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As am trying to solve this integration:

int(B*eta^(-B)*t^(B-1)*exp(-(t/eta)^B)*(t-n*h), t = n .. (n+1)*h)

where,

ETA:=1000

B:=2.5

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got 1. = 1. .. 2.

 

Please Help ..

Hi everybody.

 

There are several weeks I'm on a school project and for it we need a Maplesim Simulation. It contains a sine voltage (source), a diode bridge (simplify), a condenser and a resistor. The problem is : when I want to simulate it, an error message appears : System is undetermined. I dopn't understand why I've this and from where's the problem...

 

If you could help me asap, it will be very very nice.

 

Have a nice day.

i want to find initial condition for F(0),G(0), H(0) and thetap(0) which is are missing in this problem.. then i facing this error Error, (in dsolve/numeric/bvp) Newton iteration is not converging



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/hydronew2.mw .

Download hydronew2.mw

Hi everyone.

I'm trying to visualize some some field lines for a 3D magnetic field I have simulated, and I have read that the Student[VectorCalculus] package is the best package for this type of visualization. I tried implementing it as described online and in the manual, and I got an error:

Error, (in plots/fieldplot3d) no non-zero vectors found

 

Does anyone have any ideas as to what could be causing this issue?

Attached is the Maple document I am using. The section entitled "Problem Area" is where the issue is.

 

turtle-rec-bend.mw

Hi,

What is the reason/Why: 

 

Error, (in dsolve/numeric/bvp) unable to achieve requested accuracy of 0.1e-5 with maximum 128 point mesh (was able to get 0.66e-1), consider increasing `maxmesh` or using larger `abserr`

Thanks for the help :)

When trying to solve a set of partial differential equations, I always get the following error. I don't know what it means. Can somebody help me?

 

Please see the attached worksheet for the error at the end, any idea what happens?

Besides, anyone know how to make plot array with each element has a plot and scatterplot in it?  I made my plot by making table first and then type the cmd individually.

Raw Data

restart

avicel102_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.6621, (1, 3) = .22, (2, 1) = 100, (2, 2) = 3.33221, (2, 3) = .103, (3, 1) = 150, (3, 2) = 4.95533, (3, 3) = 0.43e-1, (4, 1) = 200, (4, 2) = 5.62147, (4, 3) = 0.37e-1, (5, 1) = 50, (5, 2) = 1.88627, (5, 3) = .207, (6, 1) = 50, (6, 2) = 1.90375, (6, 3) = .199, (7, 1) = 100, (7, 2) = 4.04708, (7, 3) = 0.89e-1, (8, 1) = 100, (8, 2) = 4.20413, (8, 3) = 0.87e-1, (9, 1) = 150, (9, 2) = 5.50509, (9, 3) = 0.41e-1, (10, 1) = 150, (10, 2) = 4.90453, (10, 3) = 0.49e-1, (11, 1) = 200, (11, 2) = 6.22001, (11, 3) = 0.16e-1, (12, 1) = 200, (12, 2) = 6.24435, (12, 3) = 0.23e-1}); avicel102_syloid := Matrix(13, 3, {(1, 1) = 50, (1, 2) = 1.76578, (1, 3) = .235, (2, 1) = 100, (2, 2) = 4.08314, (2, 3) = .128, (3, 1) = 150, (3, 2) = 4.85921, (3, 3) = 0.73e-1, (4, 1) = 200, (4, 2) = 5.66786, (4, 3) = 0.51e-1, (5, 1) = 50, (5, 2) = 2.06221, (5, 3) = .224, (6, 1) = 50, (6, 2) = 2.17294, (6, 3) = .216, (7, 1) = 100, (7, 2) = 4.03728, (7, 3) = .109, (8, 1) = 100, (8, 2) = 3.67978, (8, 3) = .116, (9, 1) = 150, (9, 2) = 5.78427, (9, 3) = 0.6e-1, (10, 1) = 150, (10, 2) = 5.43599, (10, 3) = 0.59e-1, (11, 1) = 200, (11, 2) = 6.26332, (11, 3) = 0.38e-1, (12, 1) = 200, (12, 2) = 6.10814, (12, 3) = 0.39e-1, (13, 1) = 200, (13, 2) = 6.83857, (13, 3) = 0.25e-1}); avicel301_101_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.106, (1, 3) = .2597543205, (2, 1) = 50, (2, 2) = 1.06, (2, 3) = .2564849561, (3, 1) = 50, (3, 2) = 1.129, (3, 3) = .2552025392, (4, 1) = 100, (4, 2) = 2.865, (4, 3) = .1280363098, (5, 1) = 100, (5, 2) = 2.793, (5, 3) = .127659333, (6, 1) = 100, (6, 2) = 3.088, (6, 3) = .1347147061, (7, 1) = 150, (7, 2) = 4.216, (7, 3) = 0.802489497e-1, (8, 1) = 150, (8, 2) = 4.044, (8, 3) = 0.838493001e-1, (9, 1) = 150, (9, 2) = 4.071, (9, 3) = 0.855901289e-1, (10, 1) = 200, (10, 2) = 4.826, (10, 3) = 0.627298821e-1, (11, 1) = 200, (11, 2) = 4.924, (11, 3) = 0.614759445e-1, (12, 1) = 200, (12, 2) = 4.76, (12, 3) = 0.61001365e-1})

