Solution 3 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a11 + 4*a23
Expressions
The solution is given through the following expressions:
3 32 2 87 30 2 2
r20=( - --------*a11 *b32 *r213 - -------*a11 *a23 *b32 *r213
131072 32768
3407 28 4 2 26399 26 6 2
- -------*a11 *a23 *b32 *r213 - -------*a11 *a23 *b32 *r213
24576 6144
67379 24 8 2 2138777 22 10 2
- -------*a11 *a23 *b32 *r213 - ---------*a11 *a23 *b32 *r213
768 1728
5313887 20 12 2 9308383 18 14 2
- ---------*a11 *a23 *b32 *r213 - ---------*a11 *a23 *b32 *r213
432 108
204166373 16 16 2 112834534 14 18 2
- -----------*a11 *a23 *b32 *r213 - -----------*a11 *a23 *b32 *r213
486 81
250797064 12 20 2 3375072032 10 22 2
- -----------*a11 *a23 *b32 *r213 - ------------*a11 *a23 *b32 *r213
81 729
843294208 8 24 2 902742016 6 26 2
- -----------*a11 *a23 *b32 *r213 + -----------*a11 *a23 *b32 *r213
243 243
524025856 4 28 2 186646528 2 30 2
+ -----------*a11 *a23 *b32 *r213 - -----------*a11 *a23 *b32 *r213
729 729
33554432 32 2 25 9 23 11
- ----------*a23 *b32 *r213)/(a11 *a23 + 96*a11 *a23
729
21 13 290560 19 15 17 17
+ 4032*a11 *a23 + --------*a11 *a23 + 1457664*a11 *a23
3
15 19 2337095680 13 21 2819817472 11 23
+ 14118912*a11 *a23 + ------------*a11 *a23 + ------------*a11 *a23
27 9
9 25 197999460352 7 27
+ 559480832*a11 *a23 + --------------*a11 *a23
729
12364808192 5 29 268435456 3 31
+ -------------*a11 *a23 + -----------*a11 *a23 )
243 81
1 20 2 17 18 2 2
r21=( - ------*a11 *b32 *r213 - -----*a11 *a23 *b32 *r213
2048 512
1085 16 4 2 4153 14 6 2
- ------*a11 *a23 *b32 *r213 - ------*a11 *a23 *b32 *r213
1152 288
9263 12 8 2 109307 10 10 2
- ------*a11 *a23 *b32 *r213 - --------*a11 *a23 *b32 *r213
72 162
55306 8 12 2 106376 6 14 2
- -------*a11 *a23 *b32 *r213 - --------*a11 *a23 *b32 *r213
27 27
492160 4 16 2 71680 2 18 2
- --------*a11 *a23 *b32 *r213 + -------*a11 *a23 *b32 *r213
81 81
32768 20 2 16 6 14 8 12 10
+ -------*a23 *b32 *r213)/(a11 *a23 + 60*a11 *a23 + 1440*a11 *a23
81
156032 10 12 8 14 6 16
+ --------*a11 *a23 + 105728*a11 *a23 + 273408*a11 *a23
9
8028160 4 18 262144 2 20
+ ---------*a11 *a23 + --------*a11 *a23 )
81 27
r23=0
r24=0
9 44 2 393 42 2 2
r25=( - ---------*a11 *b32 *r213 - --------*a11 *a23 *b32 *r213
2097152 524288
7841 40 4 2 285031 38 6 2
- --------*a11 *a23 *b32 *r213 - --------*a11 *a23 *b32 *r213
131072 98304
2349091 36 8 2 41889709 34 10 2
- ---------*a11 *a23 *b32 *r213 - ----------*a11 *a23 *b32 *r213
24576 18432
557117503 32 12 2 1877957315 30 14 2
- -----------*a11 *a23 *b32 *r213 - ------------*a11 *a23 *b32 *r213
13824 3456
14586016871 28 16 2
- -------------*a11 *a23 *b32 *r213
2592
29101653451 26 18 2
- -------------*a11 *a23 *b32 *r213
648
134001574409 24 20 2
- --------------*a11 *a23 *b32 *r213
486
944175777214 22 22 2
- --------------*a11 *a23 *b32 *r213
729
10105028632904 20 24 2
- ----------------*a11 *a23 *b32 *r213
2187
27167473026464 18 26 2
- ----------------*a11 *a23 *b32 *r213
2187
163124242677632 16 28 2
- -----------------*a11 *a23 *b32 *r213
6561
696664848224768 14 30 2
- -----------------*a11 *a23 *b32 *r213
19683
589942337069056 12 32 2
- -----------------*a11 *a23 *b32 *r213
19683
362179733094400 10 34 2
- -----------------*a11 *a23 *b32 *r213
59049
241679233712128 8 36 2
+ -----------------*a11 *a23 *b32 *r213
59049
149027010117632 6 38 2
+ -----------------*a11 *a23 *b32 *r213
59049
3687766294528 4 40 2
+ ---------------*a11 *a23 *b32 *r213
6561
1142461300736 2 42 2 137438953472 44 2
+ ---------------*a11 *a23 *b32 *r213 + --------------*a23 *b32 *r213)/(
19683 59049
35 11 33 13 31 15 2567360 29 17
a11 *a23 + 132*a11 *a23 + 7920*a11 *a23 + ---------*a11 *a23
9
27 19 25 21 113414299648 23 23
+ 6858240*a11 *a23 + 115697664*a11 *a23 + --------------*a11 *a23
81
329312665600 21 25 226291548160 19 27
+ --------------*a11 *a23 + --------------*a11 *a23
