I am new to Maplesoft environment. I was trying to create a nested loop as given below:

I came across this error:

                               j:=1
Error, increment of for loop must be numeric.

Could anyone kindly help?

Thanks

I'd like to know how to ask Maple to find numerical solutions to underspecified systems of nonlinear equations.  For example, suppose I had a system of equations like this:

eq1 := y1 = tanh(x1);

eq2 := y2 = cosh(x1 + x2);

eq3 := y1 + y2 = 2.0;

Typing this:

fsolve([eq1, eq2, eq3]);

results in the following error:

Error, (in fsolve) number of equations, 3, does not match number of variables, 4

In this situation I can easily artificially restrict the system to find a solution.  For example, I can do:

eq4 := x1 = 0.0;

fsolve([eq1, eq2, eq3, eq4]);

which will result in the following solution:

{x1 = 0., x2 = 1.316957897, y1 = 0., y2 = 2.000000000}

The issue here is that I pulled x1 = 0.0; out of thin air.  Setting a single variable to zero would not work to solve an arbitrary set of nonlinear equations.  How can I ask Maple to find a single (not necessarily unique) solution to an underspecified system of nonlinear equations?

Hi there,

I am trying to maximize a function given a set of values to a parameter in the function. The function is an differential equation belonging to a system of two differential equations.

I have a for loop to state different values to the parameter.

Maple yields the error:

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

When trying to maximize the function.

Supposed that I was doing something wrong in the loop, if I reproduce the contents of the loop outside, and set a value for the parameter. If I plot the solution of the ordinary differential equation, I can see where the maximum lies.

Having plot it, the Optimizamtion:-Maximize works as expected.

However, omitting the plot has a weird effect: I only get the same result depending on the bounds I set for the Maximization:

de1 := diff(A(t), t) = r*m*(1-g)*A(t)-piecewise(t < 8, r*A(t), t >= 8, (r+k)*A(t));
de2 := diff(G(t), t) = r*m*g*A(t)-l*G(t);

ics := A(0) = 25.0, G(0) = 0.;
num := dsolve({de1, de2, ics}, {A(t), G(t)}, type = numeric, output = listprocedure, parameters = [g]);

num(parameters = [g = .15]);
val := eval(G(t), num);

# odeplot(val, [t, G(t)], t = 0 .. 100);

Maximize(val);
Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val2 := Maximize(val);

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val3 := Maximize(val(t), t = 0 .. 60);

  [10267.824035766165, [t = 8.25727747134303]]

val4 := Maximize(val(t), t = 0 .. 100);

[6.863211343195069e-9, [t = 59.84184367042171]]

The right answer is [10267.824035766165, [t = 8.25727747134303]]: Why do I get two different answers even if in that range there is only one relative maximum?

I ignore whether the way I am specifying the arguments for the Maximize function is correct. val is a procedure.

What am I missing?

Attached is the worksheet: MaplePrimes_malaria_param_variation_2.mw

Thanks,

jon

I am having issues when defining functions in a loop. First, I define the first two functions as follows (here, r(x) is a function already assigned).

f_0 := x -> r(x):

f_1 := x -> r(x)*f_0(r(x)):

Then, I define successive functions in a for loop as follows.

for i from 2 to 10 do

   f_i := x -> r(x)*f_[i - 1](r(x));

end do

The loop defines the function f_2 but compiles erroneously for f_3 which, and I do admit, relies on f_2. Does someone have an idea of how to fix this issue? Any help will be greatly appreciated. Thanks.

Aslam-u-Alikum. Hope you will be fine all.  I want to plot the follwing vector in the plan z=0 at time t=0 and A=1

v := `<,>`(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, y), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t))))), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, x), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t)))), VectorCalculus[`*`](B, t))

I am waiting for your positive answer.

I am trying to alter the Virtual Solar system Maple worksheet of Yi Xie in the way that I added several objects to the eight planets and Pluto (e.g. Hale-Bopp, Sedna, 2012 VP113 etc.) and would like to adjust the array such that when zooming out and the obrit and labels overlap so that it's unreadable anymore (orbits and labels) that I can switch on and off (respectively display/not display) specific parts, e.g. the inner solar system. In the original file a single array was created from 1..18 (including 9 orbital entries and 9 label entries). What I did is to create arrays for each part of the Solar system, e.g. Inner for the planets+Pluto 1..18, an array for Hale-Bopp with an orbital entry and a label entry, so [1,2], and an array with 6 entries for 3 additional objects like Sedna, Planet X and 2012 VP113. As well as the sun, which only has a single entry as there are no orbital elements necessary and one just makes a 3dplot (I did not label it, so just one entry). All arrays are converted into lists in the end and displayed. Here is the code:

> with(linalg);

> with(plots);

> with(plottools);

