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Ronan

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13 years, 140 days
East Grinstead, United Kingdom
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Sums as hypergeometric. Why?...

Ronan 1341 Maple 2021
sum summation add
April 18 2021
2 1

I have two summations that Maple converts to hypergeometric outputs. Is there a way to stop that?

I dont know how to get Maple to expand the Hyper geometric output for a given walue of N

if the value of N is defined first the output is as I would expect.

The real problem, the sumations are nested and when I get to four nested sums Maple sits there for hours trying to evaluate the general case. 

I have only included the first 2 summations.

Any insights on this would be appreciated.
 

restart

NULL

NULL

NULL

``

``

a := -(sum(C2^(m-1)*C0^m*factorial(2*m)/(C1^(2*m-1)*factorial(m+1)*factorial(m)), m = 0 .. N))

-2*C1/(C2*(1+(-(4*C0*C2-C1^2)/C1^2)^(1/2)))+C2^N*C0^(N+1)*GAMMA(2*N+3)*(N+2)*hypergeom([1, 3/2+N], [N+3], 4*C0*C2/C1^2)/(C1^(2*N+1)*GAMMA(N+3)^2)

 (1)

N := 4

4

 (2)

a

-2*C1/(C2*(1+(-(4*C0*C2-C1^2)/C1^2)^(1/2)))+42*C2^4*C0^5*hypergeom([1, 11/2], [7], 4*C0*C2/C1^2)/C1^9

 (3)

b := -(sum(C2^(m-1)*C0^m*factorial(2*m)/(C1^(2*m-1)*factorial(m+1)*factorial(m)), m = 0 .. N))

-C1/C2-C0/C1-2*C2*C0^2/C1^3-5*C2^2*C0^3/C1^5-14*C2^3*C0^4/C1^7

 (4)

NULL

NULL``

unassign('N')

c := sum(sum((-1)^(m[3]+1)*factorial(2*m[2]+3*m[3])*C0^(1+m[2]+2*m[3])*C2^m[2]*C3^m[3]/(factorial(1+m[2]+2*m[3])*factorial(m[2])*factorial(m[3])*C1^(1+2*m[2]+3*m[3])), m[3] = 0 .. N), m[2] = 0 .. N)

sum(C2^m[2]*(-factorial(2*m[2])*C0^(1+m[2])*hypergeom([(2/3)*m[2]+1, (2/3)*m[2]+2/3, 1/3+(2/3)*m[2]], [1+(1/2)*m[2], 3/2+(1/2)*m[2]], -(27/4)*C0^2*C3/C1^3)/(factorial(1+m[2])*C1^(1+2*m[2]))-factorial(2*m[2]+3*N+3)*C0^(3+m[2]+2*N)*C3^(N+1)*hypergeom([1, (2/3)*m[2]+2+N, 5/3+(2/3)*m[2]+N, 4/3+(2/3)*m[2]+N], [N+2, 2+(1/2)*m[2]+N, 5/2+(1/2)*m[2]+N], -(27/4)*C0^2*C3/C1^3)*(-1)^N/(factorial(3+m[2]+2*N)*factorial(N+1)*C1^(4+2*m[2]+3*N)))/factorial(m[2]), m[2] = 0 .. N)

 (5)

NULL

NULLN := 4

4

 (6)

c

-C0*hypergeom([1/3, 2/3], [3/2], -(27/4)*C0^2*C3/C1^3)/C1-273*C0^11*C3^5*hypergeom([1, 16/3, 17/3], [6, 13/2], -(27/4)*C0^2*C3/C1^3)/C1^16+C2*(-C0^2*hypergeom([1, 4/3, 5/3], [3/2, 2], -(27/4)*C0^2*C3/C1^3)/C1^3-6188*C0^12*C3^5*hypergeom([1, 19/3, 20/3], [13/2, 7], -(27/4)*C0^2*C3/C1^3)/C1^18)+(1/2)*C2^2*(-4*C0^3*hypergeom([5/3, 7/3], [5/2], -(27/4)*C0^2*C3/C1^3)/C1^5-162792*C0^13*C3^5*hypergeom([1, 20/3, 22/3], [6, 15/2], -(27/4)*C0^2*C3/C1^3)/C1^20)+(1/6)*C2^3*(-30*C0^4*hypergeom([7/3, 8/3], [5/2], -(27/4)*C0^2*C3/C1^3)/C1^7-4883760*C0^14*C3^5*hypergeom([1, 22/3, 23/3], [6, 15/2], -(27/4)*C0^2*C3/C1^3)/C1^22)+(1/24)*C2^4*(-336*C0^5*hypergeom([10/3, 11/3], [7/2], -(27/4)*C0^2*C3/C1^3)/C1^9-164745504*C0^15*C3^5*hypergeom([1, 25/3, 26/3], [6, 17/2], -(27/4)*C0^2*C3/C1^3)/C1^24)

 (7)

NULL

e := sum(sum((-1)^(m[3]+1)*factorial(2*m[2]+3*m[3])*C0^(1+m[2]+2*m[3])*C2^m[2]*C3^m[3]/(factorial(1+m[2]+2*m[3])*factorial(m[2])*factorial(m[3])*C1^(1+2*m[2]+3*m[3])), m[3] = 0 .. N), m[2] = 0 .. N)