27 3
233243579514880 17 29 211515874476032 15 31
+ -----------------*a11 *a23 + -----------------*a11 *a23
729 243
108215589142528 13 33 5950366810112000 11 35
+ -----------------*a11 *a23 + ------------------*a11 *a23
81 6561
228825120112640 9 37 14259291422720 7 39
+ -----------------*a11 *a23 + ----------------*a11 *a23
729 243
335076168564736 5 41 4398046511104 3 43
+ -----------------*a11 *a23 + ---------------*a11 *a23 )
59049 19683
32 3 2 128 4
- ----*a11 *a23 *b32*r213 - -----*a11*a23 *b32*r213
9 3
r26=------------------------------------------------------
6 4 2 2 4 256 6
a11 + 24*a11 *a23 + 144*a11 *a23 + -----*a23
9
1 6 56 4 2 80 2 4
---*a11 *b32*r213 + ----*a11 *a23 *b32*r213 + ----*a11 *a23 *b32*r213
3 9 3
r27=-----------------------------------------------------------------------
6 4 3 2 5 256 7
a11 *a23 + 24*a11 *a23 + 144*a11 *a23 + -----*a23
9
r28=0
3 3 5 2
----*a11 *r213 + ---*a11*a23 *r213
32 8
r29=------------------------------------
3
a23
1 6 20 4 2 8 2 4
r210=( - ---*a11 *b32*r213 - ----*a11 *a23 *b32*r213 - ---*a11 *a23 *b32*r213
6 9 3
128 6 6 4 3 2 5
- -----*a23 *b32*r213)/(a11 *a23 + 24*a11 *a23 + 144*a11 *a23
9
256 7
+ -----*a23 )
9
r212=0
3 6 5 4 2 3 2 4 6
----*a11 *r213 + ---*a11 *a23 *r213 + ---*a11 *a23 *r213 + 4*a23 *r213
64 8 4
r214=------------------------------------------------------------------------
3 3 5
a11 *a23 + 12*a11*a23
r215=0
r216=0
3 14 33 12 2
r217=( - ------*a11 *b32*r213 - -----*a11 *a23 *b32*r213
1024 256
205 10 4 395 8 6
- -----*a11 *a23 *b32*r213 - -----*a11 *a23 *b32*r213
96 24
2167 6 8 1061 4 10
- ------*a11 *a23 *b32*r213 - ------*a11 *a23 *b32*r213
36 9
2176 2 12 256 14 9 6
- ------*a11 *a23 *b32*r213 + -----*a23 *b32*r213)/(a11 *a23
9 9
7 8 5 10 15808 3 12 1024 14
+ 36*a11 *a23 + 432*a11 *a23 + -------*a11 *a23 + ------*a11*a23 )
9 3
r218=0
r219=0
9 40 2 189 38 2 2 7227 36 4 2
c33=(---------*a11 *b32 + --------*a11 *a23 *b32 + -------*a11 *a23 *b32
1048576 131072 65536
62609 34 6 2 651265 32 8 2
+ -------*a11 *a23 *b32 + --------*a11 *a23 *b32
12288 4096
16338403 30 10 2 134212627 28 12 2
+ ----------*a11 *a23 *b32 + -----------*a11 *a23 *b32
4608 2304
2863555 26 14 2 2855157041 24 16 2
+ ---------*a11 *a23 *b32 + ------------*a11 *a23 *b32
4 432
2462671409 22 18 2 6261556723 20 20 2
+ ------------*a11 *a23 *b32 + ------------*a11 *a23 *b32
54 27
206345380688 18 22 2 4750299980816 16 24 2
+ --------------*a11 *a23 *b32 + ---------------*a11 *a23 *b32
243 2187
2752944928384 14 26 2 28899283837184 12 28 2
+ ---------------*a11 *a23 *b32 + ----------------*a11 *a23 *b32
729 6561
19008402563072 10 30 2 716730073088 8 32 2
+ ----------------*a11 *a23 *b32 - --------------*a11 *a23 *b32
6561 729
10325231403008 6 34 2 3688588378112 4 36 2
- ----------------*a11 *a23 *b32 - ---------------*a11 *a23 *b32
6561 6561
183072980992 2 38 2 30064771072 40 2 31 10
- --------------*a11 *a23 *b32 - -------------*a23 *b32 )/(a11 *a23
2187 6561
29 12 27 14 1867264 25 16
+ 120*a11 *a23 + 6480*a11 *a23 + ---------*a11 *a23
9
13096448 23 18 21 20 17227931648 19 22
+ ----------*a11 *a23 + 63164416*a11 *a23 + -------------*a11 *a23
3 27
13395951616 17 24 15 26
+ -------------*a11 *a23 + 20945108992*a11 *a23
3
44671916572672 13 28 23339333582848 11 30
+ ----------------*a11 *a23 + ----------------*a11 *a23
729 243
1518740701184 9 32 99284074627072 7 34
+ ---------------*a11 *a23 + ----------------*a11 *a23
27 6561
4209067950080 5 36 68719476736 3 38
+ ---------------*a11 *a23 + -------------*a11 *a23 )
2187 729
c23=0
9 28 2 135 26 2 2 3501 24 4 2
c22=(---------*a11 *b32 + --------*a11 *a23 *b32 + -------*a11 *a23 *b32
1048576 131072 65536
9731 22 6 2 61025 20 8 2
+ ------*a11 *a23 *b32 + -------*a11 *a23 *b32
6144 2048
858173 18 10 2 10870835 16 12 2
+ --------*a11 *a23 *b32 + ----------*a11 *a23 *b32
2304 3456
