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how can I compute these integrals symbolically?...

Asked by: Viva 15
integration
August 02 2022
2  10

.Hello everybody

.In the attached code how I can compute \lambda2(t,s) and Vbar(s) symbolically

 when I run them, some parts can't be computed. how should I solve this problem?

2.mw

Why maple give empty solutions?...

Asked by: WA573 80
differential-equations pdetools plotting
August 01 2022
2  5

Why maple give empty solutions? See ref. (12) in the attached wokrsheet. Is there anything missing when deriving Sols?

sols_tw.mw

How do i solve a system nonlinear diferential equa...

Asked by: angelisasking 10
ode syntax homework
July 31 2022
1  11

hi im currently doing my thesis and can somebody help me to develope the code? pls im stuck..

restart;
_local(I);
Digits := 15;
de1 := (1 - p)*(diff(S(t), t) + mu*S(t)) + p*(diff(S(t), t) + mu*S(t) + beta*S(t)*I(t) - rho*R(t) - varepsilon);
de2 := (1 - p)*(diff(E(t), t) + (alpha1 + mu)*E(t)) + p*(diff(E(t), t) + (alpha1 + mu)*E(t) - beta*S(t)*I(t));
de3 := (1 - p)*(diff(I(t), t) + (alpha2 + delta + mu)*I(t)) + p*(diff(I(t), t) + (alpha2 + delta + mu)*I(t) - alpha1*E(t));
de4 := (1 - p)*(diff(R(t), t) + (mu + rho)*R(t)) + p*(diff(R(t), t) + (mu + rho)*R(t) - alpha2*I(t));
ibvc := S(0) = 2304219, E(0) = 84929, I(0) = 299, R(0) = 71411;
sys1 := eval([de1, de2, de3, de4], p = 1);
dsolve(sys1);
sys0 := eval~(sys1, [{I = 0, R = 0}, {I = 0, S = 0}, {E = 0}, {I = 0}]);
sys_p := `*`~(1 - p, sys0) +~ `*`~(p, sys1);
ode1, ode2, ode3, ode4 := seq(sys_p[j], j = 1 .. 4);
ode1;
de1;
collect(expand(ode1 - de1), S(t), factor);
ode2 - de2;
ode3 - de3;
ode4 - de4;
mu := 0.133*10^(-5);
varepsilon := 0.99879;
delta := 0.004554;
beta := 0.1009*10^(-6);
alpha1 := 0.0008999;
alpha2 := 0.1997;
rho := 0.00090021;
res := dsolve({ibvc, ode1, ode2, ode3, ode4}, numeric, parameters = [p], abserr = 0.1*10^(-14), relerr = 0.1*10^(-12));
res(parameters = [0.5]);
res(50);
plots:-odeplot(res, [t, S(t)], 0 .. 100);
res(parameters = [1]);
plots:-odeplot(res, [t, S(t)], 0 .. 100);
Q := proc(p, {scene::list := [t, S(t)], range::range := 0 .. 100}) if not p::realcons then return 'procname(_passed)'; end if; res(parameters = [p]); plots:-odeplot(res, scene, range, _rest); end proc;
Q(0.5, color = blue);
plots:-animate(Q, [p, range = 0 .. 50], p = 0 .. 1, trace = 24);
n := 4;
s := unapply(add(g[k](t)*p^k, k = 0 .. n), t);
e := unapply(add(h[k](t)*p^k, k = 0 .. n), t);
i := unapply(add(i[k](t)*p^k, k = 0 .. n), t);
r := unapply(add(j[k](t)*p^k, k = 0 .. n), t);
Error, (in i[0]) too many levels of recursion
DE1 := series(eval(ode1, {E = e, I = i, R = r, S = s}), p = 0, n + 1);
DE2 := series(eval(ode2, {E = e, I = i, R = r, S = s}), p = 0, n + 1);
DE3 := series(eval(ode3, {E = e, I = i, R = r, S = s}), p = 0, n + 1);
DE4 := series(eval(ode4, {E = e, I = i, R = r, S = s}), p = 0, n + 1);
Error, (in i[0]) too many levels of recursion
Error, (in i[0]) too many levels of recursion
Error, (in i[0]) too many levels of recursion
Error, (in i[0]) too many levels of recursion
M := eval([ibvc], {E(0) = e(0), I(0) = i(0), R(0) = r(0), S(0) = s(0)});
Error, (in i[0]) too many levels of recursion

text in color in places in printf...

