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Ronan

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13 years, 111 days
East Grinstead, United Kingdom
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These are questions asked by Ronan

Trying to collect tdeg. coefficient of m...

Ronan 1022 Maple 2021
August 08 2021
2 4

I have a polynomial in c & d.  I wish to extract the coefficients of lets say 3rd order i.e c^3+c^2d+c d^2+d^3. 

The polynomials can be of 2,3,4.. variables.  

coeffs(14*c^4 + 84*c^3*d + 180*c^2*d^2 + 165*c*d^3 + 55*d^4 + 5*c^3 + 21*c^2*d + 28*c*d^2 + 12*d^3 + 2*c^2 + 5*c*d + 3*d^2 + c + d + 1, [c, d], 'l');
     14, 84, 180, 165, 55, 5, 21, 28, 12, 2, 5, 3, 1, 1, 1

l[1];
                                4
                               c 

l[2];
                               3  
                              c  d

l;
 4   3     2  2     3   4   3     2     2   3   2        2        
c , c  d, c  d , c d , d , c , d c , c d , d , c , d c, d , c, d, 

  1

 

Table output question....

Ronan 1022 Maple 2021
table 2dmath context-menu
May 04 2021
1 1

I was taking notes from a video and fromatting them in a table so I could pring them.

I an using the commands in the context panel to keep things neat.

I can't get this to work for the last row of the table. when I select the equation, the right context panel changes to information about the table and the commands for manipulating the equations are not available. This occurs on the tenth row or later. 

I have since tried interface(rtablesize = [12,12]) but that didnt help.

If I run the document I can get the 10th row to solve by displaying the output first and then using the commands from the context panel

         
             

2*a[0]*a[9]*c[2] + 2*a[1]*a[8]*c[2] + 2*a[2]*a[7]*c[2] + 2*a[3]*a[6]*c[2] + 2*a[4]*a[5]*c[2] + a[9]*c[1];
 
                              8            
                     1430 c[2]             
                     ---------- + a[9] c[1]
                           16              
                       c[1]                

                             "(->)"

solve( 1430*c[2]^8/c[1]^16 + a[9]*c[1]=0, a[9] );
                                     8
                            1430 c[2] 
                          - ----------
                                  17  
                              c[1]    

                             "(->)"

a[9] := -1430*c[2]^8/c[1]^17: 'a[9]';
                              a[9]


           

Edited:- to improve readability and add more information.

restart

 

NULL

NULL``

                                                           

 

a[0] := 0

2*a[0]*a[1]*c[2]+a[1]*c[1]+1 = 0"(->)"-1/c[1]"(->)"a[1]NULL

2*a[0]*a[2]*c[2]+a[1]^2*c[2]+a[2]*c[1] = 0"(->)"-c[2]/c[1]^3"(->)"a[2]NULL

2*a[0]*a[3]*c[2]+2*a[1]*a[2]*c[2]+a[3]*c[1] = 0"(->)"-2*c[2]^2/c[1]^5"(->)"a[3]

2*a[0]*a[4]*c[2]+2*a[1]*a[3]*c[2]+a[2]^2*c[2]+a[4]*c[1] = 0"(->)"-5*c[2]^3/c[1]^7"(->)"a[4]

2*a[0]*a[5]*c[2]+2*a[1]*a[4]*c[2]+2*a[2]*a[3]*c[2]+a[5]*c[1] = 0"(->)"-14*c[2]^4/c[1]^9"(->)"a[5]NULL

2*a[0]*a[6]*c[2]+2*a[1]*a[5]*c[2]+2*a[2]*a[4]*c[2]+a[3]^2*c[2]+a[6]*c[1]"(->)"-42*c[2]^5/c[1]^11"(->)"a[6]

2*a[0]*a[7]*c[2]+2*a[1]*a[6]*c[2]+2*a[2]*a[5]*c[2]+2*a[3]*a[4]*c[2]+a[7]*c[1]"(->)"-132*c[2]^6/c[1]^13"(->)"a[7]

2*a[0]*a[8]*c[2]+2*a[1]*a[7]*c[2]+2*a[2]*a[6]*c[2]+2*a[3]*a[5]*c[2]+a[4]^2*c[2]+a[8]*c[1]"(->)"-429*c[2]^7/c[1]^15"(->)"a[8]

2*a[0]*a[9]*c[2]+2*a[1]*a[8]*c[2]+2*a[2]*a[7]*c[2]+2*a[3]*a[6]*c[2]+2*a[4]*a[5]*c[2]+a[9]*c[1]
 

 

NULL


 

Download Table_solve_issue.mw

Factorial display question...

Ronan 1022 Maple 2021
output factorial inertform
April 23 2021
2 7

I trying to display factorials in a matrix as e.g 6!4!/5! not 144.
 

restart

with(InertForm)

[ConvertToString, Display, FromMathContainer, MakeInert, NoSimpl, Parse, SameStructure, ToMathContainer, ToMathML, Typeset, Value]

 (1)

M := Matrix(4, 4); for m from 0 to 4 do for n from 0 to 4 do M(m+1, n+1) := factorial(NoSimpl(2*m+3*n))/(factorial(NoSimpl(m+2*n+1))*factorial(NoSimpl(m))*factorial(NoSimpl(n))) end do end do; M

Matrix(%id = 36893490820101234804)

 (2)

NULL


 

Download How_to_display_factorial_unevaluated.mw

Is it possible to Add/sum by mapping mul...