NULL

 

with(LinearAlgebra):

X[1] := Column(avicel102_aero200, 3):

X[2] := Column(avicel102_syloid, 3):

X[3] := Column(avicel301_101_aero200, 3):

S := Array(1 .. 3):

S[1] := ScatterPlot(X[1], Y[1], labels = [Porocity, Tensile*Strength], title = Compactability*of*Avicel102*with*Aerosil200):

with(plots):NULL

 

vSST := Array(1 .. 3):

tpfit := proc (x, y) options operator, arrow; Fit(a*exp(-k*p)+c, x, y, p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom]) end proc:SST := proc (y) options operator, arrow; Variance(y)*(NumElems(y)-1) end proc:NULL

for i to 3 do fnTP[i] := tpfit(X[i], Y[i])[1] end do:

for i to 3 do fnPC[i] := Fit(c*p^2+b*p+a, P[i], X[i], p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom])[1] end do:

NULL

for i to 3 do vSST[i] := SST(Y[i]) end do:

for i to 3 do pSST[i] := SST(X[i]) end do:

NULL

for i to 3 do vSSR[i] := tpfit(X[i], Y[i])[2] end do:

for i to 3 do Rsquare[i] := 1-vSSR[i]/vSST[i] end do:

NULL

``

s := Array(1 .. 3):

for i to 3 do s[i] := plot(fnTP[i], p = 0 .. .26, legend = typeset(fnTP[i], R^2, "= ", Rsquare[i])) end do

for i to 3 do ps[i] := plot(fnPC[i], p = 0 .. 200, legend = typeset(fnPC[i], R^2, "= ", pRsquare[i])) end do

G := Array(1 .. 3):

G[1] := [S[1], s[1]]:

pG := [[PS[1], ps[1]], [PS[2], ps[2]], [PS[3], ps[3]]]:NULL

NULL

Table 1: Compactability Curve

display(G[1])

 

NULL

display(G[2])

 

NULL

display(G[3])

 

NULL

NULL

NULL

Table 2: Compressibility Curve

display(pG[1])

 

NULL

display(pG[2])

 

NULL

display(pG[3])

 

NULL

``

ff := proc (x) options operator, arrow; unapply(x, p) end proc:

gtp := map(ff, fnTP):

gpc := map(ff, fnPC):

TS1 := proc (pressure) options operator, arrow; (`@`(gtp[1], gpc[1]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS2 := proc (pressure) options operator, arrow; (`@`(gtp[2], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS3 := proc (pressure) options operator, arrow; (`@`(gtp[3], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

por1 := proc (p) options operator, arrow; gpc[1](p/Unit('MPa')) end proc:

(1)

por1(x*Unit('MPa'))

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x+HFloat(9.666666666666651e-6)*x^2

(2)

por1(x);

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x/Units:-Unit('MPa')+HFloat(9.666666666666651e-6)*x^2/Units:-Unit('MPa')^2

(3)

``

NULL

 

(4)

ts := 2/3*(10*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))):

Target Weight of Tablet, m__t:

m__t := 700*Unit('mg')

700*Units:-Unit('mg')

(5)

Tablet True Density:NULL

`ρ__true1` := 1.8*Unit('g'/'cm'^3)

1800.0*Units:-Unit(('kg')/('m')^3)

(6)

Width of tablet w;

d := 7.747*Unit('mm')

7.747*Units:-Unit('mm')

(7)

Length of tablet, l:

l := 17.018*Unit('mm')

17.018*Units:-Unit('mm')

(8)

Cup Depth, h:

hh := 1.6764*Unit('mm')

1.6764*Units:-Unit('mm')

(9)

Cup Volume", `v__cup`"

v__cup := 119.789438*Unit('mm'^3)

119.789438*Units:-Unit(('mm')^3)

(10)

Die cross sectional area, v__die:

a__die := 118.9610524*Unit('mm'^2)

