How to get logarithm expression using Maple command?

For example, enter log[2](x^2-3x+5)+x^3-1-log[3](x-1)

Output [x^2-3x+5,x-1]

Thank you very much for your help.

Hallo every body 

How to add vector fields to the figure of this example of a three-dimensional differential system.

in maple 18

Porgram_of_corollary_1_in_Maple.mw

Download Porgram_of_corollary_1_in_Maple.mw

Hi,

I am trying to produce two statistical tables representing a weighted series in a horizontal manner (Tab1) and in a vertical manner (Tab0). The xi and ni in Tab1 do not display well... Perhaps, there is a simpler way to do this?S5S4BoxPlotPondération.mw

Hello, 

do you have an idea how could be filtered several values from dataframe? 
I have a dataframe called "TestData". I need to select rows from data frame which are equal to the list called "SelectionList". 

Thank you for a comment. 
 

Data:=<"LC1", "LC2", "LC3", "LC4", "LC5", "LC6", "LC7", "LC8", "LC9", "LC10", "LC11", "LC12", "LC13", "LC14", "LC15", "LC16", "LC17", "LC18", "LC19", "LC20">;
LoadValue2:=<10,15,100,82,18,89,25,84,46,18,79,12,0,28,147,15,86,444,18,65>;

TestData:=DataFrame(<Data|LoadValue2>,columns=[Case,Load]);

SelectionList:={"LC3", "LC4", "LC5", "LC6", "LC7", "LC8", "LC9"};

I want to place a grid on this drawing 16x7=112 small squares. Thank you.
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
unprotect(D);
point(A, 0, 0);
point(B, 8, 0);
point(C, 8, 1);
point(D, 16, 2);
point(E, 15, 5);
line(AD, [A, D]);
line(AE, [A, E]);
line(DE, [D, E]);
line(AB, [A, B]);
segment(s1, B, C);
segment(s2, B, A);
triangle(Tr, [A, D, E]);
alpha := FindAngle(AB, AD);
beta := FindAngle(AD, AE);
is(alpha + beta = arctan(1/3));
pl := plot(gridlines = true, title = "Dessin pour montrer que arctan(1/3)=arctan(1/5)+arctan(1/8)", titlefont = ["ROMAN", 20]);
display(textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"], [coordinates(D)[], "D"], [coordinates(E)[], "E"]], align = {"above", 'right'}), draw([A(color = black, symbol = solidcircle, symbolsize = 16), D(color = black, symbol = solidcircle, symbolsize = 16), E(color = black, symbol = solidcircle, symbolsize = 16), s1(color = blue), s2(color = blue), Tr(color = orange, filled = true, transparency = 0.9), Tr(color = blue)]), pl, gridlines = true, axes = none);

Dears, 

Can you look the code bellow and send me my error please? I used Maple 18.

restart;
with(plots);
theta(t) = 19.592+1.2697*cos(.5240*t+4.3391)-.6343*cos((2*.5240)*t-.6963);
omicron(t) = 99.4876+89.8581*cos(.5232*t+15.4500)+19.1069*sin((2*.5232)*t)-8.5891*cos((3*.5232)*t+3.7723)+6.4660*sin((5*.5232)*t);
`&varphi;`(theta):=0.000203*theta*(theta - 11.7)*sqrt(42.3-theta);
mu[v](theta,omicron):=0.0886*exp(((0.01*omicron +1.01*theta  -21.211)/(14.852))^(4));
p[0](theta):=(-0.153* theta*theta + 8.61*theta - 97)/(mu[v](theta,omicron)):
p[2](omicron):=(4*0.25)/(2500)*omicron*( 50 -omicron);
p[3](omicron):=(4*0.75)/(2500)*omicron*( 50 -omicron);
p[2](theta):=exp (0.06737 - 0.00554*theta);
theta[EA](theta):=1/(-0.00094*theta*theta + 0.049*theta - 0.552);
L[v](theta,omicron):=(3.375*(4*omicron*(50-omicron))^(3)*exp(0.0054*theta+0.6737))/(50^(6)*(2+(0.00554*theta-0.06737)^(-1)));
eta(theta,omicron):=(p[0](theta)*p[1](omicron)*p[2](omicron)*p[3](omicron)*p[2](theta))/(theta[EA](theta));
lambda[v] := beta[v]*`&varphi;`(theta)*i[v](t)/n[h](t);
lambda[h] := (beta[h]*`&varphi;`(theta)*i[h](t)+beta[h]*`&varphi;`(theta)*omega*r[h](t))/n[h](t);
n[v](t):=s[v](t)+i[v](t);
beta[h] := 0.9e-1; beta[v] := 0.2e-1; Lambda[h] := .50; sigma[1] := 0.15e-1; sigma[2] := 0.71e-1; Omega[h] := .50; mu[h] := 0.128e-1; delta[h] := .45; k[v] := .66; omega := .3; mu[d] := 0.14e-2;
sys := {diff(i[h](t), t) = Omega[h]+sigma[2]*r[h](t)+lambda[v]*s[h](t)-(delta[h]+mu[d]+mu[h])*i[h](t), diff(i[v](t), t) = lambda[h]*s[v](t)-mu[v](theta, omicron)*i[v](t), diff(j[v](t), t) = L[v](theta, omicron)*(1-j[v](t)/k[v])*n[v](t)-(eta(theta, omicron)+mu[j](theta, omicron))*j[v](t), diff(r[h](t), t) = delta[h]*i[h](t)-(sigma[1]+sigma[2]+mu[h])*r[h](t), diff(s[h](t), t) = Lambda[h]+sigma[1]*r[h](t)-(lambda[v]+mu[h])*s[h](t), diff(s[v](t), t) = eta(theta, omicron)*j[v](t)-(lambda[h]+mu[v](theta, omicron))*s[v](t), i[h](0) = 100, i[v](0) = 100, j[v](0) = 200, r[h](0) = 0, s[h](0) = 10000, s[v](0) = 5000};
p1 := dsolve(sys, numeric, method = rkf45, output = procedurelist);
Error, (in dsolve/numeric/process_input) input system must be an ODE system, found {mu[j](theta, omicron), mu[v](theta, omicron)}
p1o := odeplot(p1, [theta, omicron, i[h](t)], 0 .. 10, numpoints = 100, labels = ["Time (Days)", " infectious population"], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed, legend = [front, rear, ideal]);

