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MaplePrimes Questions

put a grid on a drawing...

Asked by: JAMET 425
gridlines plotting
June 12 2024
0  1

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);

Error, (in dsolve/numeric/process_input) input sys...

Asked by: HaHu 25
ode syntax homework
June 12 2024
1  3

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);
`ϕ`(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]*`ϕ`(theta)*i[v](t)/n[h](t);
lambda[h] := (beta[h]*`ϕ`(theta)*i[h](t)+beta[h]*`ϕ`(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]);

why Maple gives same solution for two different eq...

Asked by: nm 11353
solve lambertw
June 12 2024
2  2

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?
 

15172

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Case 1. Solve first then plugin x value in solution

 
> 

eq1:=(sqrt(a^2 - 4*b*y) - a*ln(a + sqrt(a^2 - 4*b*y)))/b=x+c__1;
eq2:=(-sqrt(a^2 - 4*b*y) - a*ln(a - sqrt(a^2 - 4*b*y)))/b=x+c__1;

eq1:=eval(eq1,[a=1,b=5,c__1=2]);
eq2:=eval(eq2,[a=1,b=5,c__1=2]);

((a^2-4*b*y)^(1/2)-a*ln(a+(a^2-4*b*y)^(1/2)))/b = x+c__1

(-(a^2-4*b*y)^(1/2)-a*ln(a-(a^2-4*b*y)^(1/2)))/b = x+c__1

(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1+(-20*y+1)^(1/2)) = x+2

-(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1-(-20*y+1)^(1/2)) = x+2

> 

sol1:=simplify(solve(eq1,y));

-(1/20)*LambertW(-exp(-11-5*x))*(LambertW(-exp(-11-5*x))+2)

> 

sol2:=simplify(solve(eq2,y));

-(1/20)*LambertW(-exp(-11-5*x))*(LambertW(-exp(-11-5*x))+2)

> 

eval(sol1,x=10.);

0.3221340286e-27

> 

eval(sol2,x=10.);

0.3221340286e-27

Case 2. Plugin in same x value in equation and then solve, we get different answers

 
> 

eq1:=(sqrt(a^2 - 4*b*y) - a*ln(a + sqrt(a^2 - 4*b*y)))/b=x+c__1;
eq2:=(-sqrt(a^2 - 4*b*y) - a*ln(a - sqrt(a^2 - 4*b*y)))/b=x+c__1;

eq1:=eval(eq1,[a=1,b=5,c__1=2,x=10]);
eq2:=eval(eq2,[a=1,b=5,c__1=2,x=10]);

((a^2-4*b*y)^(1/2)-a*ln(a+(a^2-4*b*y)^(1/2)))/b = x+c__1

(-(a^2-4*b*y)^(1/2)-a*ln(a-(a^2-4*b*y)^(1/2)))/b = x+c__1

(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1+(-20*y+1)^(1/2)) = 12

-(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1-(-20*y+1)^(1/2)) = 12

> 

sol1:=evalf(solve(eq1,y));

-205.8850616

> 

sol2:=evalf(solve(eq2,y));

0.3221340286e-27


 

Download different_equations_give_same_solution_june_12_2024.mw

 

MapleSim & Modelica_LinearSystems2: Do both work t...

Asked by: C_R 3427
June 11 2024
0  1

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. 

Intersectplot line quality ...

Asked by: Ronan 1341
plotting intersectplot
June 10 2024
1  3

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.


> 

restart
> 

 

> 

 

> 

with(plottools)

[annulus, arc, arrow, circle, colorbar, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, polygonbyname, prism, project, pyramid, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate, triangulate]

 (1)
> 

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

 (2)
> 

 

> 

 

> 

DistCircle:=x^2+y^2=1

x^2+y^2 = 1

 (3)
> 

pt1:=[1/4,3/4]

[1/4, 3/4]

 (4)
> 

pt2:=[7/8,-1/3]

[7/8, -1/3]

 (5)
> 

pt3:=[-3/2,3/7]

[-3/2, 3/7]

 (6)
> 

pt4:=[3/5,-4/5]

[3/5, -4/5]

 (7)
> 

pt5:=[-1/10,-3/2]

[-1/10, -3/2]

 (8)
> 

 

> 

L12:=-(13*x)/12 - (5*y)/8 + 71/96; #LnPeqns(pt1,pt2);