Ronan 1022 Maple 2021
add nested
April 18 2021
3 15

I want to sum a series by getting multiple values from a list.  Based on the list L I was trying

add(A, [m2, m3] in L)   This seem to have dissapeared from the document but the error message remains.

restart

``

NULL

NULL

A := factorial(2*m2+3*m3)*c0^(1+m2+2*m3)*c2^m2*c3^m3/(factorial(1+m2+2*m3)*factorial(m2)*factorial(m3)*c1^(2*m2+3*m3+1))

factorial(2*m2+3*m3)*c0^(1+m2+2*m3)*c2^m2*c3^m3/(factorial(1+m2+2*m3)*factorial(m2)*factorial(m3)*c1^(2*m2+3*m3+1))

 (1)

"P:=3, N:=4"

4

 (2)

``

I found this code by Kitonum 16740  https://www.mapleprimes.com/questions/138955-How-Do-I-Create-A-Variable-Number-Of-Nested-Loops-

S := {seq(0 .. N)}; l := P-1; f := proc (T) options operator, arrow; [seq(seq([op(T[j]), S[i]], i = 1 .. nops(S)), j = 1 .. nops(T))] end proc; L := (f@@l)([[]])

[[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, 0], [4, 1], [4, 2], [4, 3], [4, 4]]

 (3)

nops(L)

25

 (4)

NULLNULL

``

nops(L)

25

 (5)

Instead of using add(add(A, m2 = 0 .. 4)*m3 = 0 .. 4)I would like to map m2 and m3 to the values in list L and sum them. This should give a method for having a variable number of loops

I tried variants off without success

 

add(A, `in`([m2, m3], L))

Error, illegal use of an object as a name

  

 

 

 

 

for the next higher order would need to map m2,m3, m4 to the generated list.

 

 

 

B := factorial(2*m2+3*m3+4*m4)*c0^(1+m2+2*m3+3*m4)*c2^m2*c3^m3*c4^m4/(factorial(1+m2+2*m3+3*m4)*factorial(m2)*factorial(m3)*factorial(m4)*c1^(2*m2+3*m3+4*m4+1))

factorial(2*m2+3*m3+4*m4)*c0^(1+m2+2*m3+3*m4)*c2^m2*c3^m3*c4^m4/(factorial(1+m2+2*m3+3*m4)*factorial(m2)*factorial(m3)*factorial(m4)*c1^(2*m2+3*m3+4*m4+1))

 (6)

P := 4; S := {seq(0 .. N)}; l := P-1; f := proc (T) options operator, arrow; [seq(seq([op(T[j]), S[i]], i = 1 .. nops(S)), j = 1 .. nops(T))] end proc; L := (f@@l)([[]])

[[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 0, 4], [0, 1, 0], [0, 1, 1], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 0], [0, 2, 1], [0, 2, 2], [0, 2, 3], [0, 2, 4], [0, 3, 0], [0, 3, 1], [0, 3, 2], [0, 3, 3], [0, 3, 4], [0, 4, 0], [0, 4, 1], [0, 4, 2], [0, 4, 3], [0, 4, 4], [1, 0, 0], [1, 0, 1], [1, 0, 2], [1, 0, 3], [1, 0, 4], [1, 1, 0], [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 1, 4], [1, 2, 0], [1, 2, 1], [1, 2, 2], [1, 2, 3], [1, 2, 4], [1, 3, 0], [1, 3, 1], [1, 3, 2], [1, 3, 3], [1, 3, 4], [1, 4, 0], [1, 4, 1], [1, 4, 2], [1, 4, 3], [1, 4, 4], [2, 0, 0], [2, 0, 1], [2, 0, 2], [2, 0, 3], [2, 0, 4], [2, 1, 0], [2, 1, 1], [2, 1, 2], [2, 1, 3], [2, 1, 4], [2, 2, 0], [2, 2, 1], [2, 2, 2], [2, 2, 3], [2, 2, 4], [2, 3, 0], [2, 3, 1], [2, 3, 2], [2, 3, 3], [2, 3, 4], [2, 4, 0], [2, 4, 1], [2, 4, 2], [2, 4, 3], [2, 4, 4], [3, 0, 0], [3, 0, 1], [3, 0, 2], [3, 0, 3], [3, 0, 4], [3, 1, 0], [3, 1, 1], [3, 1, 2], [3, 1, 3], [3, 1, 4], [3, 2, 0], [3, 2, 1], [3, 2, 2], [3, 2, 3], [3, 2, 4], [3, 3, 0], [3, 3, 1], [3, 3, 2], [3, 3, 3], [3, 3, 4], [3, 4, 0], [3, 4, 1], [3, 4, 2], [3, 4, 3], [3, 4, 4], [4, 0, 0], [4, 0, 1], [4, 0, 2], [4, 0, 3], [4, 0, 4], [4, 1, 0], [4, 1, 1], [4, 1, 2], [4, 1, 3], [4, 1, 4], [4, 2, 0], [4, 2, 1], [4, 2, 2], [4, 2, 3], [4, 2, 4], [4, 3, 0], [4, 3, 1], [4, 3, 2], [4, 3, 3], [4, 3, 4], [4, 4, 0], [4, 4, 1], [4, 4, 2], [4, 4, 3], [4, 4, 4]]

 (7)

nops(L)

125

 (8)

NULL


 

Download Sum_by_mapping_to_a_list_question.mw

Sums as hypergeometric. Why?...

Ronan 1022 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

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