Solution 37 to problem h
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem h
Equations
The following unsolved equations remain:
2 2
0=a11 + b12 *kap
Expressions
The solution is given through the following expressions:
r10=0
m3*n2*r353
r11=------------
2
b12 *kap
2 2 2 2 2 2
r12=(2*a11 *m3*n1 *r353 - 2*a11 *m3*n2 *r353 + 3*b12 *kap*m3*n1 *r353
2 2 4 2
- 2*b12 *kap*m3*n2 *r353)/(b12 *kap *n1)
4 2 2 4 2 2 4 2 2
r13=( - 4*a11 *kap*m3 *n1 *r353 + 4*a11 *kap*m3 *n2 *r353 + 4*a11 *n1 *n3 *r353
4 2 2 2 2 2 2 2
- 4*a11 *n2 *n3 *r353 - 6*a11 *b12 *kap *m3 *n1 *r353
2 2 2 2 2 2 2 2 2
+ 6*a11 *b12 *kap *m3 *n2 *r353 + 6*a11 *b12 *kap*n1 *n3 *r353
2 2 2 2 4 3 2 2
- 6*a11 *b12 *kap*n2 *n3 *r353 - b12 *kap *m3 *n1 *r353
4 3 2 2 4 2 2 2
+ 2*b12 *kap *m3 *n2 *r353 + b12 *kap *n1 *n3 *r353
4 2 2 2 6 3 2
- 2*b12 *kap *n2 *n3 *r353)/(b12 *kap *n1 )
4 2 4 3
r14=(8*a11 *n1 *n2*n3*r353 - 8*a11 *n2 *n3*r353
2 2 2 2 2 3
+ 22*a11 *b12 *kap*n1 *n2*n3*r353 - 14*a11 *b12 *kap*n2 *n3*r353
4 2 2 4 2 3 6 3 2
+ 13*b12 *kap *n1 *n2*n3*r353 - 6*b12 *kap *n2 *n3*r353)/(b12 *kap *n1 )
3 2 3 3 2 3
r15=(4*a11 *m3*n1 *n2*r353 - 4*a11 *m3*n2 *r353 - 2*a11 *b12*n1 *n3*r353
2 2 2 2
+ 2*a11 *b12*n1*n2 *n3*r353 + 4*a11*b12 *kap*m3*n1 *n2*r353
2 3 3 3
- 4*a11*b12 *kap*m3*n2 *r353 - 3*b12 *kap*n1 *n3*r353
3 2 5 2 2
+ 2*b12 *kap*n1*n2 *n3*r353)/(b12 *kap *n1 )
r20=0
r21=0
r22=0
r23=0
r24=0
2 2 2 2 2 2
r27=( - 2*a11 *n1 *r353 + 2*a11 *n2 *r353 - 3*b12 *kap*n1 *r353
2 2 3 2
+ 2*b12 *kap*n2 *r353)/(b12 *kap *n1)
4 2 4 3 2 2 2
r28=( - 8*a11 *n1 *n2*r353 + 8*a11 *n2 *r353 - 14*a11 *b12 *kap*n1 *n2*r353
2 2 3 4 2 2
+ 14*a11 *b12 *kap*n2 *r353 - 5*b12 *kap *n1 *n2*r353
4 2 3 5 3 2
+ 6*b12 *kap *n2 *r353)/(b12 *kap *n1 )
5 3 5 2
r29=( - 12*a11 *n1 *n3*r353 + 12*a11 *n1*n2 *n3*r353
4 2 4 3
- 4*a11 *b12*kap*m3*n1 *n2*r353 - 20*a11 *b12*kap*m3*n2 *r353
3 2 3 3 2 2
- 20*a11 *b12 *kap*n1 *n3*r353 + 8*a11 *b12 *kap*n1*n2 *n3*r353
2 3 2 2 2 3 2 3
- 4*a11 *b12 *kap *m3*n1 *n2*r353 - 20*a11 *b12 *kap *m3*n2 *r353
4 2 3 4 2 2 6 3
- 6*a11*b12 *kap *n1 *n3*r353 - 4*a11*b12 *kap *n1*n2 *n3*r353)/(b12 *kap
3
*n1 )
r210
2 2 2 2 2 2 2 2
2*a11 *n1 *r353 - 2*a11 *n2 *r353 + 3*b12 *kap*n1 *r353 - 2*b12 *kap*n2 *r353
=-------------------------------------------------------------------------------
3 2
b12 *kap *n1
3 2 3 2 2
r211=(4*a11 *m3*n1 *r353 - 4*a11 *m3*n2 *r353 - 8*a11 *b12*n1*n2*n3*r353
2 2 2 2
+ 6*a11*b12 *kap*m3*n1 *r353 - 4*a11*b12 *kap*m3*n2 *r353
3 4 2 2
- 8*b12 *kap*n1*n2*n3*r353)/(b12 *kap *n1 )
r212=0
r213=0
r214=0
- n2*r353
r215=------------
b12*kap