118.9610524*Units:-Unit(('mm')^2)

(11)

Equation to solve tablet thickness using tablet dimension and porocity:

Tablet bulk density:

`ρ__bulk` := `ρ__true`*sf

`ρ__true`*sf

(12)

Tablet volume:``

V__tablet := 2*V__cup+A__die*(t-2*H)

2*V__cup+A__die*(t-2*H)

(13)

NULL

Tablet bulk Density:``

`ρ__bulk` := m__tablet/V__tablet

m__tablet/(2*V__cup+A__die*(t-2*H))

(14)

NULL

eq1 := m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

(15)

Function for thickness:

thickness := unapply(simplify(solve(eq1, t), size), sf, A__die, H, V__cup, `ρ__true`, m__tablet)

proc (sf, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; (2*sf*(A__die*H-V__cup)*`ρ__true`+m__tablet)/(A__die*sf*`ρ__true`) end proc

(16)

simplify(thickness(1-por[1](100*Unit(MPa)), a__die, hh, v__cup, `ρ__true1`, m__t))

HFloat(0.005719286791216391)*Units:-Unit('m')

(17)

t2 := proc (cc, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; simplify(thickness(1-cc, A__die, H, V__cup, `ρ__true`, m__tablet)) end proc:

``

``

``

Tablet tensile strength:NULL

eq2 := `σ__t` = ts

`σ__t` = (20/3)*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))

(18)

Break force of tablet (N)

breakforce := unapply(subs(W = t-2*h, solve(eq2, P)), `σ__t`, D, h, t)

proc (`σ__t`, D, h, t) options operator, arrow; 0.9424777961e-3*`σ__t`*D*(5.*D*(t-2*h)-63.*t*D+1575.*(t-2*h)^2+1420.*t*(t-2*h))/(t-2*h) end proc

(19)

 

kp := simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, 0.5719e-2*Unit('m')))

HFloat(286.99924404612904)*Units:-Unit('N')

(20)

convert(kp, units, kilopond)

HFloat(29.265778226624693)*Units:-Unit('kilopond')

(21)

t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

HFloat(0.005719286791216391)*Units:-Unit('m')

(22)

``

hh

1.6764*Units:-Unit('mm')

(23)

simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)))

HFloat(287.02451456724083)*Units:-Unit('N')

(24)

Encounter problem while chaning variable

 BF:= 
proc (`σ__t`, D, p, A__die, hhh, V__cup, `ρ__true`, m__tablet) options operator, arrow; breakforce(`σ__f`, D, hhh, t2(p, A__die, hhh, V__cup, `ρ__true`, m__tablet)) end proc:

BF(TS1(100*Unit('MPa')), d, por1(100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

BF(HFloat(3.6712504621161846)*Units:-Unit('MPa'), 7.747*Units:-Unit('mm'), HFloat(0.09859999999999991), 118.9610524*Units:-Unit(('mm')^2), 1.6764*Units:-Unit('mm'), 119.789438*Units:-Unit(('mm')^3), 1420.00*Units:-Unit(('kg')/('m')^3), 667*Units:-Unit('mg'))

(25)

evalf(TS[1](100*Unit(MPa)))

HFloat(3.6712504621161846)*Units:-Unit('MPa')

(26)

plot(breakforce(TS1(x), d, hh, t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t)), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(evalf(por1(xx)), xx = 10 .. 200)

 

but por1 works fine on its own with units

por1(Units:-Standard:-`*`(200, Unit('MPa')))

HFloat(0.02719999999999989)

(27)

plot(evalf(por1(xx)), xx = 10 .. 200);

 

Unloading Units:-Standard

``

``

``

``

``

``

``

``

``

``

``

``

``

``

 

Fitting_worksheet.mw

I also used a lot for for loop in this worksheet, can anyone suggest another way of doing it? And I think I initiated many Array(1..3) that is of no use.  But if I do not initiate and do the following

A[1]:=a : 

A[2]:=b:

A[3]:=c:

A;

output: A

Only if I initiate A:=Array(1..3) and then define the element I can see the complete A array at the end.

 

plot tickmarks error...

March 24 2014 delta7 118

Hi,

I'm getting an error when I try to

plot(sin(x), x = -1..1, color = darkblue,tickmarks=[spacing(0.25),subticks=2]);

The error is
Error, (in plot) expecting option tickmarks to be of type list({"default", "piticks", "decimalticks", "pidefault", nonnegint, list(realcons), list(realcons = anything), spacing(realcons), spacing(realcons, realcons)}) but received [spacing(.25), subticks = 2]

What exactly am I doing wrong? After all, [...] is a list.

