Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

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

 

The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

It prints quite well (with proper equipment).  I wish you all the best for 2022.

 

(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

This is a simple problem of Chemistry. I solved the exercise, but there are three aspects I don't like about output:
1) Even kg*m2 *s-2 = J (SI unit to energy) and both are correct, one must be explicit with units in order to be totally clear, so I need an output with units of J/mol and not kg*m2 *s-2 mol-1.
2) I had to hardcode number of significant figures, so I had to analize quantitys in order to determine this number, wich as you can see, is three. I think Maple can compute significant figures automatically, but I could not find the command in documentation and even in this case is not totally needed, I would like to learn how do it because it could be very useful for more complex expressions.
3) Finally, output must be expressed using scientific notation, it's say enthalpy = 10.4*104 J/mol.
Therefore: How can I get adecuate output?
Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Sallas;
Chemist;
Postgraduate student. question4.mw

*** e1.501

 

Using this equation attributed to Clausius and Clapeyron,

ln(P[2]/P[1]) = Delta*H[vap]/R 1/T[1]-1/T[2]

and these data for the vapour pressure of liquid mercury at the indicated temperatures,

      P =  1.6 10^(-4) Pa at T = 273.15 K and P = 36.4 Pa at T = 373.15 K

estimate the enthalpy change Delta*H[vap] for vapourization of mercury over this range of temperature.

 

p := [1.6e-4*Unit('Pa'), 36.4*Unit('Pa')]:

Delta(H[vap]) = 0.105e6*Units:-Unit(m^2*kg/(s^2*mol*K))*Units:-Unit(K)

``

Download question4.mw

system_of_PDE.mw

NULL

NULL

Digits := 30; with(PDEtools); with(plots); Ops1 := numpoints = 100; Ops2 := color = magenta; Ops3 := color = blue; Ops4 := color = "BlueViolet"; Ops5 := axes = boxed, shading = zhue, orientation = [40, 50]; a := 0; b := 1; Tf := .5

axes = boxed, shading = zhue, orientation = [40, 50]

 

.5

(1)

E := 1480

1480

(2)

Ebes := 5990

5990

(3)

n0 := 900000

900000

(4)

ro := 1200

1200

(5)

m := 12.6

12.6

(6)

f := sig(x, t)-Ebes*`&varepsilon;ij`(x, t)

sig(x, t)-5990*`&varepsilon;ij`(x, t)

(7)

n := 900000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)

900000*exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(8)

NULL

P := 5

5

(9)

w := 4

4

(10)

k := 7

7

(11)

i := 5

5

(12)

eq1 := diff(sig(x, t), x, x) = ro*(diff(sig(x, t), x, x))/E+ro*(diff(sig(x, t), t)-Ebes*f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)))*(1+f/m)/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(13)

 

eq2 := diff(`&varepsilon;ij`(x, t), t) = f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(14)

NULL

sys := {eq1, eq2}

{diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)), diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))}

(15)

NULL

IBC1 := {sig(0, t) = P*sin(w*k*i), sig(10, t) = P*sin(w*k*i), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

{sig(0, t) = 5*sin(140), sig(10, t) = 5*sin(140), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

(16)

S := 1/100; Ops := spacestep = S, timestep = S; Sol1 := pdsolve(sys, IBC1, [sig, `&varepsilon;ij`], numeric, time = t, range = a .. b, Ops)

1/100

 

spacestep = 1/100, timestep = 1/100

 

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

 

``

Download system_of_PDE.mw

Sometimes its easier when doing math in maple input mode to use first the 2d maple input mode and convert this to maple input
Is there a hotkey assigned in Maple to do this toggling from 1d input to 2d input ( also from 1d output to 2d output  )

Now it must be done by mouse

In relation with the following code and its respective output:

I want get an output in wicht left side of equalitys be expressed in radical terms and not in terms of trigonometric expressions. I tried convert(expr, radical), but the result is not that I want. Could someone help me please? Also I want to know if exists a method to avoid hardcoding list of the forloop other than [seq(i, i = 1..5)];

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

Do someone tell me how can I solve this exersise using a created procedure? Also I would like to know if using a procedure is useful and if in that form code lines will be reduce. If procedures are not useful. What is the best aproach?

Here the exercise and the code:

Before to begin to learn Maple, I used to do math with python. I usually built function and classes in order to reduce code lines and to generalize the problem, but I don't know if this aproach is useful with Maple. In fact, I have another question. Is it possible to write in a document some codeblocks using Maple and another using python? If answer is yes, how can I do it?

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

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