Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am looking at the help pages, and I see Maple code using symbols never seen in Maple language before.

I tried to do ?&under to get help on this new Maple language command/symbol, but help does not show it. I read help Neutral Operators but do not understand it.

What does the following mean in plain Maple code?

And what does the following mean using Plain Maple code:

 

Could the above be written without using these `&` things?  I am having hard time understanding what the code is doing because of these. Never used them before.

These are from help on "Definition of a Structured Type in Maple"

I want to compute the following supremum of the function.

I'll write in Latex code.

I have the following term which I want to estimate:

\delta_1(\epsilon):= \sup_{|x|<100}\sup_{ 0<= t<1/\epsilon} \epsilon \cdot |\int_0^t [ f(x,\cos s , \sin s , p_0(t)+q_0(s))-g(x,t)]ds|

where p_0(t) is an unknown function that depends on t alone.

f(x,y_1,y_2,z):=x+(y_1^2)*z

g(x,t):= \lim_{T\to \infty} 1/T \int_0^T f(x,\cos s , \sin s , p_0(t)+q_0(s))ds

q_0(s):= \exp(-s)(q_0(0)+\int_0^s (h(x_0(0),\cos(r), \sin(r))-p_0(0))dr)

where h(x,y_1,y_2):=y_1^2.

Can someone lend me a hand?

Thanks!

 

Please help me to remove error from the plotting. Here I have attached a mapple file

.u_nonlinerafit.mw

I figured out what the interpolation is, but can someone please give me a reference for the publication of the person that discovered that this works thankyou. 

 


 

PolyI1 := proc (N, n) options operator, arrow; (-1)^N*(sum(n*factorial(n-1)*(-1)^k*a[k]/(factorial(n-N-1)*(n-k)*factorial(k)*factorial(N-k)), k = 0 .. N)) end proc

proc (N, n) options operator, arrow; (-1)^N*(sum(n*factorial(n-1)*(-1)^k*a[k]/(factorial(n-N-1)*(n-k)*factorial(k)*factorial(N-k)), k = 0 .. N)) end proc

(1)

PolyI2 := proc (N, n) options operator, arrow; CurveFitting[PolynomialInterpolation]([seq([k, a[k]], k = 0 .. N)], n) end proc

proc (N, n) options operator, arrow; CurveFitting[PolynomialInterpolation]([seq([k, a[k]], k = 0 .. N)], n) end proc

(2)

collect(expand(PolyI1(2, n)), n); PolyI2(2, n)

((1/2)*a[2]-a[1]+(1/2)*a[0])*n^2+(-(1/2)*a[2]+2*a[1]-(3/2)*a[0])*n+a[0]

 

((1/2)*a[2]-a[1]+(1/2)*a[0])*n^2+(-(1/2)*a[2]+2*a[1]-(3/2)*a[0])*n+a[0]

(3)

collect(expand(PolyI1(3, n)), n); PolyI2(3, n)

((1/6)*a[3]-(1/2)*a[2]+(1/2)*a[1]-(1/6)*a[0])*n^3+(-(1/2)*a[3]+a[0]-(5/2)*a[1]+2*a[2])*n^2+(-(3/2)*a[2]+(1/3)*a[3]-(11/6)*a[0]+3*a[1])*n+a[0]

 

((1/6)*a[3]-(1/2)*a[2]+(1/2)*a[1]-(1/6)*a[0])*n^3+(-(1/2)*a[3]+a[0]-(5/2)*a[1]+2*a[2])*n^2+(-(3/2)*a[2]+(1/3)*a[3]-(11/6)*a[0]+3*a[1])*n+a[0]

(4)

collect(expand(PolyI1(4, n)), n); PolyI2(4, n)

(-(1/6)*a[1]+(1/4)*a[2]-(1/6)*a[3]+(1/24)*a[0]+(1/24)*a[4])*n^4+(-(5/12)*a[0]+(3/2)*a[1]-2*a[2]+(7/6)*a[3]-(1/4)*a[4])*n^3+((35/24)*a[0]-(13/3)*a[1]+(19/4)*a[2]-(7/3)*a[3]+(11/24)*a[4])*n^2+(-(25/12)*a[0]-(1/4)*a[4]+4*a[1]-3*a[2]+(4/3)*a[3])*n+a[0]

 

(-(1/6)*a[1]+(1/4)*a[2]-(1/6)*a[3]+(1/24)*a[0]+(1/24)*a[4])*n^4+(-(5/12)*a[0]+(3/2)*a[1]-2*a[2]+(7/6)*a[3]-(1/4)*a[4])*n^3+((35/24)*a[0]-(13/3)*a[1]+(19/4)*a[2]-(7/3)*a[3]+(11/24)*a[4])*n^2+(-(25/12)*a[0]-(1/4)*a[4]+4*a[1]-3*a[2]+(4/3)*a[3])*n+a[0]