Asked by: vs140580 490
printf color
July 31 2022
1  5

I have say  I am taking for example purpose only i need in general

v:="1:1":
k:=4

printf("%s]  is %g, v, k) 

Now i want the %s] part in some other color say green or red some dark color.

the %s is inside which need to replaced by the v which will keep coming

I want it for a general say for some part of the printf in some color

At present atleast i want

let F be a function say F(v,k) and it prints out 

printf("%s]  is %g, v, k)  where it prints out the %s] part in dark color

How can an equation be sorted by numerical value o...

Asked by: Ronan 1022
polynomial sort
July 30 2022
0  11

I want to collect up the equation terms by the numerical value of the terms coefficient? Have tried sort collect combine...
So far the best I have come up with is nops(indets(on each term). And put them in seperate lists. This still doesn't quiet do the trick.
I am looking to achieve. Would to happy to have then as seperate lists or equations.

(a_1^5+a_2^5...)+5(a_1^4a_2+a_1^4a_3....)+10(a_1^3a_2^2 ....)+20(  ....   )+......+60(a_1^2a_2a_3a_4+ a_1a_2^2a_3a_4....)


 

restart

pn := (a[1]+a[2]+a[3]+a[4])^5

(a[1]+a[2]+a[3]+a[4])^5

pn1 := expand(pn)

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

els := convert({op(pn1)}, list)

[a[1]^5, a[2]^5, a[3]^5, a[4]^5, 5*a[1]*a[2]^4, 5*a[1]*a[3]^4, 5*a[1]*a[4]^4, 10*a[1]^2*a[2]^3, 10*a[1]^2*a[3]^3, 10*a[1]^2*a[4]^3, 10*a[1]^3*a[2]^2, 10*a[1]^3*a[3]^2, 10*a[1]^3*a[4]^2, 5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 5*a[2]*a[3]^4, 5*a[2]*a[4]^4, 10*a[2]^2*a[3]^3, 10*a[2]^2*a[4]^3, 10*a[2]^3*a[3]^2, 10*a[2]^3*a[4]^2, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 5*a[3]*a[4]^4, 10*a[3]^2*a[4]^3, 10*a[3]^3*a[4]^2, 5*a[3]^4*a[4], 20*a[1]*a[2]*a[3]^3, 20*a[1]*a[2]*a[4]^3, 30*a[1]*a[2]^2*a[3]^2, 30*a[1]*a[2]^2*a[4]^2, 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 20*a[1]*a[3]*a[4]^3, 30*a[1]*a[3]^2*a[4]^2, 20*a[1]*a[3]^3*a[4], 30*a[1]^2*a[2]*a[3]^2, 30*a[1]^2*a[2]*a[4]^2, 30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 30*a[1]^2*a[3]^2*a[4], 20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 20*a[1]^3*a[3]*a[4], 20*a[2]*a[3]*a[4]^3, 30*a[2]*a[3]^2*a[4]^2, 20*a[2]*a[3]^3*a[4], 30*a[2]^2*a[3]*a[4]^2, 30*a[2]^2*a[3]^2*a[4], 20*a[2]^3*a[3]*a[4], 60*a[1]*a[2]*a[3]*a[4]^2, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]^2*a[2]*a[3]*a[4]]

NULL

add(els[i], i = 1 .. nops(els))

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

L1 := []; L2 := []; L3 := []; L4 := []; for i to nops(els) do if nops(indets(els[i])) = 1 then L1 := [op(L1), els[i]] elif nops(indets(els[i])) = 2 then L2 := [op(L2), els[i]] elif nops(indets(els[i])) = 3 then L3 := [op(L3), els[i]] else L4 := [op(L4), els[i]] end if end do; L1; L2; L3; L4

[60*a[1]*a[2]*a[3]*a[4]^2, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]^2*a[2]*a[3]*a[4]]

indets(els[7])

{a[1], a[4]}

NULL

indets(els(5))

{}

`~`[op](1 .. -1, L2)

[5, a[1], a[2]^4, 5, a[1], a[3]^4, 5, a[1], a[4]^4, 10, a[1]^2, a[2]^3, 10, a[1]^2, a[3]^3, 10, a[1]^2, a[4]^3, 10, a[1]^3, a[2]^2, 10, a[1]^3, a[3]^2, 10, a[1]^3, a[4]^2, 5, a[1]^4, a[2], 5, a[1]^4, a[3], 5, a[1]^4, a[4], 5, a[2], a[3]^4, 5, a[2], a[4]^4, 10, a[2]^2, a[3]^3, 10, a[2]^2, a[4]^3, 10, a[2]^3, a[3]^2, 10, a[2]^3, a[4]^2, 5, a[2]^4, a[3], 5, a[2]^4, a[4], 5, a[3], a[4]^4, 10, a[3]^2, a[4]^3, 10, a[3]^3, a[4]^2, 5, a[3]^4, a[4]]

NULL

op(2, L2[1])

a[1]

op(3, L2[1])

a[2]^4``

Download 30-7-22_Q_sort_equation_by_numerical_coeffs.mw

Why maple return trivial solution after integratio...

