(x+sqrt(x^2+1)) + C                                                             (vb)

 

Mple geeft

 

Int(sqrt(x^2+1),x)=int(sqrt(x^2+1),x)+C[1];

Int((x^2+1)^(1/2), x) = (1/2)*x*(x^2+1)^(1/2)+(1/2)*arcsinh(x)+C[1]

(1)

 

De twee antwoorden lijken nog niet opelkaar !
In het gegeven antwoord staat er een ln en in Maple kan een expressie omgezet worden in ln termen
  

convert(%,ln);

Int((x^2+1)^(1/2), x) = (1/2)*x*(x^2+1)^(1/2)+(1/2)*ln(x+(x^2+1)^(1/2))+C[1]

(2)

(2)  is hetzelfde (vb)

Dezelfde integraal i sook gegeven als

Int(sqrt(x^2+1),x)=((x+sqrt(x^2+1))^2+4*ln(x+sqrt(x^2+1))-(x+sqrt(x^2+1))^(-2))/8+C[2];

Int((x^2+1)^(1/2), x) = (1/8)*(x+(x^2+1)^(1/2))^2+(1/2)*ln(x+(x^2+1)^(1/2))-(1/8)/(x+(x^2+1)^(1/2))^2+C[2]

(3)

Controle

een effectieve manier om twe antwoorden t evergelijken voor hetzelfde probleem is het verschil te berekenen van een vergelijking met de twee integralen

#lhs(%);

#rhs(%%);

 

#diff(lhs(%)-rhs(%)=0,x);

NULL

#diff(f,x);

diff(lhs(%)-rhs(%)=0,x);

(x^2+1)^(1/2)-(1/4)*(x+(x^2+1)^(1/2))*(1+x/(x^2+1)^(1/2))-(1/2)*(1+x/(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))-(1/4)*(1+x/(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))^3 = 0

(4)

simplify(%);

0 = 0

(5)

Strange that  diff(lhs(%)-rhs(%)=0,x);  is translated by 2 d input with round d notation for functions with two variables ?
The two integrals are functions of one variable
diff(f, x)

Download Controleren_dezelfde_antwoord_voo_expressies.mw

Here is a problem that I recently had to solve and I really liked it. I recommend it to all Maple fans:

"The contour of the Christmas tree on the occasion of the New Year 2022 is a triangle, which is divided into 7 small triangles, the bases of which are parallel. The areas of triangles and the star are measured in snowflakes, the values of which are presented on the balls (of course, the number of snowflakes must be integer). It is necessary to determine the areas of triangles, on the balls of which there are no numbers".

At first glance it seems that the area of the star is not related to the problem, but it is not. This will become clear only after the problem is solved.

                          alt text


 

Hi! I want to make animation from the sequence below to download but it's not working I mean that it's ok when I want to see animation on display but it cannot be seen as something like "display(seq(...,a=1..100),insequence=true)" which is easy to export

restart;
with(Fractals:-EscapeTime);
with(ImageTools);
with(plots);
M := seq(Mandelbrot(500, -0.17225 - evalf(a/100000) + (0.660347 + evalf(a/100000))*I, -0.17115 - evalf(a/100000) + (0.66116 + evalf(a/100000))*I, iterationlimit = 3000, output = layer1, cutoff = 10000), a = 1 .. 100);
seq([Embed(M[j])], j = 1 .. 100);

How to insert icons in a plot at given coordinates as shown below:
 

question6.mw
How you can see, in the following exercise I built five plots, every one with the graph of two functions. The exersise say that I must find coordinates of any intersection. I think I can do it with solve command. However, I want point out coordinates of  intersections inside the plots. Probably exists a command or a parameter to success with my objetive. How can I do it?