(5)

collect(expand(PolyI1(5, n)), n); PolyI2(5, n)

((1/12)*a[3]-(1/120)*a[0]+(1/24)*a[1]-(1/12)*a[2]-(1/24)*a[4]+(1/120)*a[5])*n^5+(-a[3]+(11/24)*a[4]+(1/8)*a[0]-(7/12)*a[1]+(13/12)*a[2]-(1/12)*a[5])*n^4+((49/12)*a[3]-(41/24)*a[4]+(7/24)*a[5]-(17/24)*a[0]+(71/24)*a[1]-(59/12)*a[2])*n^3+((15/8)*a[0]-(13/2)*a[3]+(61/24)*a[4]-(5/12)*a[5]-(77/12)*a[1]+(107/12)*a[2])*n^2+(-(137/60)*a[0]+5*a[1]+(10/3)*a[3]-(5/4)*a[4]+(1/5)*a[5]-5*a[2])*n+a[0]

 

((1/12)*a[3]-(1/120)*a[0]+(1/24)*a[1]-(1/12)*a[2]-(1/24)*a[4]+(1/120)*a[5])*n^5+(-a[3]+(11/24)*a[4]+(1/8)*a[0]-(7/12)*a[1]+(13/12)*a[2]-(1/12)*a[5])*n^4+((49/12)*a[3]-(41/24)*a[4]+(7/24)*a[5]-(17/24)*a[0]+(71/24)*a[1]-(59/12)*a[2])*n^3+((15/8)*a[0]-(13/2)*a[3]+(61/24)*a[4]-(5/12)*a[5]-(77/12)*a[1]+(107/12)*a[2])*n^2+(-(137/60)*a[0]+5*a[1]+(10/3)*a[3]-(5/4)*a[4]+(1/5)*a[5]-5*a[2])*n+a[0]

(6)

NULL


 

Download 21052018002.mw

Tonight I came across something that OEIS had referenced as the maximum fermi dirac divisor of a number, so i decided it might be a good idea to study this concept by first figuring out how to enumerate the subset of these divisors.

But rather than specifically about this subject, i wanted to ask if my way of "enumeration of numbers meeting specific criteria" is inferior to other methods i have seen. For example this guy named Alois Heinz uses select in the following manner to obtain  the least divisor of a number that is greater than it's square root:

 

Where as I have always been constructing piecewise expressions as seen in the example of what i have been doing tonight:


 

with(numtheory):

`&Fscr;` := proc (n) options operator, arrow; {seq(seq(piecewise(frac(ln(ln(divisors(n)[k])/ln(ithprime(j)))/ln(2)) = 0 and divisors(n)[k] <> 1 and divisors(n)[k] <> 2, divisors(n)[k], NULL), j = 1 .. pi(divisors(n)[k])), k = 1 .. nops(divisors(n)))} end proc

`&Fscr;`(200000)

{4, 5, 16, 25, 625}

(1)

``


 

Download 21052018.mw

 

So basically, because it is very hard for me to break habits once i have formed them, my question is, is it going to be beneficial for me to switch to this persons method of enumeration, or am i ok just to continue my way?

 

 

Sorry I am just having difficulties understanding what this error means exactly, normally maple returns an error message stating the procedure that was being executed when the error was encountered, but in this situation it says (in unknown) which doesnt really make sense, i mean how can a procedure unknown to maple be being executed in the first place, or is this a procedure name itself?

Up to swMATH   Maple is referenced in 4183 articles   in zbMATH   and

up to swMATH Mathematica is referenced in 4654 articles  in zbMATH.

These numbers are sure unexpected to me. I think the ratio of the prices of academic editions MMA/Maple (which approximately equals 2 ) truly reflects their abilities.

Hi.

I am attempting to obtain a solution to, what appears to be a simple PDE system (3 equations) and have encountered an error with the initial / boundary conditions. Can anyone provide and guidance / help with this?

The worksheet follows. 

PDE_System.mw

Thanks in advance.

I'm  trying to converting an infinite series from several terms to sigma form.