1291141 14 14 2 88826021 12 16 2
+ ---------*a11 *a23 *b32 + ----------*a11 *a23 *b32
72 1296
28724759 10 18 2 972163 8 20 2
+ ----------*a11 *a23 *b32 + --------*a11 *a23 *b32
162 3
30762880 6 22 2 1901056 4 24 2
+ ----------*a11 *a23 *b32 + ---------*a11 *a23 *b32
81 27
720896 2 26 2 458752 28 2 19 10
- --------*a11 *a23 *b32 - --------*a23 *b32 )/(a11 *a23
27 81
17 12 15 14 311552 13 16
+ 72*a11 *a23 + 2160*a11 *a23 + --------*a11 *a23
9
941312 11 18 9 20 273780736 7 22
+ --------*a11 *a23 + 1542144*a11 *a23 + -----------*a11 *a23
3 81
32374784 5 24 1048576 3 26
+ ----------*a11 *a23 + ---------*a11 *a23 )
27 9
c13=0
c12=0
1 6 3 4 2 9 2 4 6
----*a11 *b32 + ---*a11 *a23 *b32 + ---*a11 *a23 *b32 - 8*a23 *b32
32 4 2
b33=--------------------------------------------------------------------
3 3 5
a11 *a23 + 12*a11*a23
b31=0
b21=0
3 6 5 4 2 3 2 4 1 6
- -----*a11 *b32 - ----*a11 *a23 *b32 - ----*a11 *a23 *b32 - ---*a23 *b32
512 64 32 2
b11=----------------------------------------------------------------------------
5
a11*a23
3 3 9 2
----*a11 + ---*a11*a23
16 4
a33=--------------------------
2
a23
3 6 9 4 2 27 2 4 6
----*a11 + ---*a11 *a23 + ----*a11 *a23 + 8*a23
32 4 2
a22=-----------------------------------------------------
3 2 4
a11 *a23 + 12*a11*a23
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
r213, b32, a11, a23
Inequalities
In the following not identically vanishing expressions are shown.
Any auxiliary variables g00?? are used to express that at least
one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3
means that either p4 or p3 or both are non-vanishing.
{a22,a23,a11,r213,b32,a33}
Relevance for the application:
Modulo the following equation:
2 2
0=a11 + 4*a23
the system of equations related to the Hamiltonian HAM:
2 32 10 30 12 28 14
HAM=(u1 *(a11 *a23 + 120*a11 *a23 + 6480*a11 *a23
1867264 26 16 13096448 24 18
+ ---------*a11 *a23 + ----------*a11 *a23
9 3
22 20 17227931648 20 22
+ 63164416*a11 *a23 + -------------*a11 *a23
27
13395951616 18 24 16 26
+ -------------*a11 *a23 + 20945108992*a11 *a23
3
44671916572672 14 28 23339333582848 12 30
+ ----------------*a11 *a23 + ----------------*a11 *a23
729 243
1518740701184 10 32 99284074627072 8 34
+ ---------------*a11 *a23 + ----------------*a11 *a23
27 6561
4209067950080 6 36 68719476736 4 38
+ ---------------*a11 *a23 + -------------*a11 *a23 ) + u1*v1*(
2187 729
3 36 5 25 34 7 759 32 9
- -----*a11 *a23 *b32 - ----*a11 *a23 *b32 - -----*a11 *a23 *b32
512 32 16
5201 30 11 764197 28 13
- ------*a11 *a23 *b32 - --------*a11 *a23 *b32
3 18
26 15 27559264 24 17
- 733848*a11 *a23 *b32 - ----------*a11 *a23 *b32
3
2271178240 22 19 5066816128 20 21
- ------------*a11 *a23 *b32 - ------------*a11 *a23 *b32
27 9
664130840576 18 23 6959330619392 16 25
- --------------*a11 *a23 *b32 - ---------------*a11 *a23 *b32
243 729
5844303413248 14 27 96505132777472 12 29
- ---------------*a11 *a23 *b32 - ----------------*a11 *a23 *b32
243 2187
357510370820096 10 31 21647222374400 8 33
- -----------------*a11 *a23 *b32 - ----------------*a11 *a23 *b32
6561 729
50874156056576 6 35 2123861327872 4 37
- ----------------*a11 *a23 *b32 - ---------------*a11 *a23 *b32
6561 2187
34359738368 2 39 2 3 34 8
- -------------*a11 *a23 *b32) + u2 *(----*a11 *a23
729 32
99 32 10 1485 30 12 80246 28 14
+ ----*a11 *a23 + ------*a11 *a23 + -------*a11 *a23
8 2 3
26 16 24 18 396123904 22 20
+ 643536*a11 *a23 + 10874304*a11 *a23 + -----------*a11 *a23
3
20 22 18 24
+ 1157432320*a11 *a23 + 7240660992*a11 *a23
7622852452352 16 26 7202925740032 14 28
+ ---------------*a11 *a23 + ---------------*a11 *a23
243 81
4025614204928 12 30 274851140993024 10 32
+ ---------------*a11 *a23 + -----------------*a11 *a23
27 2187
13090993209344 8 34 984621252608 6 36
+ ----------------*a11 *a23 + --------------*a11 *a23
243 81
9079560863744 4 38 137438953472 2 40