-(13/12)*x-(5/8)*y+71/96

 (9)
> 

L13:=-(9*x)/28 + (7*y)/4 - 69/56; #LnPeqns(pt1,pt3);

-(9/28)*x+(7/4)*y-69/56

 (10)
> 

L23:=(16*x)/21 + (19*y)/8 + 1/8; #LnPeqns(pt2,pt3);

(16/21)*x+(19/8)*y+1/8

 (11)
> 

L35:=(27*x)/14 + (7*y)/5 + 321/140; #LnPeqns(pt5,pt3)

(27/14)*x+(7/5)*y+321/140

 (12)
> 

nullline:=3/5*x-4/5*y-1

(3/5)*x-(4/5)*y-1

 (13)
> 

ptplt:=point([pt1,pt2,pt3,pt4,pt5],color="Green",symbol=solidcircle,symbolsize=10):
txtplt:=textplot([pt4[],typeset("pt4")],align={below,right}):
> 

plt1:=display(txtplt,implicitplot([DistCircle,L12,L13,L23,L35,nullline],x=-2..2,y=-1.5...1.5,color=[red,blue,blue,blue,blue,cyan]),ptplt,scaling=constrained)
> 

 

 
> 

# Projective Geometry Version
> 

DistCirclez:=x^2+y^2-z^2;  #a Cone
> 

 

x^2+y^2-z^2

 (14)
> 

pt1p:=[pt1[],1];
pt2p:=[pt2[],1];
pt3p:=[pt3[],1];
pt4p:=[pt4[],1];
pt5p:=[pt5[],1];

[1/4, 3/4, 1]

  

[7/8, -1/3, 1]

  

[-3/2, 3/7, 1]

  

[3/5, -4/5, 1]

  

[-1/10, -3/2, 1]

 (15)
> 

 

> 

 

> 

 

> 

L12p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt2p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

 (16)
> 

L13p:=(13*x)/12 + (5*y)/8 - (71*z)/96;#LnPeqns([pt1p,pt3p,[0,0,0]]);

(13/12)*x+(5/8)*y-(71/96)*z

 (17)
> 

L23p:=(9*x)/28 - (7*y)/4 + (69*z)/56;#LnPeqns([pt2p,pt3p,[0,0,0]]);

(9/28)*x-(7/4)*y+(69/56)*z

 (18)
> 

L35p:=(27*x)/14 + (7*y)/5 + (321*z)/140;#LnPeqns([pt3p,pt5p,[0,0,0]]);

(27/14)*x+(7/5)*y+(321/140)*z

 (19)
> 

L04p:=3/5*x-4/5*y-1*z;

(3/5)*x-(4/5)*y-z

 (20)
> 

ptpltp:=point([pt1p,pt2p,pt3p,pt4p,pt5p],symbol=solidsphere, symbolsize=8,color="green"):
intp1:=intersectplot(DistCirclez,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,linestyle=solid):#unit circle at z=1
intp12p:=intersectplot(L12p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp13p:=intersectplot(L13p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp23p:=intersectplot(L23p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp35p:=intersectplot(L35p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=blue):
intp04p:=intersectplot(L04p,z=1,x=-2.5..2.5,y=-2.5..2.5,z=0..1,color=cyan):
> 

 
> 

display(ptpltp,intp1,intp12p,intp13p,intp23p,intp35p,intp04p,scaling=constrained,caption="Projective Co-ords on plane z=1",axes=normal,axis[3]=[tickmarks=[1]])

 
> 

 


Download 2024-06-10_Q_Intersectplot_quality.mw

How to do SumOverRepeatedIndices...

Asked by: oudiné 10
June 10 2024
2  1

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.

How to divide the step size...

Asked by: KIRAN SAJJAN 40
homework pde numeric
June 10 2024
0  6

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

Numerical test of the solution of the differential...

Asked by: delvin 60
mathematica incomplete-question
June 10 2024
0  2

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 ...

Asked by: pallav 90
solve
June 10 2024
0  2

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. 

examples of hard ode solutions to show they satisf...

Asked by: nm 11353
ode differential-equations odetest
June 09 2024
1  3

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.