The series in question is:

x-x^2/(t*Log[t])+(2/3)*x^3/(t^2*Log[t]^2)+(-1/(2*t^3*Log[t]^3)-1/(4*t^3*Log[t]^2)-1/(6*t^3*Log[t]))*x^4+(2/(5*t^4*Log[t]^4)+2/(5*t^4*Log[t]^3)+4/(15*t^4*Log[t]^2))*x^5+(-1/(3*t^5*Log[t]^5)-1/(2*t^5*Log[t]^4)-5/(12*t^5*Log[t]^3)-5/(36*t^5*Log[t]^2)-1/(15*t^5*Log[t]))*x^6+(2/(7*t^6*Log[t]^6)+4/(7*t^6*Log[t]^5)+25/(42*t^6*Log[t]^4)+1/(3*t^6*Log[t]^3)+46/(315*t^6*Log[t]^2))*x^7+(-1/(4*t^7*Log[t]^7)-5/(8*t^7*Log[t]^6)-19/(24*t^7*Log[t]^5)-19/(32*t^7*Log[t]^4)-19/(60*t^7*Log[t]^3)-7/(80*t^7*Log[t]^2)-1/(28*t^7*Log[t]))*x^8+(2/(9*t^8*Log[t]^8)+2/(3*t^8*Log[t]^7)+1/(t^8*Log[t]^6)+25/(27*t^8*Log[t]^5)+163/(270*t^8*Log[t]^4)+106/(405*t^8*Log[t]^3)+88/(945*t^8*Log[t]^2))*x^9+(-1/(5*t^9*Log[t]^9)-7/(10*t^9*Log[t]^8)-73/(60*t^9*Log[t]^7)-4/(3*t^9*Log[t]^6)-149/(144*t^9*Log[t]^5)-691/(1200*t^9*Log[t]^4)-18569/(75600*t^9*Log[t]^3)-761/(12600*t^9*Log[t]^2)-1/(45*t^9*Log[t]))*x^10I've attached the worksheet 1.mw.

The example below works but not for the above I just get:

Error, invalid arguments to coeffs

Not sure where I'm going wrong any idea how to do this?

EXAMPLE that works from https://math.stackexchange.com/questions/2786296/strategy-or-software-for-representing-infinite-series-in-sigma-form

I've also attached the worksheet for this 2.mw

=>

S:= 1-x+4/3*(x^2)-2*x^3+16/5*(x^4)-16/3*(x^5)+64/7*(x^6)-16*x^7+256/9*(x^8)-256/5*(x^9)+1024/11*(x^10);

Coeffs:= [seq(coeff(S, x, j), j=0..10)];

g:= gfun:-guessgf(Coeffs,x);

convert(g[1], FPS, x);

results in:

Sum((-1)^k*2^k*x^k/(k+1), k = 0 .. infinity)

or 

rec:= gfun:-listtorec(Coeffs, a(n));

aa:= rsolve(rec[1],a(n));

Sum(aa*x^n, n=0..infinity);

results in the same desired result.

 

I have little bit knowledge about mapple and tried to solve nonlinear system of partial differential equation by numerical method. The same process I have done for solving system of ordinary partial differential equation.

For the system of ordinary differential equations, I have used the following process

ode:=(&DifferentialD;)/(&DifferentialD;t) x[1](t)=-x[1](t)+95* x[2](t), (&DifferentialD;)/(&DifferentialD;t) x[2](t)=-x[1](t)-97*x[2](t): ics:=x[1](0)=1,x[2](0)=1: 

dsol := dsolve({ics, ode}, numeric, method = rosenbrock, range = 0 .. 20, stiff = true)

p1:=odeplot`(dsol,[t,x[1](t)-x1E(t)],color=blue):

p2:=odeplot`(dsol,[t,x[2](t)-x2E(t)],color=green) :  

display({p1,p2});

points := 8000;
aa := 0; bb := 10;
#`SAMPLING OF NUMERICAL SOLUTION`

 ti:=[seq(rhs(dsol((i*bb)/(points))[1]),i=0..points)];

x1i:=[seq(rhs(dsol((i*bb)/(points))[2]),i=0..points)];

x2i:=[seq(rhs(dsol((i*bb)/(points))[3]),i=0..points)];

T:=Vector(ti,datatype=float):

 X1:=Vector(x1i,datatype=float): 

X2:=Vector(x2i,datatype=float): 

nfop:=optimalitytolerance=1e-20,iterationlimit=10000,method=modifiednewton: newU:=unapply(convert(NonlinearFit(eval(U(t),p=1), T,X1,t, nfop),rational),t): newV:=unapply(convert(NonlinearFit(eval(V(t),p=1), T,X2,t, nfop),rational) ,t)

Finally i have solution for U(t), V(t)

 newU(t);  

newV(t);

But in case of PDE I have no idea how the similar process will be excute?