+ ---------------*a11 *a23 + --------------*a11 *a23 ) + u2*u3*(
6561 2187
31 11 29 13 27 15
2*a11 *a23 + 240*a11 *a23 + 12960*a11 *a23
3734528 25 17 26192896 23 19
+ ---------*a11 *a23 + ----------*a11 *a23
9 3
21 21 34455863296 19 23
+ 126328832*a11 *a23 + -------------*a11 *a23
27
26791903232 17 25 15 27
+ -------------*a11 *a23 + 41890217984*a11 *a23
3
89343833145344 13 29 46678667165696 11 31
+ ----------------*a11 *a23 + ----------------*a11 *a23
729 243
3037481402368 9 33 198568149254144 7 35
+ ---------------*a11 *a23 + -----------------*a11 *a23
27 6561
8418135900160 5 37 137438953472 3 39 2
+ ---------------*a11 *a23 + --------------*a11 *a23 ) + u3 *(
2187 729
3 34 8 99 32 10 30 12
----*a11 *a23 + ----*a11 *a23 + 1485*a11 *a23
16 4
160444 28 14 26 16 24 18
+ --------*a11 *a23 + 1285344*a11 *a23 + 21665664*a11 *a23
3
2355825152 22 20 6818723840 20 22
+ ------------*a11 *a23 + ------------*a11 *a23
9 3
18 24 14243733127168 16 26
+ 13974171648*a11 *a23 + ----------------*a11 *a23
243
12626687492096 14 28 6119597277184 12 30
+ ----------------*a11 *a23 + ---------------*a11 *a23
81 27
282995747454976 10 32 8361361801216 8 34
+ -----------------*a11 *a23 + ---------------*a11 *a23
2187 243
352187318272 6 36 17179869184 4 38
+ --------------*a11 *a23 + -------------*a11 *a23 ) + u3*v2*(
81 81
31 10 29 12 27 14
a11 *a23 *b32 + 120*a11 *a23 *b32 + 6480*a11 *a23 *b32
1867264 25 16 13096448 23 18
+ ---------*a11 *a23 *b32 + ----------*a11 *a23 *b32
9 3
21 20 17227931648 19 22
+ 63164416*a11 *a23 *b32 + -------------*a11 *a23 *b32
27
13395951616 17 24 15 26
+ -------------*a11 *a23 *b32 + 20945108992*a11 *a23 *b32
3
44671916572672 13 28 23339333582848 11 30
+ ----------------*a11 *a23 *b32 + ----------------*a11 *a23 *b32
729 243
1518740701184 9 32 99284074627072 7 34
+ ---------------*a11 *a23 *b32 + ----------------*a11 *a23 *b32
27 6561
4209067950080 5 36 68719476736 3 38
+ ---------------*a11 *a23 *b32 + -------------*a11 *a23 *b32) + u3
2187 729
1 34 7 33 32 9 495 30 11
*v3*(----*a11 *a23 *b32 + ----*a11 *a23 *b32 + -----*a11 *a23 *b32
32 8 2
80150 28 13 26 15
+ -------*a11 *a23 *b32 + 213360*a11 *a23 *b32
9
24 17 1146535168 22 19
+ 3569472*a11 *a23 *b32 + ------------*a11 *a23 *b32
27
3220556800 20 21 18 23
+ ------------*a11 *a23 *b32 + 2075453440*a11 *a23 *b32
9
5618908897280 16 25 3644597764096 14 27
+ ---------------*a11 *a23 *b32 + ---------------*a11 *a23 *b32
729 243
162351939584 12 29 258561928069120 10 31
+ --------------*a11 *a23 *b32 - -----------------*a11 *a23 *b32
81 6561
22550256025600 8 33 2249489121280 6 35
- ----------------*a11 *a23 *b32 - ---------------*a11 *a23 *b32
729 243
8151847927808 4 37 137438953472 2 39
- ---------------*a11 *a23 *b32 - --------------*a11 *a23 *b32) +
6561 2187
2 9 40 2 189 38 2 2
v2 *(---------*a11 *b32 + --------*a11 *a23 *b32
1048576 131072
7227 36 4 2 62641 34 6 2
+ -------*a11 *a23 *b32 + -------*a11 *a23 *b32
65536 12288
652673 32 8 2 16433443 30 10 2
+ --------*a11 *a23 *b32 + ----------*a11 *a23 *b32
4096 4608
135925907 28 12 2 2935315 26 14 2
+ -----------*a11 *a23 *b32 + ---------*a11 *a23 *b32
2304 4
2986975793 24 16 2 7996151059 22 18 2
+ ------------*a11 *a23 *b32 + ------------*a11 *a23 *b32
432 162
2390554705 20 20 2 259808968016 18 22 2
+ ------------*a11 *a23 *b32 + --------------*a11 *a23 *b32
9 243
6994469047312 16 24 2 5164693132928 14 26 2
+ ---------------*a11 *a23 *b32 + ---------------*a11 *a23 *b32
2187 729
74639829803264 12 28 2
+ ----------------*a11 *a23 *b32
6561
76496572850176 10 30 2 383826460672 8 32 2
+ ----------------*a11 *a23 *b32 + --------------*a11 *a23 *b32
6561 81
1669806948352 6 34 2 627518210048 4 36 2
+ ---------------*a11 *a23 *b32 - --------------*a11 *a23 *b32
6561 2187
148713242624 2 38 2 30064771072 40 2 2
- --------------*a11 *a23 *b32 - -------------*a23 *b32 ) + v3 *(
