MaplePrimes Questions

Hello friends!

I have one question, whenever I solved system of ODEs using numerical solution (bilton command i.e., dsolve(dsys1, numeric, output = listprocedure, range = 0 .. 1)), its accutacy always like 10 or 12 digits not above at all. I want to how i improve the accuracy. I am waiting your postive answer.

HI MaplePrimes,

Is the Goldbach Weak Conjecture proven?

Consider odd primes p, q, and r.  The question is, Is the sum p+q+r sufficient to reach all odd numbers greater than 9?

See - 

https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

I tried an example.

looping_for_Goldbach_Weak_Conjecture_8.mw

looping_for_Goldbach_Weak_Conjecture_8.pdf

Regards,

Matt

 

restart;

Digits := 18;
with(LinearAlgebra);
f := proc (n) 3*sin(x[n]) end proc;

g := proc (n) 3*cos(x[n])

end proc;

#problem call.
for n from 0 to 0 do

e1 := expand(-y[n+3/2]+y[n]-3*y[n+1/2]+3*y[n+1]+1/11612160*(5856*h^4*g(n+1/2)-19968*h^4*g(n+3/2)+2343*h^4*g(n)-76356*h^4*g(n+1)-7058*h^4*g(n+2)+608864*h^3*f(n+1/2)+104864*h^3*f(n+3/2)+28489*h^3*f(n)+702864*h^3*f(n+1)+6439*h^3*f(n+2)));

e2 := expand(-y[n+2]+3*y[n]-8*y[n+1/2]+6*y[n+1]+1/5806080*(18768*h^4*g(n+1/2)-32880*h^4*g(n+3/2)+3867*h^4*g(n)-76356*h^4*g(n+1)-2229*h^4*g(n+2)+965728*h^3*f(n+1/2)+461728*h^3*f(n+3/2)+45953*h^3*f(n)+1405728*h^3*f(n+1)+23903*h^3*f(n+2)));

e3 := expand(-z[n]+(1/383201280*(-4207440*h^4*g(n+1/2)-930192*h^4*g(n+3/2)+371973*h^4*g(n)-3631932*h^4*g(n+1)-41259*h^4*g(n+2)+16136096*h^3*f(n+1/2)+3866720*h^3*f(n+3/2)+5752543*h^3*f(n)+5810400*h^3*f(n+1)+367681*h^3*f(n+2))+4*y[n+1/2]-3*y[n]+y[n+1])/h);

e4 := expand(-z[n+1/2]+(1/191600640*(376320*h^4*g(n+1/2)+118896*h^4*g(n+3/2)-29469*h^4*g(n)+532764*h^4*g(n+1)+5079*h^4*g(n+2)-5812112*h^3*f(n+1/2)-508016*h^3*f(n+3/2)-381553*h^3*f(n)-1236168*h^3*f(n+1)-45511*h^3*f(n+2))-y[n]+y[n+1])/h);

e5 := expand(-z[n+1]+(1/383201280*(-31920*h^4*g(n+1/2)-433776*h^4*g(n+3/2)+71547*h^4*g(n)-2519748*h^4*g(n+1)-17493*h^4*g(n+2)+18565216*h^3*f(n+1/2)+1933216*h^3*f(n+3/2)+885665*h^3*f(n)+10391328*h^3*f(n+1)+158015*h^3*f(n+2))-5*y[n+1/2]+y[n]+3*y[n+1])/h);

e6 := expand(-z[n+3/2]+(1/95800320*(250224*h^4*g(n+1/2)-730680*h^4*g(n+3/2)+61266*h^4*g(n)-1526256*h^4*g(n+1)-22044*h^4*g(n+2)+15680504*h^3*f(n+1/2)+4712456*h^3*f(n+3/2)+735469*h^3*f(n)+22576428*h^3*f(n+1)+203623*h^3*f(n+2))-8*y[n+1/2]+3*y[n]+5*y[n+1])/h);

e7 := expand(-z[n+2]+(1/383201280*(3873264*h^4*g(n+1/2)+332976*h^4*g(n+3/2)+497649*h^4*g(n)-1407564*h^4*g(n+1)-720255*h^4*g(n+2)+114710816*h^3*f(n+1/2)+93716192*h^3*f(n+3/2)+5705827*h^3*f(n)+191366496*h^3*f(n+1)+9635389*h^3*f(n+2))-12*y[n+1/2]+5*y[n]+7*y[n+1])/h);