3 2 3 2 2 2
r217=(4*a11 *m3*n1 *r353 - 4*a11 *m3*n2 *r353 + 6*a11*b12 *kap*m3*n1 *r353
2 2 4 2 2
- 4*a11*b12 *kap*m3*n2 *r353)/(b12 *kap *n1 )
r218=0
r219=0
r220=0
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
4 2 4 2 2 2 2
r310=(4*a11 *n1 *r353 - 4*a11 *n2 *r353 + 6*a11 *b12 *kap*n1 *r353
2 2 2 4 2 2 4 2 2
- 6*a11 *b12 *kap*n2 *r353 + b12 *kap *n1 *r353 - 2*b12 *kap *n2 *r353)/(
4 3 2
b12 *kap *n1 )
r311=0
4 2 4 2 2 2 2
r312=(4*a11 *n1 *r353 - 4*a11 *n2 *r353 + 6*a11 *b12 *kap*n1 *r353
2 2 2 4 2 2 4 2 2
- 6*a11 *b12 *kap*n2 *r353 + b12 *kap *n1 *r353 - 2*b12 *kap *n2 *r353)/(
4 3 2
b12 *kap *n1 )
r313=0
r314=0
4 2 4 2 2 2 2
r315=(4*a11 *n1 *r353 - 4*a11 *n2 *r353 + 6*a11 *b12 *kap*n1 *r353
2 2 2 4 2 2 4 2 2
- 6*a11 *b12 *kap*n2 *r353 + b12 *kap *n1 *r353 - 2*b12 *kap *n2 *r353)/(
4 3 2
b12 *kap *n1 )
r316=0
2 2
- 2*a11 *m3*n2*r353 - 2*b12 *kap*m3*n2*r353
r317=----------------------------------------------
2 2
b12 *kap*n1
2 2
- 2*a11 *m3*r353 - 2*b12 *kap*m3*r353
r318=----------------------------------------
2
b12 *kap*n1
8 4 2 8 4 2 2 2 2 2 2
r319=( - ---*a11 *n1 *r353 + ---*a11 *n2 *r353 - ---*a11 *b12 *kap *m3 *r353
3 3 3
10 2 2 2 14 2 2 2
- ----*a11 *b12 *kap*n1 *r353 + ----*a11 *b12 *kap*n2 *r353
3 3
2 2 2 2 2 4 3 2
+ ---*a11 *b12 *kap*n3 *r353 - ---*b12 *kap *m3 *r353
3 3
1 4 2 2 4 2 2 2 4 2 2
+ ---*b12 *kap *n1 *r353 + 2*b12 *kap *n2 *r353 + ---*b12 *kap *n3 *r353)
3 3
4 2 2
/(b12 *kap *n1 )
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
r326=0
r327=0
3 2 3 2 2 2
r328=(4*a11 *n1 *r353 - 4*a11 *n2 *r353 + 6*a11*b12 *kap*n1 *r353
2 2 3 2 2
- 4*a11*b12 *kap*n2 *r353)/(b12 *kap *n1 )
2 2
2*a11 *n2*n3*r353 + 2*b12 *kap*n2*n3*r353
r329=-------------------------------------------
2 2
b12 *kap*n1
r330=0
r331=0
r332=0
r333
2 2 2 2 2 2 2 2
2*a11 *n1 *r353 - 2*a11 *n2 *r353 + 3*b12 *kap*n1 *r353 - 2*b12 *kap*n2 *r353
=-------------------------------------------------------------------------------
2 2
b12 *kap*n1
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r341=0
3 2 3 2 2 2
r342=( - 4*a11 *n1 *r353 + 4*a11 *n2 *r353 - 6*a11*b12 *kap*n1 *r353
2 2 3 2 2
+ 4*a11*b12 *kap*n2 *r353)/(b12 *kap *n1 )
r343=0
2 2
2*a11 *n3*r353 + 2*b12 *kap*n3*r353
r344=-------------------------------------
2
b12 *kap*n1
r345=0
r346=0
r347=0
2 2
- 4*a11 *n2*r353 - 4*b12 *kap*n2*r353
r348=----------------------------------------
2
b12 *kap*n1
r349=0
r350=0
r351=0
r352=0
r354=0
r355=0
r40=0
r41=0
r42=0
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r423=0
r424=0
r426=0
r427=0
r428=0
r429=0
r430=0
4 3 4 2