2187 6561
9 40 2 189 38 2 2
---------*a11 *b32 + --------*a11 *a23 *b32
1048576 131072
7227 36 4 2 62609 34 6 2
+ -------*a11 *a23 *b32 + -------*a11 *a23 *b32
65536 12288
651265 32 8 2 16338403 30 10 2
+ --------*a11 *a23 *b32 + ----------*a11 *a23 *b32
4096 4608
134212627 28 12 2 2863555 26 14 2
+ -----------*a11 *a23 *b32 + ---------*a11 *a23 *b32
2304 4
2855157041 24 16 2 2462671409 22 18 2
+ ------------*a11 *a23 *b32 + ------------*a11 *a23 *b32
432 54
6261556723 20 20 2 206345380688 18 22 2
+ ------------*a11 *a23 *b32 + --------------*a11 *a23 *b32
27 243
4750299980816 16 24 2 2752944928384 14 26 2
+ ---------------*a11 *a23 *b32 + ---------------*a11 *a23 *b32
2187 729
28899283837184 12 28 2 19008402563072 10 30 2
+ ----------------*a11 *a23 *b32 + ----------------*a11 *a23 *b32
6561 6561
716730073088 8 32 2 10325231403008 6 34 2
- --------------*a11 *a23 *b32 - ----------------*a11 *a23 *b32
729 6561
3688588378112 4 36 2 183072980992 2 38 2
- ---------------*a11 *a23 *b32 - --------------*a11 *a23 *b32
6561 2187
30064771072 40 2 31 10 29 12
- -------------*a23 *b32 ))/(a11 *a23 + 120*a11 *a23
6561
27 14 1867264 25 16 13096448 23 18
+ 6480*a11 *a23 + ---------*a11 *a23 + ----------*a11 *a23
9 3
21 20 17227931648 19 22
+ 63164416*a11 *a23 + -------------*a11 *a23
27
13395951616 17 24 15 26
+ -------------*a11 *a23 + 20945108992*a11 *a23
3
44671916572672 13 28 23339333582848 11 30
+ ----------------*a11 *a23 + ----------------*a11 *a23
729 243
1518740701184 9 32 99284074627072 7 34
+ ---------------*a11 *a23 + ----------------*a11 *a23
27 6561
4209067950080 5 36 68719476736 3 38
+ ---------------*a11 *a23 + -------------*a11 *a23 )
2187 729
has apart from the Hamiltonian and Casimirs only the following first integral:
3 24 5 15 22 7 193 20 9
FI=u1*v1*( - ------*a11 *a23 *b32 - ----*a11 *a23 *b32 - -----*a11 *a23 *b32
1024 64 24
925 18 11 32447 16 13
- -----*a11 *a23 *b32 - -------*a11 *a23 *b32
6 18
356120 14 15 1623424 12 17
- --------*a11 *a23 *b32 - ---------*a11 *a23 *b32
27 27
13846912 10 19 26813888 8 21
- ----------*a11 *a23 *b32 - ----------*a11 *a23 *b32
81 81
36662272 6 23 2637824 4 25
- ----------*a11 *a23 *b32 - ---------*a11 *a23 *b32
81 81
262144 2 27 2 3 22 8 55 20 10
+ --------*a11 *a23 *b32) + u2 *(----*a11 *a23 + ----*a11 *a23
27 64 16
423 18 12 5285 16 14 154004 14 16
+ -----*a11 *a23 + ------*a11 *a23 + --------*a11 *a23
4 3 9
292976 12 18 8752576 10 20 55919872 8 22
+ --------*a11 *a23 + ---------*a11 *a23 + ----------*a11 *a23
3 27 81
31698944 6 24 32702464 4 26 1048576 2 28
+ ----------*a11 *a23 + ----------*a11 *a23 + ---------*a11 *a23 ) +
27 81 27
19 11 17 13 15 15
u2*u3*(a11 *a23 + 72*a11 *a23 + 2160*a11 *a23
311552 13 17 941312 11 19 9 21
+ --------*a11 *a23 + --------*a11 *a23 + 1542144*a11 *a23
9 3
273780736 7 23 32374784 5 25
+ -----------*a11 *a23 + ----------*a11 *a23
81 27
1048576 3 27 1 19 10
+ ---------*a11 *a23 ) + u2*v3*( - ---*a11 *a23 *b32
9 6
92 17 12 760 15 14 86912 13 16
- ----*a11 *a23 *b32 - -----*a11 *a23 *b32 - -------*a11 *a23 *b32
9 3 27
1780352 11 18 711680 9 20
- ---------*a11 *a23 *b32 - --------*a11 *a23 *b32
81 9
13359104 7 22 8519680 5 24
- ----------*a11 *a23 *b32 - ---------*a11 *a23 *b32
81 27
524288 3 26 2 3 22 8 59 20 10
- --------*a11 *a23 *b32) + u3 *(----*a11 *a23 + ----*a11 *a23
9 32 8
495 18 12 13786 16 14 459464 14 16
+ -----*a11 *a23 + -------*a11 *a23 + --------*a11 *a23
2 3 9
1022048 12 18 34579328 10 20 180218368 8 22
+ ---------*a11 *a23 + ----------*a11 *a23 + -----------*a11 *a23
3 27 81
20529152 6 24 655360 4 26
+ ----------*a11 *a23 + --------*a11 *a23 ) + u3*v2*(
27 9
1 19 10 200 17 12 1840 15 14
---*a11 *a23 *b32 + -----*a11 *a23 *b32 + ------*a11 *a23 *b32
3 9 3
242176 13 16 5942528 11 18
+ --------*a11 *a23 *b32 + ---------*a11 *a23 *b32
27 81
2877440 9 20 1789952 7 22