e8 := expand(-p[n]+(1/191600640*(13423440*h^4*g(n+1/2)+3068304*h^4*g(n+3/2)-1621317*h^4*g(n)+11615292*h^4*g(n+1)+137451*h^4*g(n+2)-32503712*h^3*f(n+1/2)-12664928*h^3*f(n+3/2)-32539039*h^3*f(n)-16869600*h^3*f(n+1)-1223041*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e9 := expand(-p[n+1/2]+(1/191600640*(-3053856*h^4*g(n+1/2)-213216*h^4*g(n+3/2)+98049*h^4*g(n)-509436*h^4*g(n+1)-10191*h^4*g(n+2)-1045120*h^3*f(n+1/2)+831104*h^3*f(n+3/2)+1331083*h^3*f(n)-1207008*h^3*f(n+1)+89941*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e10 := expand(-p[n+1]+(1/63866880*(194160*h^4*g(n+1/2)-373968*h^4*g(n+3/2)+52329*h^4*g(n)-2514924*h^4*g(n+1)-14727*h^4*g(n+2)+14006304*h^3*f(n+1/2)+1695712*h^3*f(n+3/2)+634955*h^3*f(n)+15463008*h^3*f(n+1)+133461*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e11 := expand(-p[n+3/2]+(1/191600640*(1491168*h^4*g(n+1/2)-4758240*h^4*g(n+3/2)+190977*h^4*g(n)-509436*h^4*g(n+1)-103119*h^4*g(n+2)+46274944*h^3*f(n+1/2)+48151168*h^3*f(n+3/2)+2215307*h^3*f(n)+93985056*h^3*f(n+1)+974165*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2);

e12 := expand(-p[n+2]+(1/191600640*(4772688*h^4*g(n+1/2)+11719056*h^4*g(n+3/2)+338619*h^4*g(n)+11615292*h^4*g(n+1)-1822485*h^4*g(n+2)+59770976*h^3*f(n+1/2)+79609760*h^3*f(n+3/2)+3528289*h^3*f(n)+109647648*h^3*f(n+1)+34844287*h^3*f(n+2))-8*y[n+1/2]+4*y[n]+4*y[n+1])/h^2) end do;
M := {e || (1 .. 12)};

y_init := 1;

z_init := 0;

p_init := -2;

x_init := 0; A := 0; B := 1; N := 40;

h := evalf((B-A)/N); count := 1;

X := y[k], y[k+1/2], y[k+1], y[k+3/2], z[k], z[k+1/2], z[k+1], z[k+3/2], p[k], p[k+1/2], p[k+1], p[k+3/2];

step := seq(eval(x, x = n*h), n = 1 .. N);

y_exact := ([seq])(eval(3*cos(x)+(1/2)*x^2-2, x = n*h), n = 1 .. N);

z_exact := ([seq])(eval((1/3*(3*x^2+6*x+3))/(x^3+3*x^2+3*x+1), x = n*h), n = 1 .. N);

p_exact := ([seq])(eval((1/3*(6*x+6))/(x^3+3*x^2+3*x+1)-(1/3)*(3*x^2+6*x+3)^2/(x^3+3*x^2+3*x+1)^2, x = n*h), n = 1 .. N);
vars := seq(X, k = 1);
printf("\n%4s%13s%15s%15s\n", "@", "y_Num", "y_Exact", "y_Error");

for q to N do

for ix to 4 do

x[ix] := h*ix+x_init end do;

result := eval(`<,>`(vars), fsolve(eval(M, [x[0] = x_init, x[1/2] = x_init, x[3/2] = x_init, y[0] = y_init, y[1/2] = y_init, y[3/2] = y_init, z[0] = z_init, z[1/2] = z_init, z[3/2] = z_init, p[0] = p_init, p[1/2] = p_init, p[3/2] = p_init]), {vars}));

for k to 4 do

printf("%5.2f %14.15f", step[count], result[k]);

printf("%20.15f %10.18G \n", y_exact[count], abs(result[k]-y_exact[count]));

count := count+1;

P := [result[k]]

end do;

x_init := x[ix-1];

y_init := result[4];

z_init := result[8];

p_init := result[12]

end do;

 

please that is the code i write to solve the problem after using the matrix form to generate the value but is given me error of the form


   @        y_Num        y_Exact        y_Error
Error, invalid input: eval received fsolve({-6398.00004614630940+6400.00000000000000*y[1], -6397.99992849910140+6400.00000000000000*y[1], -6397.99909739580050+6400.00000000000000*y[1], -199.999989717789185+200.000000000000000*y[1], -40.0000000791700798+40.0000000000000000*y[1], -2.99999993737911015+3*y[1], 39.999999768462113+40.0000000000000000*y[1], -p[1]-6399.99961623646730+6400.00000000000000*y[1], -p[2]-6399.99798489466010+6400.00000000000000*y[1], -y[2]-4.99999972458202552+6*y[1], -z[1]-159.999999048856193+120.000000000000000*y[1], -z[2]-279.999973921987948+280.000000000000000*y[1]}, {p[1], p[2], p[3/2], p[5/2], y[1], y[2], y[3/2], y[5/...
 