Even more confusingly, tickmarks=[[spacing(0.25),subticks=2],default] doesn't work either.

Any help appreciated!

Hi, the following Maple code produces an error for the value x=0: 0 instead of 1.

 

> for x from 0 to 5 do 

>print(evalf(sum((-1)^k*x^(2*k)/factorial(2*k), k = 0 .. 10)), evalf(cos(x))) 

> end do; 

0., 1. 
0.5403023059, 0.5403023059 
-0.4161468365, -0.4161468365 
-0.9899924966, -0.9899924966 
-0.6536436057, -0.6536436209 
0.2836642141, 0.2836621855 

Why such an error?

My solution to obtain the good value is:

> for x from 0 to 5 do 

> print(evalf(subs(y=x,sum((-1)^k*y^(2*k)/factorial(2*k), k = 0 .. 10))), evalf(cos(x))) 

> end do; 
                                1., 1. 


                      0.5403023059, 0.5403023059 


                     -0.4161468365, -0.4161468365 


                     -0.9899924966, -0.9899924966 


                     -0.6536436057, -0.6536436209 


                      0.2836642141, 0.2836621855 

Thanks.

Hello,

I have trouble in using the function factors. For example, I expect

factor(Pi*(t^2+1), {I});

to output

-Pi*(-t+I)*(t+I)

but instead the result is

Pi*(t^2+1)

This problem does not appear if Pi gets replaced by a general symbol:

factor(pi*(t^2+1), {I});

produces (as I expect it should)

-pi*(-t+I)*(t+I)

The problem seems to be tied to symbols representing constants, as for example replacing Pi by Catalan also results in no factorization being performed. It further seems to be tied to specifying a splitting field, because

factor(Pi*(t^2-1));

results in

Pi*(t-1)*(t+1)

Is this behaviour intended? Probably the reason is that the polynomial does not have algebraic coefficients (as it includes Pi). Indeed,

factor(Pi*(t^2-1),{});

produces the error message

Error, (in factor) expecting a polynomial over an algebraic number field

But why does this error then not appear for the call factor(Pi*(t^2-1))? If this would assume complex coefficients, it should factor using I. Considering coefficients in an algebraic number field, also the original call factor(Pi*(t^2+1), {I}); should raise an error!?

Thanks,

Erik


intsolve(int(f1(u)*(x-y), u = a .. b) = (12)*cos(x)+5*x^2-12, f1(x));I try to resolve the integral equation but i received all the time the followinf message error 

Error, (in intsolve) invalid input: rhs received {f1(x) = ?}, which is not valid for its 1st argument, expr
I try to use different form but i do not how to resolve the help center do not help to much.

I preciate any help thanks

 

 

I have a procedure which give an approximate solution for ode.

This our procedure

RKadaptivestepsize := proc (f, a, b, epsilon, N).

It's working ( afther some 3 mistake found by a member in Mapleprime).

Then I would like to compute the error between exact and approximate.

RKadaptivestepsize: compute the approximate solution

analyticsol: analytic solution

 

## here, I compute the error
for N from 2 by 2 to 500 do
dataerror:= N->evalf(abs(RKadaptivestepsize(f,0,1,epsilon,N)[1+N][2]-(eval(analyticsol, x = 1))));
##  sequence of data error
data[error] := [seq([N, dataerror(N)], N = 2 .. 500, 2)]:
if  data[error][k][2]<=epsilon then   
printf("%a  is the number of steps required using 3-step Runge Kutta Method to achieve an  eroor of 1e-6 .", k)
break ;
end if;   
end do;
end do;

But its gives an error.: Error, reserved word `error` unexpected

Have any one an idea.

 

Hello,

I am having trouble using the programmer entry point interface to convert/parfrac. As an example consider x/(I*x-1): While

> convert([x, [I*(x+I), 1]], parfrac, x);                   

         [-I, [(I + x) I, -I]]

correctly computes a partial fraction decomposition, the equivalent input

> convert([x, [I*x-1, 1]], parfrac, x);  

results in the error message (both in Maple 16 and 17)

Error, (in convert/parfrac) denominator factors must be coprime

which does not make any sense to me, since there is only a single denominator factor present (and it is even the same factor as in the previous call, only written differently).

What is the reason for this behaviour and how can I use convert/parfrac in a way that avoids such errors?

Thanks,

Erik

Dear all;

Please I need your help to find the error in my code.