+ ---------*a11 *a23 *b32 + ---------*a11 *a23 *b32
9 3
327680 5 24 32 16 13
+ --------*a11 *a23 *b32) + u3*v3*( - ----*a11 *a23 *b32
3 9
640 14 15 12 17
- -----*a11 *a23 *b32 - 5120*a11 *a23 *b32
3
4984832 10 19 3350528 8 21
- ---------*a11 *a23 *b32 - ---------*a11 *a23 *b32
81 9
2785280 6 23 524288 4 25 2
- ---------*a11 *a23 *b32 - --------*a11 *a23 *b32) + v1 *(
3 3
9 28 2 129 26 2 2
- ---------*a11 *b32 - --------*a11 *a23 *b32
2097152 262144
3161 24 4 2 8225 22 6 2
- --------*a11 *a23 *b32 - -------*a11 *a23 *b32
131072 12288
143675 20 8 2 620731 18 10 2
- --------*a11 *a23 *b32 - --------*a11 *a23 *b32
12288 4608
7203359 16 12 2 2342977 14 14 2
- ---------*a11 *a23 *b32 - ---------*a11 *a23 *b32
6912 432
49079477 12 16 2 14537777 10 18 2
- ----------*a11 *a23 *b32 - ----------*a11 *a23 *b32
2592 324
11950781 8 20 2 1862272 6 22 2
- ----------*a11 *a23 *b32 - ---------*a11 *a23 *b32
162 27
485120 4 24 2 966656 2 26 2
+ --------*a11 *a23 *b32 + --------*a11 *a23 *b32
27 81
32768 28 2 1 23 5 2
+ -------*a23 *b32 ) + v2*v3*( - ------*a11 *a23 *b32
27 2048
5 21 7 2 193 19 9 2 463 17 11 2
- -----*a11 *a23 *b32 - -----*a11 *a23 *b32 - -----*a11 *a23 *b32
128 144 18
10861 15 13 2 179704 13 15 2
- -------*a11 *a23 *b32 - --------*a11 *a23 *b32
36 81
273920 11 17 2 770048 9 19 2
- --------*a11 *a23 *b32 - --------*a11 *a23 *b32
27 27
4321696 7 21 2 5834240 5 23 2
- ---------*a11 *a23 *b32 - ---------*a11 *a23 *b32
81 81
892928 3 25 2 131072 27 2 2
+ --------*a11 *a23 *b32 + --------*a11*a23 *b32 ) + v3 *(
81 27
3 26 2 2 69 24 4 2
- --------*a11 *a23 *b32 - -------*a11 *a23 *b32
131072 32768
521 22 6 2 3007 20 8 2
- ------*a11 *a23 *b32 - ------*a11 *a23 *b32
6144 1536
21871 18 10 2 466441 16 12 2
- -------*a11 *a23 *b32 - --------*a11 *a23 *b32
768 1728
119939 14 14 2 117521 12 16 2
- --------*a11 *a23 *b32 - --------*a11 *a23 *b32
72 18
2566843 10 18 2 680254 8 20 2
- ---------*a11 *a23 *b32 - --------*a11 *a23 *b32
162 27
654464 6 22 2 2489344 4 24 2
- --------*a11 *a23 *b32 + ---------*a11 *a23 *b32
27 81
65536 2 26 2 131072 28 2
- -------*a11 *a23 *b32 - --------*a23 *b32 )
81 81
{HAM,FI} = 0
And again in machine readable form:
HAM=(u1**2*(a11**32*a23**10 + 120*a11**30*a23**12 + 6480*a11**28*a23**14 +
1867264/9*a11**26*a23**16 + 13096448/3*a11**24*a23**18 + 63164416*a11**22*a23**
20 + 17227931648/27*a11**20*a23**22 + 13395951616/3*a11**18*a23**24 + 20945108992
*a11**16*a23**26 + 44671916572672/729*a11**14*a23**28 + 23339333582848/243*a11**
12*a23**30 + 1518740701184/27*a11**10*a23**32 + 99284074627072/6561*a11**8*a23**
34 + 4209067950080/2187*a11**6*a23**36 + 68719476736/729*a11**4*a23**38) + u1*v1
*( - 3/512*a11**36*a23**5*b32 - 25/32*a11**34*a23**7*b32 - 759/16*a11**32*a23**9
*b32 - 5201/3*a11**30*a23**11*b32 - 764197/18*a11**28*a23**13*b32 - 733848*a11**
26*a23**15*b32 - 27559264/3*a11**24*a23**17*b32 - 2271178240/27*a11**22*a23**19*
b32 - 5066816128/9*a11**20*a23**21*b32 - 664130840576/243*a11**18*a23**23*b32 - 6959330619392
/729*a11**16*a23**25*b32 - 5844303413248/243*a11**14*a23**27*b32 - 96505132777472
/2187*a11**12*a23**29*b32 - 357510370820096/6561*a11**10*a23**31*b32 - 21647222374400
/729*a11**8*a23**33*b32 - 50874156056576/6561*a11**6*a23**35*b32 - 2123861327872
/2187*a11**4*a23**37*b32 - 34359738368/729*a11**2*a23**39*b32) + u2**2*(3/32*a11
**34*a23**8 + 99/8*a11**32*a23**10 + 1485/2*a11**30*a23**12 + 80246/3*a11**28*
a23**14 + 643536*a11**26*a23**16 + 10874304*a11**24*a23**18 + 396123904/3*a11**
22*a23**20 + 1157432320*a11**20*a23**22 + 7240660992*a11**18*a23**24 + 7622852452352
/243*a11**16*a23**26 + 7202925740032/81*a11**14*a23**28 + 4025614204928/27*a11**
12*a23**30 + 274851140993024/2187*a11**10*a23**32 + 13090993209344/243*a11**8*
a23**34 + 984621252608/81*a11**6*a23**36 + 9079560863744/6561*a11**4*a23**38 + 137438953472