-C0/C1-5*C2^3*C0^4/C1^7-C2*C0^2/C1^3-2*C2^2*C0^3/C1^5-3*C0^5*C3^2/C1^7+12*C0^7*C3^3/C1^10-55*C0^9*C3^4/C1^13-14*C0^5*C2^4/C1^9+C0^3*C3/C1^4+330*C0^7*C2^4*C3/C1^12-5005*C0^9*C2^4*C3^2/C1^15+61880*C0^11*C2^4*C3^3/C1^18-678300*C0^13*C2^4*C3^4/C1^21+5*C0^4*C2*C3/C1^6-28*C0^6*C2*C3^2/C1^9+165*C0^8*C2*C3^3/C1^12-1001*C0^10*C2*C3^4/C1^15+21*C0^5*C2^2*C3/C1^8-180*C0^7*C2^2*C3^2/C1^11+1430*C0^9*C2^2*C3^3/C1^14-10920*C0^11*C2^2*C3^4/C1^17+84*C0^6*C2^3*C3/C1^10-990*C0^8*C2^3*C3^2/C1^13+10010*C0^10*C2^3*C3^3/C1^16-92820*C0^12*C2^3*C3^4/C1^19

 (8)

NULL


 

Download why_hypergeom.mw

How to rearrange an equation by coeffici...

Ronan 1341 Maple 2019
sort
February 13 2021
1 3

I am trying to rearrange the elements of an equation by the absolute value of their coefficients. eg -3y^2 x+2x z^2+6z^2 to

2x z^2 -3y^2 +6z^2 

 

Download Rearange_test.mwRearange_test.mw

Boole Mobius Transform Procedure efficie...

Ronan 1341 Maple 2019
performance procedure vector
January 17 2021
2 14

I have this procedure to perform a Boole-Mobius Transform. I took me quite a while to figure out. Whereas it works, I wonder how it should be done efficiently? The document is also attached which shows the steps I went through to derive the procedure. I can't get the document to display.

BooleMobiusTransform := proc(V) 
local n, im, istep, jm, h, istart, i, j, k; n := ilog2(numelems(V)); im := 2^n/2; istep := im; jm := 1; h := 2^n; 
for k to n do
 istart := 1; 
for j to jm do 
for i from istart to im - 1 + istart do 
V(istep + i) := (V[istep + i] + V[i]) mod 2;
 end do;
 istart := istart + h; 
end do;
 im := 1/2*im; istep := 1/2*istep; jm := 2*jm; h := 1/2*h; 
end do; 
return V; 
end proc

Boole-Mobius_Transform.mw

A few queries on using units...

Ronan 1341 Maple 2019
units
June 12 2020
1 0

I am experimenting with using units especially for when there are awkard conversion factors. 

The document is for motor gearbox torques inertia ration and frequency.

I have documented my specific questions in the worksheet.

I am interested is see different ways of setting this up. Like I would rather setup the formulas at the start, then supply figures.


 

restart

``

with(Units[Natural])

UseSystem('SI')

UseSystem(SI)

 (1)

Can I set the units for mass, accel, etc. so I don't have to re enter the default units if I change the figures later?

``

Mass := 3000*'kg'

3000*Units:-Unit(kg)

 (2)

Accel := 1.5*'m'/'s'^2

1.5*Units:-Unit(m/s^2)

 (3)

Rat := 5

5

 (4)

``

Radius := (1/2)*(0.8282e-1-0.6e-2)*'m'

0.3841000000e-1*Units:-Unit(m)

 (5)

Torque := Mass*Accel*Radius

172.8450000*Units:-Unit(J)

 (6)

````

MotorTorque := Torque/Rat

34.56900000*Units:-Unit(J)

 (7)

Jload := Mass*Radius^2

4.425984300*Units:-Unit(kg*m^2)

 (8)

Jmtr := 1.42*10^(-2)*'kg'*'m'^2

0.1420000000e-1*Units:-Unit(kg*m^2)

 (9)

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

12.46756141

 (10)

stiff := convert(48, 'units', 'N'*'m(radius)'/'arcmin', 'N'*'m(rarius)'/'rad', 'symbolic')

518400/Pi

 (11)

/rad

518400/Pi

 (12)

"(->)"

0.16501e6

 (13)

``

Freq := sqrt(stiff/Jload)/(2*Pi)/s   i.e. Hertz

30.73072153*Units:-Unit(1/(kg^(1/2)*m))

 (14)

stiff := 4567

4567

 (15)

Freq

30.73072153*Units:-Unit(1/(kg^(1/2)*m))

 (16)

``


 

Download Units_questions.mw

Can isolve be used with irem?...

Ronan 1341 Maple 2019
April 21 2019
4 6

I am trying to get this to work

{seq(isolve({a = k, irem(a*b, 10000) = 2391}), k = 1 .. 9999)}

but am not getting any answer. One solution is irem(297*9503, 10000).

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