I have the following function which came from a collaborator of a collaborator. It computes a generating function for a family of function's we're using.

GF_Generate := proc (n) 
	local summand, i, j;
	summand := U[0]^x[0]*mul(U[i]^y[i], i = 1 .. n)*mul(binomial(x[0]+add(w[j], j = 1 .. i), y[i])*p^y[i]*(1-p)^(x[0]+add(w[j], j = 1 .. i)-y[i])*binomial(x[0]-1+add(w[j], j = 1 .. i), x[0]-1+add(w[j], j = 1 .. i-1))*v[i]^(x[0]+add(w[j], j = 1 .. i-1))*(1-v[i])^w[i], i = 1 .. n);

	for j from n by -1 to 1 do summand := normal(sum(summand, y[j] = 0 .. infinity)) end do;
	for j from n by -1 to 1 do summand := normal(sum(summand, w[j] = 0 .. infinity)) end do;
	
	sum(summand, x[0] = 0 .. infinity) 
end proc;

For arguments of 2 and 3 it's quick and works fine on Maple18 (tested both GUI and terminal client on OS X), Maple2015 (tested terminal client only on RHEL linux), but generates a "too many levlels of recursion" error in Maple2016 (tested terminal client only on RHEL linux; same server as Maple2015 was tested). It's slow for arguments of 4 and above (45 minutes for n=4 on my mac laptop), so I haven't tested it thoroughly with larger arguments.

Any idea why this code fails in Maple 2016?

 

Hi Guys,

I will like to know how I can use Maple to plot a line of best fit given some data.

e.g for data like [x = 21.2, 24.7, 20.8, 20.8, 20.3] and [y = 16.6, 19.7,16.4,16.8,16.9].

Thanks.

I want to write a procedure ThirdDer := proc(f,x0,h) which, given the funcion f, the point x0 and the step size h returns the value of f'''(x0). where f'''(x0) = (f(x0 +2h)−2f(x0 +h)+2f(x0 −h)−f(x0 −2h))/2h^3 

help

I tried splitting f''' up and assigning the 4 different parts as a letter then putting it all together but that didnt work..

Morning all,

I repeatedly solve (command solve) a collection of systems of inequalies. Some of them can have no solution, but I am able to check if a solution has been found or not, and then take some decision about the system in question.

I have placed a few print commands at different critical locations within the loop where those systems are constructed and possibly solved.
Every time solve fails finding a solution it returns me a "no solution found" warning.
In order to keep my printings readable, could it be possible to avoid those warnings ?
Is there some "try & catch" like mechanism to manage warnings ?

Thank you all in advance

I can't understand how to install this package "SADE" in Maple 17. Secondly, I am new to Maple. So Please guide me the process to install this package and how to use it. Thanks!

I'm trying plot  with implicitplot a expresion which involve Lambert W, but the result is very confuse, is it normal? Could i improve the result?, how?. Thank!

 

I've encountered a very strange issue with Maple.

The result returns differently with solve and fsolve after/before a variable is given a certain value. See attachment.

The result comes from solve (with variable epsilon) returns value of the same variable with imaginary part while the fsolve returns the correct answer.

Now how can I achieve the same result as fsolve via solve?

Thanks!

Maple_Question_Solve_Fsolve.mw

Maple_Question_Solve_Fsolve.pdf  (exported PDF from Maple)

Hi everyone,

 

I'm to simplify the expression cos(x)/sin(x) to cot(x). None of the "simplify" commands seem to work, I've tried assigning the expression to a name "a", then using the "simplify(a,trig)" command and it doesn't work either.

Anyone have any ideas on how I can tell maple to simplify this?

I've got some points:

I have to find the (equation of) line which has minimum distance from these points but the distance formula that I have to use is:
 (-m*x[i]-q+y[i])^2

I think we should settle with a for loop.

Thanks in advance

 

 

Hey guyz, I am in trouble with calculation attached integral. it is a simple function but a bit long. I can't solve it with maple, Do U have any idea?