---*a11 *m3*r353 + ---*a11*b12 *kap*m3*r353
3 3
r431=---------------------------------------------
2 2
b12 *kap*n1
2 2
2*a11 *r353 + 2*b12 *kap*r353
r432=-------------------------------
b12*kap*n1
2 2
- 2*a11 *n2*r353 - 2*b12 *kap*n2*r353
r433=----------------------------------------
2
b12*kap*n1
8 3 8 2
- ---*a11 *n3*r353 - ---*a11*b12 *kap*n3*r353
3 3
r434=------------------------------------------------
2 2
b12 *kap*n1
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r445=0
r446=0
r447=0
r448=0
r449=0
r450=0
2 2
- 2*a11 *r353 - 2*b12 *kap*r353
r451=----------------------------------
b12*kap*n1
r452=0
r453=0
8 3 8 2
- ---*a11 *n2*r353 - ---*a11*b12 *kap*n2*r353
3 3
r454=------------------------------------------------
2 2
b12 *kap*n1
r455=0
r456=0
r457=0
r458=0
r459=0
r460=0
r461=0
r462=0
r463=0
r464=0
r465=0
r466=0
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r479=0
r480=0
r482=0
r483=0
r484=0
r485=0
2 2
2*a11 *n2*r353 + 2*b12 *kap*n2*r353
r486=-------------------------------------
2
b12*kap*n1
r487=0
r488=0
8 3 8 2
- ---*a11 *r353 - ---*a11*b12 *kap*r353
3 3
r489=------------------------------------------
2
b12 *kap*n1
r490=0
r491=0
r492=0
r493=0
r494=0
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
r4110=0
r4111=0
r4112=0
r4113=0
r4114=0
r4115=0
r4116=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
r50=0
r51=0
r52=0
r53=0
r54=0
r55=0
r56=0
r57=0
r58=0
r59=0
r510=0
r511=0
r512=0
r513=0
r514=0
r515=0
r516=0
r517=0
r518=0
r519=0
r520=0
r521=0
r522=0
r523=0
r524=0
r525=0
r526=0
r527=0
r528=0
r529=0
r530=0
r531=0
r532=0
r533=0
r534=0
r535=0
r536=0
r537=0
r538=0
r539=0
r540=0
r541=0
r542=0
r543=0
r544=0
r545=0
2 2 2 2
---*a11 *r353 + ---*b12 *kap*r353
3 3
r546=-----------------------------------
2
kap*n1
r547=0
2 2 2 2
---*a11 *r353 + ---*b12 *kap*r353
3 3
r548=-----------------------------------
2
kap*n1
r549=0
r550=0
2 2 2 2
---*a11 *r353 + ---*b12 *kap*r353
3 3
r551=-----------------------------------
2
kap*n1
r552=0
r553=0
r554=0
8 4 38 2 2 2 4 2
---*a11 *r353 + ----*a11 *b12 *kap*r353 - ----*b12 *kap *r353
3 15 15
r555=---------------------------------------------------------------
2 2
b12 *kap*n1
r556=0
r557=0
r558=0
r559=0
r560=0
r561=0
r562=0
r563=0
r564=0
r565=0
r566=0
r567=0
r568=0
r569=0
r570=0
r571=0
r572=0
r573=0
r574=0
r575=0
r576=0
r577=0
r578=0
r579=0
r580=0
r581=0
r582=0
r583=0
r584=0
r585=0
r586=0
r587=0
r588=0
4 3 4 2
- ---*a11 *r353 - ---*a11*b12 *kap*r353
3 3
r589=------------------------------------------
2
b12*kap*n1
r590=0
r591=0
r592=0
r593=0
r594=0