> P1 := matrix([[cos(omega[j]), -sin(omega[j]), 0], [sin(omega[j]), cos(omega[j]), 0], [0, 0, 1]]); P2 := matrix([[1, 0, 0], [0, cos(i[j]), -sin(i[j])], [0, sin(i[j]), cos(i[j])]]); P3 := matrix([[cos(Omega[j]), -sin(Omega[j]), 0], [sin(Omega[j]), cos(Omega[j]), 0], [0, 0, 1]]);

> A:=matrix([[a[j]*(cos(E[j])-e[j])],[a[j]*sqrt(1-e[j]^2)*sin(E[j])],[0]]);

> R:=multiply(P3,P2,P1);

> B:=multiply(R,A);

> a := [.38709893, .72333199, 1.00000011, 1.52366231, 5.20336301, 9.53707032, 19.19126393, 30.06896348, 39.48168677, 1/0.5454e-2, 268.2509283, 532.7838156, 300];

> e := [.20563069, 0.677323e-2, 0.1671022e-1, 0.9341233e-1, 0.4839266e-1, 0.5415060e-1, 0.4716771e-1, 0.858587e-2, .24880766, .994920, .7005635, .8570973, .1];

> i := [7.00487, 3.39471, 0.5e-4, 1.85061, 1.30530, 2.48446, .76986, 1.76917, 17.14175, 89.5328, 24.01830, 11.92859, 10];

> Omega := [48.33167, 76.68069, -11.26064, 49.57854, 100.55615, 113.71504, 74.22988, 131.72169, 110.30347, 282.1476, 90.88303, 144.53190, 45];

> omega := [77.45645, 131.53298, 102.94719, 336.04084, 14.75385, 92.43194, 170.96424, 44.97135, 224.06676, 130.8038, 293.03200, 311.18311, 150];

> i := map(x→ convert(x, units, deg, rad) end proc, i);

> Omega := map(x→ convert(x, units, deg, rad) end proc, Omega);

> omega := map(x→ convert(x, units, deg, rad) end proc, omega);

> for j to 13 do omega[j] := arcsin(sin(omega[j]-Omega[j])/sin(arccos(sin(i[j])*cos(omega[j]-Omega[j])))) end do;

> x := array(1 .. 13);

> y := array(1 .. 13);

> z := array(1 .. 13);

> for j to 13 do x[j] := B[1, 1]; y[j] := B[2, 1]; z[j] := B[3, 1] end do;

> Sun := array([1]);

> Inner := array(1 .. 18); for j to 9 do Colors := [black, green, blue, red, black, yellow, green, violet, brown, aquamarine, black, black, red]; Linestyle := [solid, solid, solid, solid, solid, solid, solid, solid, solid, longdash, solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Comet := array([1, 2]); if j = 10 then Colors := [aquamarine]; Linestyle := [longdash]; Comet[1] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end if;

> Oort := array(1 .. 6); for j from 11 to 13 do Colors := [black, black, red]; Linestyle := [solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Sun[1] := plot3d(0.1e-1, 0 .. 2*Pi, 0 .. Pi, style = PATCHNOGRID, coords = spherical, color = red);

> Inner[10] := textplot3d([subs(E[1] = 0, x[1]), subs(E[1] = 0, y[1]), subs(E[1] = 0, z[1]), "Mercury"]); Inner[11] := textplot3d([subs(E[2] = 0, x[2]), subs(E[2] = 0, y[2]), subs(E[2] = 0, z[2]), "Venus"]); Inner[12] := textplot3d([subs(E[3] = 0, x[3]), subs(E[3] = 0, y[3]), subs(E[3] = 0, z[3]), "Earth"]); Inner[13] := textplot3d([subs(E[4] = 0, x[4]), subs(E[4] = 0, y[4]), subs(E[4] = 0, z[4]), "Mars"]); Inner[14] := textplot3d([subs(E[5] = 0, x[5]), subs(E[5] = 0, y[5]), subs(E[5] = 0, z[5]), "Jupiter"]); Inner[15] := textplot3d([subs(E[6] = 0, x[6]), subs(E[6] = 0, y[6]), subs(E[6] = 0, z[6]), "Saturn"]); Inner[16] := textplot3d([subs(E[7] = 0, x[7]), subs(E[7] = 0, y[7]), subs(E[7] = 0, z[7]), "Uranus"]); Inner[17] := textplot3d([subs(E[8] = 0, x[8]), subs(E[8] = 0, y[8]), subs(E[8] = 0, z[8]), "Neptune"]); Inner[18] := textplot3d([subs(E[9] = 0, x[9]), subs(E[9] = 0, y[9]), subs(E[9] = 0, z[9]), "Pluto"]); Comet[2] := textplot3d([subs(E[10] = 0, x[10]), subs(E[10] = 0, y[10]), subs(E[10] = 0, z[10]), Hale-Bopp]); Oort[4] := textplot3d([subs(E[11] = 0, x[11]), subs(E[11] = 0, y[11]), subs(E[11] = 0, z[11]), "2012 VP113"]); Oort[5] := textplot3d([subs(E[12] = 0, x[12]), subs(E[12] = 0, y[12]), subs(E[12] = 0, z[12]), "Sedna"]); Oort[6] := textplot3d([subs(E[13] = 0, x[13]), subs(E[13] = 0, y[13]), subs(E[13] = 0, z[13]), "Planet X ?", color = red]);