NULL

*** e2.103

 

Plot the following couples of formulae; note in particular the contrasting forms of two curves in each case, and find the coordinates of any intersections.

i)    {x, x^3},

ii)    {x^2, x^4},

iii)    {1/x, 1/x^2},

 iv)   {x^2, sqrt(x)},

 v)   {x^3, abs(x^(1/3))}

 

restart:

NULL

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student at University of Costa Rica;

Download question6.mw

restart:

``

K__vxa[1] := 2.0154553049*10^17

0.2015455305e18

(1)

`#mrow(mi("\`K__vxa\`"),mfenced(mn("1"),open = "[",close = "]"))`+K__vxa[1]

`#mrow(msub(mi("\`K"),mi("vxa\`")),mfenced(mn("1"),open = "[",close = "]"))`+0.2015455305e18

(2)

``

Download Prj.mw

(Maple 2015)

Why is m1(t) not evaluated correctly when I use a compound condition?

restart:
m2(t) = piecewise(x1(t) < c and v1(t) < 0, 1,  0);
       m2(t) = piecewise(x1(t) < e2 and v1(t) < 0, 1, 0)

m1(t) = piecewise(x1(t) = c and v1(t) > 0, 0,  1);
                           m1(t) = 1

This doesn't happen for simple conditions
 

m2(t) = piecewise(x1(t) < c, 1,  0);
m1(t) = piecewise(x1(t) = c, 0,  1);
               m2(t) = piecewise(x1(t) < c, 1, 0)
               m1(t) = piecewise(x1(t) = c, 0, 1)

TIA

In Matlab I can copy a Figure as a vector graphic and paste it into Adobe Illustrator, where it is perfectly scalable and it can be exported as a say 100cm by 100cm 300 DPI jpg file.

In Maple I struggle to produce similar quality files

Thanks,

Peter

question5.mw

In document uploaded I tried to write a code to get as output 11 plots. I would like a format as this: 9 plots in 3 columns an 3 rows, and a fourth row with two center plots. To explain me better, I drew a rustic sketch of what I want, basically something like this:

However I tried but I fail and my output is horrible. So, I want to ask: Does exists some option to the plot[display] command or should I try another aproach?

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student.

As part of my course work I've encountered a block wherein I need to convert a 4th order TF to a SmithForm but am unable to do so.

Can anyone help me with the code as attatched.

A := Matrix([[(.3384*x^3-26.13*x^2-.3659*x+0.1678e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (.4755*s^3-25.3*s^2-51.36*s-1.387)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)], [(-.3349*s^3+18.21*s^2+.3487*s-0.5939e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (-.3107*s^3+17.81*s^2+35.49*s+1.027)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)]])

Matrix(%id = 36893488152131246308)

(1)

"->"

Error, (in gcdex) invalid arguments

 

"->"

SmithForm(Matrix(%id = 36893488152131266788))``

(2)

with(LinearAlgebra)

NULL

S := SmithForm(A, s)

Error, (in gcdex) invalid arguments

 

with(LinearAlgebra); A := Matrix([[1, 2*x, 2*x^2+2*x], [1, 6*x, 6*x^2+6*x], [1, 3, x]])

Matrix(%id = 36893488152361731844)

(3)

S := SmithForm(A, x)

Matrix(%id = 36893488152348668020)

(4)

NULL

Download SmithForm.mw

Hello!

how to find the solutions of a system of recursive equations? And the plot too.

I tried but...

B := rsolve({a(0) = 0, a(i) = (1 + 10^(-5)*(0.01*(i - 1) - 0.007)/0.0001)*a(i - 1) + 0.1*10^(-5)*c(i - 1), c(0) = 0, c(i) = 0.01*10^(-5)*(i - 1)/0.0001*a(i - 1) + (1 - 10^(-5))*0.1*c(i - 1)}, {a(i), c(i)}, 'genfunc'(t));
B := rsolve({a(i) = (0.9983000000 + 0.001000000000 i) a(i - 1)

   + 0.000001000000000 c(i - 1), 

  c(i) = 0.001000000000 (i - 1) a(i - 1) + 0.09999900000 c(i - 1)

  }, {a(i), c(i)}, genfunc(t))

rsolve_for_system_of_recursive_equations.mw

thanks

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