28148

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Example 1

 
> 

_EnvTry:='hard';
ode:=y(x) = arcsin(diff(y(x), x)) + ln(1 + diff(y(x), x)^2);
sol:=dsolve(ode);
r:=odetest(sol,ode);
coulditbe(r=0);

hard

y(x) = arcsin(diff(y(x), x))+ln(1+(diff(y(x), x))^2)

x-Intat(1/sin(RootOf(-_a+_Z+ln(sin(_Z)^2+1))), _a = y(x))-c__1 = 0

-arcsin(sin(RootOf(-y(x)+_Z+ln(3/2-(1/2)*cos(2*_Z)))))+RootOf(-y(x)+_Z+ln(3/2-(1/2)*cos(2*_Z)))

FAIL

Example 2

 
> 

ode:=(1 + diff(y(x), x)^2)*(arctan(diff(y(x), x)) + a*x) + diff(y(x), x) = 0;
sol:=dsolve(ode);
r:=odetest(sol,ode);
coulditbe(r=0)

(1+(diff(y(x), x))^2)*(arctan(diff(y(x), x))+a*x)+diff(y(x), x) = 0

y(x) = Int(tan(RootOf(a*x*tan(_Z)^2+tan(_Z)^2*_Z+a*x+tan(_Z)+_Z)), x)+c__1

(-arctan(tan(RootOf(2*a*x+sin(2*_Z)+2*_Z)))+RootOf(2*a*x+sin(2*_Z)+2*_Z))*tan(RootOf(2*a*x+sin(2*_Z)+2*_Z))/(a*x+RootOf(2*a*x+sin(2*_Z)+2*_Z))

FAIL

 

 

Download showing_solution_satisfies_ode.mw

Is there a way to create the BoxPlot using 2 list...

Asked by: jalal 435
plotting statistics boxplot
June 09 2024
0  3

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

solve elliptic PDEs...

Asked by: NIMA112 50
homework pde numeric
June 09 2024
1  5

As Maple is not equipped to handle numerical solutions of elliptic PDEs, can anyone help top solve PDEs by finite differences or any other numerical solver?

pde.mw

Travelling wave reduction of a PDE...

Asked by: dds 20
ode pde wave
June 09 2024
0  1

Dear Maple Community,

I would like to ask you a question which will certainly be elementary for you. Imagine that I have a PDE (or, more generally, a system of PDEs) with (t, x) being independent variables, and the dependent variable defining the wave height or the fluid particle velocity u(t,x). The best example is the famous KdV equation:

u[t] + u*u[x] + u[x,x,x] = 0.

Now, I would like to automatically derive the ODE(s) that satisfy the travelling waves of this equation. Namely, we have to substitute the travelling wave ansatz u(t,x) = U(X) = U(x - c*t), where c is the travelling wave speed. In the case of the KdV equation, we obtain the following ODE:

-c*U' + U*U' + U''' = 0,

where prime ' denotes the derivative with respect to the new variable X.

My question is the following: What is the best way to automatically obtain this PDE -> ODE reduction in Maple?

Thanks a lot in advance!

Kind regards,

DDe

simplifying a/sqrt(tan(x+c__1)^2+1);...

Asked by: nm 11353
simplify simplification trig
June 09 2024
2  10

How to make Maple simplify a/sqrt(tan(x+c__1)^2+1); to a/sqrt(sec(x+c__1)^2);  ?

Below is worksheet. since the second one is smaller in leaf size, expected simplify(...,size) to do it, But it did not. Any suggestions?

24832

> 

LC:=MmaTranslator:-Mma:-LeafCount;
e1:=a/sqrt(tan(x+c__1)^2+1);
e2:=a/sqrt(sec(x+c__1)^2);

MmaTranslator:-Mma:-LeafCount

a/(tan(x+c__1)^2+1)^(1/2)

a/(sec(x+c__1)^2)^(1/2)

> 

LC(e1);

12

> 

LC(e2);

10

> 

#we see they are same
simplify(e1-e2);

0

> 

#both nothing below make e1 to e2
simplify(e1); #not good simplification at all. Adds csgn.
LC(%);

a*csgn(sec(x+c__1))*cos(x+c__1)

11

> 

#expected this to do it but no
simplify(e1,size);
LC(%);

a/(tan(x+c__1)^2+1)^(1/2)

12

> 

simplify(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

combine(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

 


Using some other software:

 

 

 

Download tan_sec_simplification_june_9_2024.mw

Where is the code that simplifies this ...

Asked by: janhardo 700
programming simplification
June 08 2024
1  43

Can't figure out what code makes this simplification.
If this simplification works, it will be a part of a larger simplication procedure ( if it not conflicts hopefully) 
vereenvouding_hoe_-vraag_MPF.mw

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