/2187*a11**2*a23**40) + u2*u3*(2*a11**31*a23**11 + 240*a11**29*a23**13 + 12960*
a11**27*a23**15 + 3734528/9*a11**25*a23**17 + 26192896/3*a11**23*a23**19 +
126328832*a11**21*a23**21 + 34455863296/27*a11**19*a23**23 + 26791903232/3*a11**
17*a23**25 + 41890217984*a11**15*a23**27 + 89343833145344/729*a11**13*a23**29 + 46678667165696
/243*a11**11*a23**31 + 3037481402368/27*a11**9*a23**33 + 198568149254144/6561*
a11**7*a23**35 + 8418135900160/2187*a11**5*a23**37 + 137438953472/729*a11**3*a23
**39) + u3**2*(3/16*a11**34*a23**8 + 99/4*a11**32*a23**10 + 1485*a11**30*a23**12
+ 160444/3*a11**28*a23**14 + 1285344*a11**26*a23**16 + 21665664*a11**24*a23**18
+ 2355825152/9*a11**22*a23**20 + 6818723840/3*a11**20*a23**22 + 13974171648*a11
**18*a23**24 + 14243733127168/243*a11**16*a23**26 + 12626687492096/81*a11**14*
a23**28 + 6119597277184/27*a11**12*a23**30 + 282995747454976/2187*a11**10*a23**
32 + 8361361801216/243*a11**8*a23**34 + 352187318272/81*a11**6*a23**36 + 17179869184
/81*a11**4*a23**38) + u3*v2*(a11**31*a23**10*b32 + 120*a11**29*a23**12*b32 +
6480*a11**27*a23**14*b32 + 1867264/9*a11**25*a23**16*b32 + 13096448/3*a11**23*
a23**18*b32 + 63164416*a11**21*a23**20*b32 + 17227931648/27*a11**19*a23**22*b32
+ 13395951616/3*a11**17*a23**24*b32 + 20945108992*a11**15*a23**26*b32 + 44671916572672
/729*a11**13*a23**28*b32 + 23339333582848/243*a11**11*a23**30*b32 + 1518740701184
/27*a11**9*a23**32*b32 + 99284074627072/6561*a11**7*a23**34*b32 + 4209067950080/
2187*a11**5*a23**36*b32 + 68719476736/729*a11**3*a23**38*b32) + u3*v3*(1/32*a11
**34*a23**7*b32 + 33/8*a11**32*a23**9*b32 + 495/2*a11**30*a23**11*b32 + 80150/9*
a11**28*a23**13*b32 + 213360*a11**26*a23**15*b32 + 3569472*a11**24*a23**17*b32 +
1146535168/27*a11**22*a23**19*b32 + 3220556800/9*a11**20*a23**21*b32 + 2075453440
*a11**18*a23**23*b32 + 5618908897280/729*a11**16*a23**25*b32 + 3644597764096/243
*a11**14*a23**27*b32 + 162351939584/81*a11**12*a23**29*b32 - 258561928069120/
6561*a11**10*a23**31*b32 - 22550256025600/729*a11**8*a23**33*b32 - 2249489121280
/243*a11**6*a23**35*b32 - 8151847927808/6561*a11**4*a23**37*b32 - 137438953472/
2187*a11**2*a23**39*b32) + v2**2*(9/1048576*a11**40*b32**2 + 189/131072*a11**38*
a23**2*b32**2 + 7227/65536*a11**36*a23**4*b32**2 + 62641/12288*a11**34*a23**6*
b32**2 + 652673/4096*a11**32*a23**8*b32**2 + 16433443/4608*a11**30*a23**10*b32**
2 + 135925907/2304*a11**28*a23**12*b32**2 + 2935315/4*a11**26*a23**14*b32**2 + 2986975793
/432*a11**24*a23**16*b32**2 + 7996151059/162*a11**22*a23**18*b32**2 + 2390554705
/9*a11**20*a23**20*b32**2 + 259808968016/243*a11**18*a23**22*b32**2 + 6994469047312
/2187*a11**16*a23**24*b32**2 + 5164693132928/729*a11**14*a23**26*b32**2 + 74639829803264
/6561*a11**12*a23**28*b32**2 + 76496572850176/6561*a11**10*a23**30*b32**2 + 383826460672
/81*a11**8*a23**32*b32**2 + 1669806948352/6561*a11**6*a23**34*b32**2 - 627518210048
/2187*a11**4*a23**36*b32**2 - 148713242624/2187*a11**2*a23**38*b32**2 - 30064771072
/6561*a23**40*b32**2) + v3**2*(9/1048576*a11**40*b32**2 + 189/131072*a11**38*a23
**2*b32**2 + 7227/65536*a11**36*a23**4*b32**2 + 62609/12288*a11**34*a23**6*b32**
2 + 651265/4096*a11**32*a23**8*b32**2 + 16338403/4608*a11**30*a23**10*b32**2 +
134212627/2304*a11**28*a23**12*b32**2 + 2863555/4*a11**26*a23**14*b32**2 + 2855157041
/432*a11**24*a23**16*b32**2 + 2462671409/54*a11**22*a23**18*b32**2 + 6261556723/
27*a11**20*a23**20*b32**2 + 206345380688/243*a11**18*a23**22*b32**2 + 4750299980816
/2187*a11**16*a23**24*b32**2 + 2752944928384/729*a11**14*a23**26*b32**2 + 28899283837184
/6561*a11**12*a23**28*b32**2 + 19008402563072/6561*a11**10*a23**30*b32**2 - 716730073088
/729*a11**8*a23**32*b32**2 - 10325231403008/6561*a11**6*a23**34*b32**2 - 3688588378112
/6561*a11**4*a23**36*b32**2 - 183072980992/2187*a11**2*a23**38*b32**2 - 30064771072
/6561*a23**40*b32**2))/(a11**31*a23**10 + 120*a11**29*a23**12 + 6480*a11**27*a23