 

 

intg.mw

 

 

hello, i just try to plot the relation between my outputs (u, and phat) with i from 0 to 10 , but i have aproblem any suggestions? 
 

M := .4556;

.4556

(1)

K := 18;

18

(2)

c := .2865;

.2865

(3)

Nabla(t) := .1NULL

.1

(4)

Khat := 206.1055;

206.1055

(5)

NULL

N := 10NULL

10

(6)

``

NULL

NULL

a__1 := 4/.1^2*.4556+2/(.1)*.2865NULL

187.9700000

(7)

``

NULL

NULL

a__2 := 4/(.1)*.4556+.2865NULL

18.51050000

(8)

``

NULL

NULL

a__3 := .4556NULL

.4556

(9)

NULL

NULLNULL

fu := Array(0 .. 10):

p:=Array(0..10):
  p[0]:=0:
  for i from 0 to 4 do
      p[i+1]:=50*sin(3.14*(i+1)*(4)/0.6):
      phat[i+1]:= p[i+1]+((7)*u[i])+((8)*u__dot[i])+((9)*u__doubledot[i]):
      u[i+1]:= phat[i+1]/(5):
      u__dot[i+1]:=(20*(u[i+1]-u[i]))-u__dot[i]:
      u__doubledot[i+1]:= ((400*(u[i+1]-u[i]))-(40*u__dot[i])-(u__doubledot[i])):
end do;
for i from 5 to 9 do
      p[i+1]:=0.0:
      phat[i+1]:= p[i+1]+((7)*u[i])+((8)*u__dot[i])+((9)*u__doubledot[i]):
      u[i+1]:= phat[i+1]/(5):
      u__dot[i+1]:=(20*(u[i+1]-u[i]))-u__dot[i]:
      u__doubledot[i+1]:= ((400*(u[i+1]-u[i]))-(40*u__dot[i])-(u__doubledot[i])):
  end do;

 

 

24.98850513

 

24.98850513

 

.1212413309

 

2.424826618

 

48.49653236

 

43.28799198

 

133.0574982

 

.6455795610

 

8.061937982

 

64.24569494

 

49.99998414

 

349.8504158

 

1.697433673

 

12.97514426

 

34.01843056

 

43.32779001

 

618.0696023

 

2.998802081

 

13.05222390

 

-32.47683816

 

25.05744793

 

815.5490181

 

3.956949320

 

6.11072088

 

-106.3532218

 

0.

 

808.4457346

 

3.922485012

 

-6.80000704

 

-151.8613364

 

0.

 

542.2499525

 

2.630933927

 

-19.03101466

 

-92.7588160

 

0.

 

100.0021368

 

.4851987783

 

-23.88368831

 

-4.2946573

 

0.

 

-352.8528440

 

-1.712001106

 

-20.06030938

 

80.7622360

 

0.

 

-656.3359300

 

-3.184465868

 

-9.38898586

 

132.6642346

(10)

 

``

fd_table:=eval(seq[u(i),phat(i)],i=0..N);

seq[(table( [( 0 ) = 0, ( 1 ) = .1212413309, ( 2 ) = .6455795610, ( 3 ) = 1.697433673, ( 4 ) = 2.998802081, ( 5 ) = 3.956949320, ( 6 ) = 3.922485012, ( 7 ) = 2.630933927, ( 9 ) = -1.712001106, ( 8 ) = .4851987783, ( 10 ) = -3.184465868 ] ))('i'), (table( [( 1 ) = 24.98850513, ( 2 ) = 133.0574982, ( 3 ) = 349.8504158, ( 4 ) = 618.0696023, ( 5 ) = 815.5490181, ( 6 ) = 808.4457346, ( 7 ) = 542.2499525, ( 9 ) = -352.8528440, ( 8 ) = 100.0021368, ( 10 ) = -656.3359300 ] ))('i')]

(11)

``

plot([u(i+1), p(i+1)])

Error, (in plot) invalid input: assigned expects its 1st argument, n, to be of type assignable, but received table( [( 0 ) = 0, ( 1 ) = .1212413309, ( 2 ) = .6455795610, ( 3 ) = 1.697433673, ( 4 ) = 2.998802081, ( 5 ) = 3.956949320, ( 6 ) = 3.922485012, ( 7 ) = 2.630933927, ( 9 ) = -1.712001106, ( 8 ) = .4851987783, ( 10 ) = -3.184465868 ] )

 

``

``


 

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