Asked by: Ahmed111 130
July 30 2022
1  1

Why maple return trivial solution after integration (see (11) in the attached .mw))? The result should be some non-trivial solution.

solutionsg.mw

Why can't Maple solve the below code for some par...

Asked by: Viva 15
integration numeric
July 30 2022
1  2

Hello everybody.

I wrote the attached code. this code gives a good result when "H" parameter is equal to 0.5. Even in this condition if I change other parameters, I can get a true result as well. But when I change "H" parameter to 0.6,0.7,0.8 or 0.9 the code can't be executed anymore and I can't get a result.

based on the paper, for H=0.6,0.7,0.8 or 0.9. we have a result.

what's the problem?

can anyone please help me to solve this problem?

thank you for your help in advance.

1.mw

How can I compare the values of A_0, A_1, B_1 in M...

Asked by: delvin 35
coefficients duplicate-question
July 30 2022
1  4

plot three dimensional curve using data points...

Asked by: Zeineb 520
plotting
July 30 2022
1  3

Dear all

I need your help to plot

1)   First:  a three dimensionl curve, that is plot F(X,Y), where X, Y, and F(X,y) is given  

curve_three_d.mw

2) Second: can plot all the curves in the same graph ( 2-dimensional curve)  obtained from the following idea 
for j from 0 by 5 to 40
plot( F(X,j), X)
end for

thank you for your help

Drawgraph of very large size neatly...

Asked by: vs140580 490
graphtheory drawgraph stylesheet
July 30 2022
3  5

Need help to use DrawGraph to align vertices and edges and length etc for very large large size graph which i want to analyze 

even if the graph even if it requires to writen to a file to make it more big and neatly visible.

kind kind help please it will be acknowledged

Program attached those cartesian product graphs are huge extra parameters and layouts and may others may be required to make such big big graphs visible. Kind help please.

Please help i am not that great on the stylesheet options please please help

 

Some kind of patterned way to set vertex positions for least crossings in grid form say I am trying but not able to achive kind help.

Any progression type loop based on size number of vertices et.

Graph_draw.mw

More Newbie Format Questions...

Asked by: Jno 45
plotting numeric-formatting
July 29 2022
2  7

Hi,

I am making good progress in getting Maple to do the simple tasks I need it to do, but there are a few things that I am unable to get looking the way I want. I have looked repeatedly for answers, but I have come up empty every time.

1. No Leading Zero: If I have a variable equal to 0.75, I want it to display as 0.75 not .75. This is not a problem when I do calculations, but when I, for example, display the value in a plot legend, I would like it to have a leading zero.

2. Scientific Notation Threshold: Is there a threshold defining when the display of a value changes from a regular decimal number to a number in scientific notation? For example, I have a number with a value of 0.0094, and I would like it to display (again, in a plot legend) as 0.0094, but it keeps coming out as .94e-2. Yes, it is the same value.

3. Scientific Notation Format: The number in #2 shows up as .94e-2, but it seems like it should be 9.4e-3. Am I missing something? It seems like I was always taught that the mantissa should be between 1 and 10, but Maple seems to want to give me a number between 0 and 1.

Thanks,

John

Equation of an ellpise after rotation...

Asked by: JAMET 375
geometry ellipse
July 29 2022
0  4

restart:local D:
with(plots):
with(plottools):

a := 7;
b := a/2;
NULL;

r := b/2;
c := 2*sqrt(10)*r;
A := [c/2, c/2];
B := [c/2, -1/2*c];
C := [-c/2, (-c)/2];
D := [-c/2, c/2];
f := (x, y) -> x^2/a^2 + y^2/b^2 = 1;
Ell1 := rotate(implicitplot(f(x, y), x = -9 .. 9, y = -6 .. 6, color = blue), Pi/4);

g := (x, y) -> x^2/b^2 + y^2/a^2 = 1;
Ell2 := rotate(implicitplot(g(x, y), x = -10 .. 10, y = -10 .. 10, color = blue), Pi/4);

quadri := plot([A, B, C, D, A], x = -6 .. 6, y = -6 .. 6, filled = true, color = red, transparency = 0.7);
Cir1 := disk([c/2 - r, -c/2 + r], r, color = blue);
Cir2 := disk([-c/2 + r, -c/2 + r], r, color = blue);
Cir3 := disk([-c/2 + r, c/2 - r], r, color = blue);
Cir4 := disk([c/2 - r, c/2 - r], r, color = blue);
display([quadri, Ell1, Ell2, Cir1, Cir2, Cir3, Cir4], scaling = constrained, axes = normal);
how to find the equations of ellipses in order to fit them to discs and whiten the interior of ellipses ? Thank you.