**14 + 1867264/9*a11**25*a23**16 + 13096448/3*a11**23*a23**18 + 63164416*a11**21
*a23**20 + 17227931648/27*a11**19*a23**22 + 13395951616/3*a11**17*a23**24 + 20945108992
*a11**15*a23**26 + 44671916572672/729*a11**13*a23**28 + 23339333582848/243*a11**
11*a23**30 + 1518740701184/27*a11**9*a23**32 + 99284074627072/6561*a11**7*a23**
34 + 4209067950080/2187*a11**5*a23**36 + 68719476736/729*a11**3*a23**38)$
FI=u1*v1*( - 3/1024*a11**24*a23**5*b32 - 15/64*a11**22*a23**7*b32 - 193/24*a11**
20*a23**9*b32 - 925/6*a11**18*a23**11*b32 - 32447/18*a11**16*a23**13*b32 -
356120/27*a11**14*a23**15*b32 - 1623424/27*a11**12*a23**17*b32 - 13846912/81*a11
**10*a23**19*b32 - 26813888/81*a11**8*a23**21*b32 - 36662272/81*a11**6*a23**23*
b32 - 2637824/81*a11**4*a23**25*b32 + 262144/27*a11**2*a23**27*b32) + u2**2*(3/
64*a11**22*a23**8 + 55/16*a11**20*a23**10 + 423/4*a11**18*a23**12 + 5285/3*a11**
16*a23**14 + 154004/9*a11**14*a23**16 + 292976/3*a11**12*a23**18 + 8752576/27*
a11**10*a23**20 + 55919872/81*a11**8*a23**22 + 31698944/27*a11**6*a23**24 +
32702464/81*a11**4*a23**26 + 1048576/27*a11**2*a23**28) + u2*u3*(a11**19*a23**11
+ 72*a11**17*a23**13 + 2160*a11**15*a23**15 + 311552/9*a11**13*a23**17 + 941312
/3*a11**11*a23**19 + 1542144*a11**9*a23**21 + 273780736/81*a11**7*a23**23 +
32374784/27*a11**5*a23**25 + 1048576/9*a11**3*a23**27) + u2*v3*( - 1/6*a11**19*
a23**10*b32 - 92/9*a11**17*a23**12*b32 - 760/3*a11**15*a23**14*b32 - 86912/27*
a11**13*a23**16*b32 - 1780352/81*a11**11*a23**18*b32 - 711680/9*a11**9*a23**20*
b32 - 13359104/81*a11**7*a23**22*b32 - 8519680/27*a11**5*a23**24*b32 - 524288/9*
a11**3*a23**26*b32) + u3**2*(3/32*a11**22*a23**8 + 59/8*a11**20*a23**10 + 495/2*
a11**18*a23**12 + 13786/3*a11**16*a23**14 + 459464/9*a11**14*a23**16 + 1022048/3
*a11**12*a23**18 + 34579328/27*a11**10*a23**20 + 180218368/81*a11**8*a23**22 +
20529152/27*a11**6*a23**24 + 655360/9*a11**4*a23**26) + u3*v2*(1/3*a11**19*a23**
10*b32 + 200/9*a11**17*a23**12*b32 + 1840/3*a11**15*a23**14*b32 + 242176/27*a11
**13*a23**16*b32 + 5942528/81*a11**11*a23**18*b32 + 2877440/9*a11**9*a23**20*b32
+ 1789952/3*a11**7*a23**22*b32 + 327680/3*a11**5*a23**24*b32) + u3*v3*( - 32/9*
a11**16*a23**13*b32 - 640/3*a11**14*a23**15*b32 - 5120*a11**12*a23**17*b32 -
4984832/81*a11**10*a23**19*b32 - 3350528/9*a11**8*a23**21*b32 - 2785280/3*a11**6
*a23**23*b32 - 524288/3*a11**4*a23**25*b32) + v1**2*( - 9/2097152*a11**28*b32**2
- 129/262144*a11**26*a23**2*b32**2 - 3161/131072*a11**24*a23**4*b32**2 - 8225/
12288*a11**22*a23**6*b32**2 - 143675/12288*a11**20*a23**8*b32**2 - 620731/4608*
a11**18*a23**10*b32**2 - 7203359/6912*a11**16*a23**12*b32**2 - 2342977/432*a11**
14*a23**14*b32**2 - 49079477/2592*a11**12*a23**16*b32**2 - 14537777/324*a11**10*
a23**18*b32**2 - 11950781/162*a11**8*a23**20*b32**2 - 1862272/27*a11**6*a23**22*
b32**2 + 485120/27*a11**4*a23**24*b32**2 + 966656/81*a11**2*a23**26*b32**2 +
32768/27*a23**28*b32**2) + v2*v3*( - 1/2048*a11**23*a23**5*b32**2 - 5/128*a11**
21*a23**7*b32**2 - 193/144*a11**19*a23**9*b32**2 - 463/18*a11**17*a23**11*b32**2
- 10861/36*a11**15*a23**13*b32**2 - 179704/81*a11**13*a23**15*b32**2 - 273920/
27*a11**11*a23**17*b32**2 - 770048/27*a11**9*a23**19*b32**2 - 4321696/81*a11**7*
a23**21*b32**2 - 5834240/81*a11**5*a23**23*b32**2 + 892928/81*a11**3*a23**25*b32
**2 + 131072/27*a11*a23**27*b32**2) + v3**2*( - 3/131072*a11**26*a23**2*b32**2 -
69/32768*a11**24*a23**4*b32**2 - 521/6144*a11**22*a23**6*b32**2 - 3007/1536*a11
**20*a23**8*b32**2 - 21871/768*a11**18*a23**10*b32**2 - 466441/1728*a11**16*a23
**12*b32**2 - 119939/72*a11**14*a23**14*b32**2 - 117521/18*a11**12*a23**16*b32**
2 - 2566843/162*a11**10*a23**18*b32**2 - 680254/27*a11**8*a23**20*b32**2 -
654464/27*a11**6*a23**22*b32**2 + 2489344/81*a11**4*a23**24*b32**2 - 65536/81*
a11**2*a23**26*b32**2 - 131072/81*a23**28*b32**2)$