Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

I input print(lambda*I) and I get I*lambda (Greek lambda symbol); Why is the order reversed?
Maple 13 (GUI) is doing it.
Thanks!

mapleatha

The expression exp(2*t) gives us the number e^(2t). Can we get rid of the parentheses around 2t?
Thank you!

mapleatha

 

 I wand to plot the following expression involving an imaginary number. Can I get some help??

 

((1/10)*exp((2/135)*sqrt(-11)*sqrt(225)*t-(2/3*I)*x+1/15)/((3/10)*exp((2/135)*sqrt(-11)*sqrt(225)*t-(2/3*I)*x+1/5)

 

 


 

`` 

``

sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2 = 0, diff(diff(diff(g(eta), eta), eta), eta)+f(eta)*(diff(diff(g(eta), eta), eta))+2*g(eta)*(diff(diff(f(eta), eta), eta))-3*(diff(g(eta), eta))*(diff(f(eta), eta)) = 0, (diff(diff(g(eta), eta), eta))*(diff(diff(g(eta), eta), eta))-g(eta)*(diff(diff(diff(g(eta), eta), eta), eta))*f(0) = 1, (D(f))(0) = 1, (D(f))(5) = 0, g(0) = 1, (D(g))(0) = -1, (D(g))(5) = 0], numeric, method = bvp); plots[odeplot](sol1, color = red)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

 

``

``


 In this link i attache the code , which is working on this Download Three_euqtions.mw and i got an error which is i couldnot understand. So, kindly can you help on this ??

Hi MaplePrimes,

another_recursive_sequence.mw

another_recursive_sequence.pdf

These two files have the same content.  One is a .pdf and the other is a Maple Worksheet.  I explore integer sequences of the form - 

a(r) = c*a(r-1)+d*a(r-2) with a(1) and a(2) given.

Some of these sequences are in (the Online Encyclopedia of Integer Sequences) OEIS.org and some are not.  If we restrict c to 1 and assume that a(1)=1 and a(2) = 2 we have the parameter d remaining.  See additional webpage - 

https://sites.google.com/site/recrusivefunction/

Let me know if you like the code.

Regards,

Matt

 

What method is implemented in the procedure int with option numeric? Does the method depend on the integrand? Where can I find this information? 

I am trying to solve the particular system of partial differential equation. But I get the following error.pdsolve.mw
 

"restart;  f(x,y):=x*y:  yy:={diff(f(x,y),x)=0,diff(f(x,y),y)=0}:  ee:=pdsolve(yy,numeric);"

Error, (in pdsolve/numeric) invalid subscript selector

 

``


 

Download pdsolve.mw

 

HI MaplePrimes,

The input -

rsolve(f(n)=f(n-1)+10*f(n-2),f(k))

returns a large expression.

My had calculations reduce this to

f(k) = [(41-19*sqrt(41))/820]*[((1-sqrt(41))/2)^k+((1+sqrt(41))/2)^k)].

There may be an error.

We let f(1)=1 and f(2)=2.

The sequence, starting with 1 should read -

1,2,12,32,152,472,...

What is the correct expression for f(k)?

 

Regards,

Matt

Hi Mapleprimes people and robots,


My question is regarding a recursive sequence.  It can be defined non-recursively as - 


a(r) :=  0.8*3^r + 0.2*(-2)^r.

The first few terms are - 

1,2,8,20,68,188, and so on.

Here is my Maple Worksheet.
recursive_sequence_A133467.mw      recursive_sequence_A133467.pdf

I want some Maple code that will produce 30 terms of this sequence.  It is defined as

s[1]:=1:
s[2]:=2:

for n>2 we let s[n] = s[n-1] + 6*s[n-2].

Let me know if my question does not make sense.

Regards,
Matt

 

HI experts,

fibonacci_sequence_with_coefficient.pdf

Is there a Last name associated with a double 'hailstone problem' with variable integer coefficients?

Just curious.

Regards,

Matt

 

I am trying to solve system consisting of two equations and two unknowns. I tried solve but it gives back unevaluated then I tried fsolve which gives an error.
 

restart; x := 2.891022275*`ε`^4*sin(phi)^5*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.9885168554*`ε`^8*sin(phi)^9*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi); y := 2.891022275*`ε`^4*sin(phi)^5*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.9885168554*`ε`^8*sin(phi)^9*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi); evalf(solve({x = 0, y = 0}, {phi, `ε`})); fsolve({x = 0, y = 0}, {phi, `ε`})

.9885168554*`ε`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+2.891022275*`ε`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

.9885168554*`ε`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+2.891022275*`ε`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