Numerical schemes for second order mixed PDEs in ...

Asked by: ijuptilk 100
pde numeric differential-equations
July 28 2022
0  15

Is it possible to solve the mixed PDEs below using the method of lines or any other numerical scheme?

B.C:

theta(0,t) = theta(d,t) = 0

v(0,t) = v(d,t) = 0

I.C: theta(z,0) = \thetab*sin(pi/2)*z,  v(z,0) =0 at t =0  for both the initial conditions, where thetab = 0.0001 

% parameters.

K3 = 7.5*10^(-12);

eta2 = 0.1361;

alpha2 = -0.1104;

gamma1 = 0.1093;

d = 0.0002;

xi = 0.1; 

Note: xi is the controlling parameter. For instance, we can plot theta and v for different values of xi.

I tried matlab but no standard scheme to solve the problem because of the partial^2 theta/partial d partial t term. It would have been possible to use pdepe in Matlab if not for the mixed derivative. Please any help.

Thank you

How to solve a set of equaions using fsolve?...

Asked by: mehdibgh 235
matrix indexing fsolve
July 28 2022
0  11

I have a set of equations gathered in a vector. The number of equations varies each time. Here in this example it is 4. How you suggest so solve them with fsolve? I tried to use seq but faced error.

> 

restart
> 

EQ := Matrix(4, 1, {(1, 1) = 32.1640740637930*Tau[1]-0.172224519601111e-4*Tau[2]-0.270626540730518e-3*Tau[3]+0.1570620334e-9*P[1]+0.3715450960e-14*sin(t), (2, 1) = -0.172224519601111e-4*Tau[1]+32.1667045885952*Tau[2]+0.587369829416537e-4*Tau[3]-0.1589565489e-8*P[1]+0.1004220091e-12*sin(t), (3, 1) = -0.270626540730518e-3*Tau[1]+0.587369829416537e-4*Tau[2]+32.1816411689934*Tau[3]-0.7419658527e-8*P[1]+0.5201228088e-12*sin(t), (4, 1) = 0.1570620334e-9*Tau[1]-0.1589565489e-8*Tau[2]-0.7419658527e-8*Tau[3]+601.876235436204*P[1]})
> 

V := Matrix(1, 4, {(1, 1) = Tau[1], (1, 2) = Tau[2], (1, 3) = Tau[3], (1, 4) = P[1]})
> 

q := 0
> 

X := Matrix(4, 1, {(1, 1) = -0.1156532164e-15*sin(t), (2, 1) = -0.3121894613e-14*sin(t), (3, 1) = -0.1616209235e-13*sin(t), (4, 1) = -0.2074537757e-24*sin(t)})
> 

t := 1
> 

Xf := fsolve({seq(EQ[r], r = 1 .. 4)}, {seq(V[r] = q .. X[r], r = 1 .. 4)})

Error, Matrix index out of range``

``

Download SoalNewton.mw

Should there be a Maple language reference manual?...

by: nm 8552 Maple
syntax programming documentation
July 27 2022
5  3

According to Wikipedia

"In computing, a programming language reference or language reference manual is
part of the documentation associated with most mainstream programming languages. It is
written for users and developers, and describes the basic elements of the language and how
to use them in a program. For a command-based language, for example, this will include details
of every available command and of the syntax for using it.

The reference manual is usually separate and distinct from a more detailed
 programming language specification meant for implementors of the language rather than those who simply use it to accomplish some processing task."

 

And no, Maple's Programming guide is not a Language reference manual. This is a guide to how to program in Maple. But it is not reference manual for the language itself. i.e. description of the Language itself.

Examples of Language reference manuals are

C

Original C++ 

Python

Ada

Fortran 77

 

and so on.

Why is there no LRM for Maple? Should there be one? I find Maple semantics sometime confusing, and many times I find how things work by trial and error. Having a reference to look at will be good. 

I know for a language as large as Maple, this is not easy to do. But it will good for Maplesoft to invest into making one.

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