Maple gives same solution for two different equations.

eq1 := 1/5*sqrt(-20*y + 1) - 1/5*ln(1 + sqrt(-20*y + 1)) = x + 2;
eq2 := -1/5*sqrt(-20*y + 1) - 1/5*ln(1 - sqrt(-20*y + 1)) = x + 2;

Solving these for y, gives same exact solution. But this is not correct. As this worksheet shows.

Is this a bug? How could two different equations give same solution?
 

Download different_equations_give_same_solution_june_12_2024.mw

On the corresponding Modelica page I find

Since MapleSim 2024 now has been upgraded to Modelica 4.0 (which I appreciate very much by the way - Thank you), I was wondering if I could give this libraray a try?

I am looking for simple ways to set up digital controllers in the context of developement of code for micro-controllers. From the github page:

Furthermore, in sublibrary Controller about 20 input/output blocks of linear systems are provided that are based on the different representation forms, e.g., PID, StateSpace, Filter blocks. A unique feature of these blocks is that it is very convenient to quickly switch between a continuous and a discrete block representation. Also, templates are provide to quickly built-up standard controller structures. 

I am using intersectplot  to make projective coordinate plots. Everything intersects the plane z=1. I find the plot quality poor, i.e. dotty dashy lines and circle. This seem to be the best linestyle=solid can do here. gridrefine can't be applied here. 
Any suggestions to improve quality here?
Maybe intersectplot is not the best aprroach here but so far it is all if have figured out.

Download 2024-06-10_Q_Intersectplot_quality.mw

restart:with(Physics):

Setup(dimension=3,coordinates=(X=[x,y,z])):

Define(Tp3[~alpha,~beta,~gamma],B[~lambda,mu],T3[~rho,~epsilon,~sigma]):

Tp3[~alpha,~beta,~gamma]=B[~alpa,rho]B[~beta,epsilon]B[~gamma,sigma]T3[~rho,~epsilon,~sigma]

SumOverRepeatedIndices of the expression does not do anything. Why?

Thanks for the answer.

Dear sir,

In the given problem, eta = 0 to 20, I want the table value of eta for a step size of 1000 (0 to 20 in thousand parts).

i have calculated only for one value, zero

Download Demo_paper_work.mw

hi,

I don't know how to test the answers I got in Mathematica, can you help me?
I can't send the file here, I really need help.

Can I solve the given biquadratic equation in terms of sigma. I only need real positive root, if any

6125*_Z^4 + 68644*_Z^3*sigma - 219625*_Z^3 + 255712*_Z^2*sigma - 959250*_Z^2 + 238144*_Z*sigma - 1113500*_Z - 245000

I tried with solve for variable but it does not work. 

These are two examples of challenging ode solutions to show they satisfy the ode.

I tried many things myself but can't do it. Feel free to use any method or trick you want. The goal is simply to show that the solution is correct. The solutions are correct as far as I know, but hard to show by back substitution since the solutions are given in form of integrals and RootOf in them.

Extra credit points will be awarded for those who manage to do both.

Download showing_solution_satisfies_ode.mw

Hi,

I am exploring the boxplot, and I see that I do not have the option to integrate 2 lists: One for observations and one for frequencies. The BoxPlot command only accepts one list (List A in my example). Is there a way to create the BoxPlot using the 'Obs' and 'Eff' lists? Thank you for your insight

QBoxPlot.mw