> Sun1 := convert(Sun, 'list');
> Inner1 := convert(Inner, 'list');
> Comet1 := convert(Comet, 'list');
> Oort1 := convert(Oort, 'list');
> display(Sun1, Inner1, Comet1, Oort1, scaling = CONSTRAINED);

 

The first error message appears after the if-condition. Can you tell me where I am making a mistake? Beware: when copy paste the code from Maple to Word and from Word in here the colons at the end of lines have changed into semi-colons. Hope this is no problem in executing the code despite the lines being in the same ">..." e.g. where the labels are defined.

Good day everyone, could you please help use Gauss Elimination method for these system of equations. See the worksheet here F1.mw

Thanks.

Dear All,

I am solving 6 ODE equations with boundary conditions using Runge kutta Felbergh 45 (Maple 12). then, i got this problem.. any suggestion??

Thank you :)

ISPC3.mw

Download ISPC3.mw

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); 

s := 1/(273.16+50); s1 := 1/(273.16+145); s3 := 1/(273.16+250); s2 := 1/(273.16+197.5); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0.15e-2; beta := -3800;
c := 300; n := 200; tau1 := 99; tau2 := 120;

Delta := solve(1-exp(-(gam0*tau1+(1/2)*gam1*tau1^2)*exp(beta*s1)) = 1-exp(-(gam0*a+(1/2)*gam1*a^2)*exp(beta*s2)), a);
a := Delta[1];

Theta := solve(1-exp(-(gam0*(a+tau2-tau1)+(1/2)*gam1*(a+tau2-tau1)^2)*exp(beta*s2)) = 1-exp(-(gam0*b+(1/2)*gam1*b^2)*exp(beta*s3)), b);
b := Theta[1];

n1 := n*(int((gam1*t+gam0)*exp(beta*s1)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s1)), t = 0 .. tau1));
200. - 200. exp(-0.01119474511 gam0 - 0.5541398828 gam1)
n2 := (n-n1)*(int((gam1*t+gam0)*exp(beta*s2)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s2)), t = a .. a+tau2-tau1));

g1 := -n1(gam0, gam1)*(int((1/(gam1*t+gam0)-t*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-evalf(n2(gam0, gam1)*(int((1/(gam0+gam1*(a+t-tau1))-(a+t-tau1)*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2)))

g2 := -n1*(int((t/(gam1*t+gam0)-(1/2)*t^2*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-evalf(n2*(int(((a+t-tau1)/(gam0+gam1*(a+t-tau1))-(1/2)*(a+t-tau1)^2*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2)))

solve({g1 = 0, g2 = 0}, {gam0, gam1})

I want to find the answer of gam0 and gam1. It takes me 20 hours until now...and still evaluating...

Please Help ..

I can't directly copy Maple code into messages but have to insert into Word first, apply some changes that for better readability and copy it from there via Word-paste. Is there a direct way?

there is a solution of equation,so the equation can be divided by the solution,but because the equation is complex,it can't be simplify by the soution,can anyone give me some help?thanks a lot.

Hi,

I want to compute the determinant of a matrix A with this formula:

 Can someone help me to do it.  Of course, here I am using Einstein's convention.

Thank you in advance.

--------------------------------------
Mario Lemelin

Maple 18 Ubuntu 14.04 LTS - 64 bits
Maple 18 Win 7 Pro -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

Hi all,

I'm having some trouble trying to make it so the answer Max(3,1,x,4) turns into Max(x,4), that is, only the greates number and the non numerical values are returned. I've tried a bunch of different things, but have gone out of ideas.

This is the link to the Maple file :6-1.mw and this is the code:

Would really appreaciate your help with this

Download 6-1.mw

Hello,

I would like to solve this kind of system with any numeric method.


With any kind of IBCs.

My code :

Maple says : Error, (in pdsolve/numeric/plot) unable to compute solution for t<HFloat(0.0):
matrix is singular
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
matrix is singular

Any idea why ? Any help ?

Thank you

a curve has residual p if it is linked, in a complete intersection, to a curve with residual p-1

0 residual if is a complete intersection of two surfaces

do complete intersection means two surfaces totally overlapped?

why they are not the same one if complete intersection?