{phi = 0., `ε` = `ε`}, {phi = 1.570796327, `ε` = `ε`}, {phi = phi, `ε` = RootOf(1560418629*_Z^18+(47406901510+493307879100*sin(phi)^2)*_Z^16+(40772142920000*sin(phi)^4+9608710101000*sin(phi)^2+958254350600)*_Z^14+(14148147310000+124975377900000*sin(phi)^2+534992600200000*sin(phi)^4+1277730241000000*sin(phi)^6)*_Z^12+(11242690220000000*sin(phi)^6+1186386550000000*sin(phi)^2+17424832170000000*sin(phi)^8+156264947800000+4588193106000000*sin(phi)^4)*_Z^10+(8234222560000000*sin(phi)^2+61944229700000000*sin(phi)^6+98851685540000000*sin(phi)^8+108012832000000000*sin(phi)^10+27756452360000000*sin(phi)^4+1283200926000000)*_Z^8+(7437311918000000+114825016900000000*sin(phi)^4+297577152600000000*sin(phi)^12+325818464400000000*sin(phi)^8+365611302800000000*sin(phi)^10+224213950200000000*sin(phi)^6+39816168440000000*sin(phi)^2)*_Z^6+(485772994700000000*sin(phi)^6+628227500400000000*sin(phi)^10+522269744600000000*sin(phi)^12+329395988600000000*sin(phi)^14+25653813580000000+617046303500000000*sin(phi)^8+116888409900000000*sin(phi)^2+289102227500000000*sin(phi)^4)*_Z^4+(22127156830000000+137581086300000000*sin(phi)^2+468911919600000000*sin(phi)^10+352010205100000000*sin(phi)^12+225275316300000000*sin(phi)^14+528250625500000000*sin(phi)^8+327003543500000000*sin(phi)^4+113436430000000000*sin(phi)^16+482074590900000000*sin(phi)^6)*_Z^2-62572261930000000-13317339210000000*sin(phi)^2+12655803050000000*sin(phi)^16+54673602200000000*sin(phi)^4+86678520620000000*sin(phi)^8+43371363110000000*sin(phi)^12+66451398020000000*sin(phi)^10+88614086100000000*sin(phi)^6+24941899980000000*sin(phi)^14+5208654259000000*sin(phi)^18)}

 

Error, (in fsolve) number of equations, 1, does not match number of variables, 2

 

``


 

Download equations_solve.mw

 

the program shows that the error please verify it sirprogram11.mw

I am trying to evaluate the following double integral where hypergeom([x,1/2],[3/2],C) is gauss hypergeometric function 2f1. maple gives back it unevaluated. I doubt it may be due to slow convergence of hypergeometric function. 
 

restart; x := (1/6)*Pi; evalf(int(evalf(int(cos(x)*hypergeom([x, 1/2], [3/2], sin(x)/(r*cos(x)+k-2*r*sin(x))^2)/(r*sin(x)^2+r*cos(x)+k)^4, k = 0 .. 10)), r = 1 .. 2))

Int(Int(.8660254040*hypergeom([.5000000000, .5235987758], [1.500000000], .5000000000/(-.1339745960*r+k)^2)/(1.116025404*r+k)^4, k = 0. .. 10.), r = 1. .. 2.)

(1)

``


 

Download DOUBLE_INT_2.mw

I am trying to evaluate the following triple integral but it takes much time so i kill the job.


 

restart; R := 5; KK := proc (theta) options operator, arrow; evalf(int(int(int(1/(R*sin(theta)^2+(R*cos(theta)+Z)^2+(2*R*k.sin(theta))*cos(p))^2, p = 0 .. 2*Pi), Z = 0 .. 60), k = 1 .. 10, numeric)) end proc; evalf(KK((1/6)*Pi))

Warning,  computation interrupted

 

``


 

Download int_maple_prime2.mw

hi

i want to solve a function which contains below series, but I can't.

SS:=sum(F[k-m]*sum(F[m-L]*sum(F[L-j]*F[j],j=0..L),L=0..m),m=0..k);

or

SS:sum(F[k-m],m=0..k)*sum(F[m-L],L=0..m)*sum(F[L-j]*F[j],j=0..L);

eq:=(-1/(k+1))*(F[k]+0.5*sum((k-m+1)*F[k-m+1]*F[m],m=0..k)+0.05*SS);

n:=8;
for k from 0 to n do
F[k+1]:=solve(eq);
end do;

with the first SS I have gotten a wrong nswer and with the second SS this error has been seen:

Error, (in solve) cannot solve expressions with sum(F[L-j]*F[j], j = 0 .. L) for F[j]

is there qny one hepl me please.

thanks

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