The PDE I would like to solve is

PDESYS := [diff(U(x, t), t)-(diff(U(x, t), x, x))-2*U(x, t)*(diff(U(x, t), x))+diff(U(x, t)*V(x, t), x), diff(V(x, t), t)-(diff(V(x, t), x, x))-2*V(x, t)*(diff(V(x, t), x))+diff(U(x, t)*V(x, t), x)]

ICs := [u(x, 0) = sin(x), v(x, 0) = sin(x)]

M:=5;N:=4:

U:=t->((&sum;)u[j](t)*p^(j))/(1+(&sum;)alpha[j]*t^(j)p^(j)):         V:=t->((&sum;)v[j](t)*p^(j))/(1+(&sum;)beta[j]*t^(j)p^(j)):

U(x, t) = (sin(x)+sin(x)*a[1]*x*t-sin(x)*t+(cos(x)*sin(x)*b[1]*t^2*x+(1/2)*sin(x)*t^2-sin(x)*((1/2)*cos(x)*a[1]*x*t^2+(1/2)*sin(x)*a[1]*t^2-(1/2)*cos(x)*t^2)-cos(x)*((1/2)*sin(x)*b[1]*x*t^2-(1/2)*sin(x)*t^2)+cos(x)*((1/2)*sin(x)*a[1]*x*t^2-(1/2)*sin(x)*t^2)-sin(x)*((1/2)*cos(x)*b[1]*x*t^2+(1/2)*sin(x)*b[1]*t^2-(1/2)*cos(x)*t^2)+a[1]*x*((1/2)*sin(x)*a[1]*x*t^2-(1/2)*sin(x)*t^2)-cos(x)*sin(x)*t^2+sin(x)*a[2]*t^2*x^2+(1/2*(sin(x)*a[1]*x-sin(x)))*a[1]*t^2*x-sin(x)*a[1]^2*x^2*t^2+(1/2)*sin(x)^2*a[1]*t^2+(1/2)*sin(x)^2*b[1]*t^2))/(t^2*x^2*a[2]+t*x*a[1]+1)

V(x, t) = sin(x)+sin(x)*b[1]*x*t-sin(x)*t+(cos(x)*sin(x)*a[1]*t^2*x+sin(x)*b[2]*t^2*x^2+(1/2*(sin(x)*b[1]*x-sin(x)))*b[1]*t^2*x-sin(x)*b[1]^2*x^2*t^2+(1/2)*sin(x)*t^2-sin(x)*((1/2)*cos(x)*a[1]*x*t^2+(1/2)*sin(x)*a[1]*t^2-(1/2)*cos(x)*t^2)+cos(x)*((1/2)*sin(x)*b[1]*x*t^2-(1/2)*sin(x)*t^2)-cos(x)*((1/2)*sin(x)*a[1]*x*t^2-(1/2)*sin(x)*t^2)-sin(x)*((1/2)*cos(x)*b[1]*x*t^2+(1/2)*sin(x)*b[1]*t^2-(1/2)*cos(x)*t^2)-cos(x)*sin(x)*t^2+(1/2)*sin(x)^2*a[1]*t^2+(1/2)*sin(x)^2*b[1]*t^2+b[1]*x*((1/2)*sin(x)*b[1]*x*t^2-(1/2)*sin(x)*t^2)

For numerical process

PDE := [diff(w(x, t), t)-(diff(w(x, t), x, x))-2*w(x, t)*(diff(w(x, t), x))+diff(w(x, t)*r(x, t), x), diff(r(x, t), t)-(diff(r(x, t), x, x))-2*r(x, t)*(diff(r(x, t), x))+diff(w(x, t)*r(x, t), x)]

IBC := [u(x, 0) = sin(x), v(x, 0) = sin(x)]

Which numerical method is suitable for this type of equation and how that method is execute in mapple?

I am attaching a code in case of ordinary differential equ .

Odecode.mw

 

 

Hellow , Any body can help me to write the codes for the differential equation to solve by Galerkin finite element method by four elements by taking step size h=pi/2 and compare with homotropy method by plotting the graph of Galerkin method, homotropy method and exact, here is my codes

ode := diff(y(x), x, x) + y(x)-1=0:
ics := y(0) = 0, y(2*pi) = 0:
dsolve({ics, ode}):
 

How to do a full reinstall so that no settings are kept?

I tried deleting the maple 2017 folder in program files after I uninstalled but that did not help.

Hello everybody! 

I just wrote my first Maple Worksheet for a Uni course and was trying to export it to LaTeX for the report that I have to hand in, but sadly it isn't working properly. I managed to get it to produce an output PDF in LaTeX, but the formatting is horrible and for some reason all text appears twice. 

I already searched for other threads on this topic, but all of them appear to be pretty old and I wanted to aks if anyone has andy advice/experiences on how to make the LaTeX export work with more current Maple versions. 

I'd be grateful for any advice! 

- Chris 

Hi everyone 

I need help, I have downloaded Maple, and I have read about the student package, which can show the step by step solution, I would like to see the step by step solution than just a final solution to the equation problem. 

I have the maple 2017, but does anyone know, how to download this package, and use it in maple?

https://www.maplesoft.com/support/help/maple/view.aspx?path=Student%2FBasics%2FLinearSolveSteps 

There is several links to this, but I cant find it where to download the package, I hope that someone is able to help me 

 

Helo, guys, i am a beginner here I want solve a system of first order differential equation using RK4. Please I need help please.

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