I want to solve an ode, with condition on step size.

ode := diff(y(x), x) = 2*x+y(x);
f:=(x,y)->2*x-y;

analyticsol := rhs(dsolve({ode, y(0) = 1}));
RKadaptivestepsize := proc (f, a, b, epsilon, N)
local x, y, n, h,k,z,R,p;
p:=2;
h := evalf(b-a)/N; ## we begin with this setpsize
x[0] := a; y[0] := 1; ## Initialisation
for n from 0 to N-1 do  ##loop
x[n+1] := a+(n+1)*h;  ## noeuds
k[1] := f(x[n], y[n]);
k[2] := f(x[n]+h, y[n]+h*k[1]);
k[3] := f(x[n]+h/2, y[n]+h/4*(k[1]+k[2]));
z[n+1] := z[n]+(h/2)*(k[1]+k[2]);## 2-stage runge Kutta.
y[n+1] := y[n]+(h/6)*(k[1]+k[2]+4*k[3]);
R:=abs(y[n+1]-z[n+1]); ## local erreur
hstar:=sqrt(epsilon/R)
if R=<=epsilon    then
   x[n] := x[n+1]+h;
   y[n]:=y[n+1];
   n:=n+1;

else

h:=hstar;
end if
 end do;
[seq([x[n], y[n]], n = 0 .. N)];
[seq([x[n], z[n]], n = 0 .. N)];
end proc:

epsilon:=1e-8;
RKadaptivestepsize((x,y)->2*x-y,0,1, epsilon,20)

When I check the length of the optimal tour found by TravelingSalesman (GraphTheory package), it's different from the given result. What goes wrong?

See attached file.

``

restart: with(GraphTheory):

G := GRAPHLN(undirected,weighted,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],Array(1..25, [{17, 19},{10, 22

},{10, 14, 23},{6, 12, 14},{6, 7, 19},{4, 5},{5, 13, 15, 16},{12, 13, 14, 15},

{20, 25},{2, 3},{22, 25},{4, 8, 13},{7, 8, 12},{3, 4, 8},{7, 8, 21, 23},{7, 17

, 18},{1, 16, 18, 19},{16, 17, 25},{1, 5, 17},{9, 21, 22},{15, 20, 24},{2, 11,

20, 24},{3, 15, 24},{21, 22, 23},{9, 11, 18}]),`GRAPHLN/table/2`,Matrix(25, 25

, {(12, 13) = 137, (14, 4) = 920, (3, 14) = 902, (5, 6) = 561, (17, 18) = 443,

(22, 11) = 670, (16, 17) = 573, (19, 17) = 330, (18, 17) = 280, (10, 2) = 1630

, (16, 18) = 727, (23, 15) = 760, (17, 1) = 900, (4, 6) = 1216, (16, 7) = 600,

(14, 8) = 260, (12, 4) = 580, (1, 19) = 665, (4, 12) = 733, (19, 5) = 750, (8,

14) = 368, (11, 25) = 1366, (24, 22) = 300, (17, 19) = 495, (21, 15) = 930, (6

, 4) = 1110, (11, 22) = 1049, (12, 8) = 100, (15, 21) = 995, (17, 16) = 520, (

1, 17) = 866, (15, 23) = 833, (5, 19) = 930, (9, 20) = 184, (19, 1) = 630, (7,

15) = 598, (13, 8) = 110, (24, 21) = 250, (3, 10) = 471, (24, 23) = 550, (2,

10) = 1682, (13, 12) = 80, (8, 12) = 202, (21, 24) = 287, (23, 3) = 590, (15,

8) = 410, (14, 3) = 800, (23, 24) = 688, (7, 13) = 526, (8, 15) = 477, (20, 21

) = 245, (2, 22) = 547, (15, 7) = 990, (22, 20) = 420, (10, 3) = 300, (4, 14)

= 933, (5, 7) = 690, (18, 25) = 328, (25, 18) = 270, (21, 20) = 130, (25, 9) =

240, (7, 16) = 406, (20, 9) = 140, (6, 5) = 380, (8, 13) = 236, (20, 22) = 452

, (22, 2) = 500, (9, 25) = 227, (13, 7) = 640, (7, 5) = 670, (25, 11) = 1640,

(3, 23) = 518, (22, 24) = 495, (18, 16) = 700}, storage = sparse));

GRAPHLN(undirected, weighted, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], Array(%id = 4487072130), `GRAPHLN/table/2`, Matrix(%id = 4488755818))

(1)

P:=TravelingSalesman(G);

15471, [1, 19, 5, 6, 4, 14, 3, 10, 2, 22, 11, 25, 9, 20, 21, 24, 23, 15, 8, 12, 13, 7, 16, 18, 17, 1]

(2)

add(GetEdgeWeight(G,{P[2][i],P[2][i+1]}),i=1..nops(P[2])-1);

16570

(3)

 

 

``


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