Maple 13 Questions and Posts

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

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? 

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

I'm having a trouble with this trivial code in Maple. The output is, well, ... stupid ! I'm askingMaple to do a vectorial sum and substraction of 5 cross products, and what I get is silly : a sum of vectors, but it doesn't give the total vector ! What the hell !?

with(linalg):
with(DEtools):

ly := 9.4607*10^15:
M0 := 1.99*10^30:

M1 := 2.20*M0:
M2 := 2.00*M0:
M3 := 1.50*M0:
M4 := 3.00*M0:

r1 := [-3, 3, 0]*ly:
r2 := [0, -2, 0]*ly:
r3 := [1, 2, 0]*ly:
r4 := [6, 4, 0]*ly:

v1 := [25, 15, 0]*10^3:
v2 := [20, -20, 0]*10^3:
v3 := [-5, -25, 0]*10^3:
v4 := [15, 0, 0]*10^3:

Mtot := M1 + M2 + M3 + M4:

rcm := (M1*r1 + M2*r2 + M3*r3 + M4*r4)/Mtot:
vcm := (M1*v1 + M2*v2 + M3*v3 + M4*v4)/Mtot:

Ltot := crossprod(r1, M1*v1) + crossprod(r2, M2*v2) + crossprod(r3, M3*v3) + crossprod(r4, M4*v4) - crossprod(rcm, Mtot*vcm);

I have done other codes with vectors like these, using the crossprod command, and they are all working great.  So I don't understand what is going on here.  I'm using Maple 13.

I'm not a strong user of Maple, so I may have done a simple mistake somewhere, but I really don't see what and where. So what is wrong with this Maple code ?

 

Dear sir,

in the program boundary conditions D(f)(0)=0 doesn't showing result but when use d(f)(0)=1 it will execute, why is this can you explain this ?program.mw
 

Hi MaplePrimes,

As an amataeur with this computer tool, I want to know the arrow notation.

For example " l -> 8*l ".

a_quandry_MaplePrimes.mw

I'm sure this easy question is okay.

Regards,

Matt

 

 

HI Maple primes.  We try to make sense of 'rsolve' in the Maple world.  What is command for source code?

 

Regards,

Matt

 

Hi Mapleprimes,

We know that '' rsolve '' is a recurrence equation solver.  It is more than an expression simplifier.

Congratulations to the Maple computer algebra team for creating such a great computer tool.  simply want to know more.

rsolve_on_May_16_2017.pdf

Surely there are many steps to determine the values to place.

Regards,

Matt

 

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