r595=0
r596=0
r597=0
r598=0
r599=0
r5100=0
r5101=0
r5102=0
r5103=0
r5104=0
r5105=0
r5106=0
r5107=0
r5108=0
r5109=0
4 4 2 2 2 4 2
---*a11 *r353 + 2*a11 *b12 *kap*r353 + ---*b12 *kap *r353
3 3
r5110=-----------------------------------------------------------
2 2
b12 *kap*n1
r5111=0
r5112=0
r5113=0
r5114=0
r5115=0
r5116=0
r5117=0
r5118=0
r5119=0
r5120=0
r5121=0
r5122=0
r5123=0
r5124=0
r5125=0
r5126=0
r5127=0
r5128=0
r5129=0
r5130=0
r5131=0
r5132=0
r5133=0
r5134=0
r5135=0
r5136=0
r5137=0
r5138=0
r5139=0
r5140=0
r5141=0
r5142=0
r5143=0
r5144=0
r5145=0
r5146=0
r5147=0
r5148=0
r5149=0
r5150=0
r5151=0
r5152=0
r5153=0
r5154=0
r5155=0
r5156=0
r5157=0
4 3 4 2
---*a11 *r353 + ---*a11*b12 *kap*r353
3 3
r5158=---------------------------------------
2
b12*kap*n1
r5159=0
r5160=0
r5161=0
r5162=0
r5163=0
r5164=0
r5165=0
r5166=0
r5167=0
r5168=0
r5169=0
r5170=0
r5171=0
r5172=0
r5173=0
r5174=0
r5175=0
r5176=0
r5177=0
r5178=0
r5179=0
r5180=0
r5181=0
r5182=0
r5183=0
r5184=0
r5185=0
r5186=0
r5187=0
r5188=0
r5189=0
r5190=0
r5191=0
r5192=0
r5193=0
r5194=0
r5195=0
r5196=0
r5197=0
r5198=0
r5199=0
r5200=0
r5201=0
r5202=0
r5203=0
r5204=0
r5205=0
r5206=0
r5207=0
r5208=0
r5209=0
r5210=0
r5211=0
r5212=0
r5213=0
r5214=0
4 4 2 2 2 4 2
---*a11 *r353 + 2*a11 *b12 *kap*r353 + ---*b12 *kap *r353
3 3
r5215=-----------------------------------------------------------
2 2
b12 *kap*n1
r5216=0
r5217=0
r5218=0
r5219=0
r5220=0
r5221=0
r5222=0
r5223=0
r5224=0
r5225=0
r5226=0
r5227=0
r5228=0
r5229=0
r5230=0
r5231=0
r5232=0
r5233=0
r5234=0
r5235=0
r5236=0
r5237=0
r5238=0
r5239=0
r5240=0
r5241=0
r5242=0
r5243=0
r5244=0
r5245=0
r5246=0
r5247=0
r5248=0
r5249=0
r5250=0
r5251=0
m2=0
m1=0
a33= - a11
a23=0
a22=a11
a13=0
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:
r353, m3, a11, n3, n2, n1, b12
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,
n3,
n2,
n1,
b12,
a11,
r353,
4 5 3 3 5 2 7 2
{---*a11 *b12 *n1*r353 + 2*a11 *b12 *kap*n1*r353 + ---*a11*b12 *kap *n1*r353,
3 3
4 4 3 4 2 5
---*a11 *b12 *n1*r353 + ---*a11 *b12 *kap*n1*r353,
3 3
4 5 3 3 5 2 7 2
---*a11 *b12 *n1*r353 + 2*a11 *b12 *kap*n1*r353 + ---*a11*b12 *kap *n1*r353,
3 3
4 4 3 4 2 5
---*a11 *b12 *n1*r353 + ---*a11 *b12 *kap*n1*r353,
3 3
8 5 3 38 3 5
---*a11 *b12 *n1*r353 + ----*a11 *b12 *kap*n1*r353
3 15
2 7 2
- ----*a11*b12 *kap *n1*r353,
15
2 3 3 2 5
---*a11 *b12 *n1*r353 + ---*a11*b12 *kap*n1*r353,
3 3
2 3 3 2 5
---*a11 *b12 *n1*r353 + ---*a11*b12 *kap*n1*r353,
3 3
2 3 3 2 5
---*a11 *b12 *n1*r353 + ---*a11*b12 *kap*n1*r353}}
3 3
Relevance for the application:
Modulo the following equation:
2 2
0=a11 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u1*v2*b12 + u1*n1 + u2 *a11 - u2*v1*b12 + u2*n2 - u3 *a11 + u3*n3
+ v3*m3
has apart from the Hamiltonian and Casimirs only the following first integral:
2 3 4 4 2 2 6 3 8 4
FI=u1 *u3 *(20*a11 *b12 *kap *n1 + 30*a11 *b12 *kap *n1 + 10*b12 *kap *n1)
2 6 3 3
+ 15*u1 *u3*b12 *kap *n1
2 4 2 2 6 3 2
+ u1*u2*u3*( - 60*a11 *b12 *kap *n1 *n2 - 60*b12 *kap *n1 *n2)
3 3 5 2 7 3
+ u1*u3 *v2*(20*a11 *b12 *kap *n1 + 20*a11*b12 *kap *n1)
3 3 4 2 2 6 3 2
+ u1*u3 *( - 40*a11 *b12 *kap *n1 - 40*a11*b12 *kap *n1 )
2 2 5 2 7 3
+ u1*u3 *v3*(30*a11 *b12 *kap *n1*n2 + 30*b12 *kap *n1*n2)
2 2 4 2 2 6 3 2
+ u1*u3 *(30*a11 *b12 *kap *n1 *n3 + 30*b12 *kap *n1 *n3) + u1*u3*v2*(
3 3 3 3 3 2 5 2 3
- 60*a11 *b12 *kap*n1 + 60*a11 *b12 *kap*n1*n2 - 90*a11*b12 *kap *n1
5 2 2 3 2 3
+ 60*a11*b12 *kap *n1*n2 ) + u1*v1*(60*a11 *b12 *kap*m3*n1
3 2 2 4 2 3
- 60*a11 *b12 *kap*m3*n1*n2 + 90*a11*b12 *kap *m3*n1
4 2 2 5 2 3
- 60*a11*b12 *kap *m3*n1*n2 ) - 15*u1*v3*b12 *kap *n1 *n2 + u1*(
3 3 3 3
60*a11 *b12*kap*m3*n1 *n2 - 60*a11 *b12*kap*m3*n1*n2
2 2 4 2 2 2 2
- 30*a11 *b12 *kap*n1 *n3 + 30*a11 *b12 *kap*n1 *n2 *n3
3 2 3 3 2 3
+ 60*a11*b12 *kap *m3*n1 *n2 - 60*a11*b12 *kap *m3*n1*n2
4 2 4 4 2 2 2
- 45*b12 *kap *n1 *n3 + 30*b12 *kap *n1 *n2 *n3)
2 3 4 4 2 2 6 3 8 4
+ u2 *u3 *(20*a11 *b12 *kap *n1 + 30*a11 *b12 *kap *n1 + 10*b12 *kap *n1) +
2 2 4 2 3 2 4 2 2 6 3 3
u2 *u3*(30*a11 *b12 *kap *n1 - 30*a11 *b12 *kap *n1*n2 + 45*b12 *kap *n1
6 3 2
- 30*b12 *kap *n1*n2 )
3 3 5 2 7 3
+ u2*u3 *v1*( - 20*a11 *b12 *kap *n1 - 20*a11*b12 *kap *n1)
3 3 4 2 6 3
+ u2*u3 *( - 40*a11 *b12 *kap *n1*n2 - 40*a11*b12 *kap *n1*n2)
2 2 5 2 2 7 3 2
+ u2*u3 *v3*( - 30*a11 *b12 *kap *n1 - 30*b12 *kap *n1 )
2 2 4 2 6 3
+ u2*u3 *(30*a11 *b12 *kap *n1*n2*n3 + 30*b12 *kap *n1*n2*n3) + u2*u3*v1*(
3 3 3 3 3 2 5 2 3
60*a11 *b12 *kap*n1 - 60*a11 *b12 *kap*n1*n2 + 90*a11*b12 *kap *n1
5 2 2 3 2 3
- 60*a11*b12 *kap *n1*n2 ) + u2*v2*(60*a11 *b12 *kap*m3*n1
3 2 2 2 3 2
- 60*a11 *b12 *kap*m3*n1*n2 - 120*a11 *b12 *kap*n1 *n2*n3
4 2 3 4 2 2
+ 90*a11*b12 *kap *m3*n1 - 60*a11*b12 *kap *m3*n1*n2
5 2 2 2 3 4
- 120*b12 *kap *n1 *n2*n3) + u2*v3*(30*a11 *b12 *kap*n1
2 3 2 2 5 2 4 5 2 2 2
- 30*a11 *b12 *kap*n1 *n2 + 45*b12 *kap *n1 - 30*b12 *kap *n1 *n2 ) +
4 3 4 3 2 2 3
u2*(120*a11 *n1 *n2*n3 - 120*a11 *n1*n2 *n3 + 330*a11 *b12 *kap*n1 *n2*n3
2 2 3 4 2 3
- 210*a11 *b12 *kap*n1*n2 *n3 + 195*b12 *kap *n1 *n2*n3
4 2 3
- 90*b12 *kap *n1*n2 *n3)
5 4 4 2 2 6 3 8 4
+ u3 *(40*a11 *b12 *kap *n1 + 38*a11 *b12 *kap *n1 - 2*b12 *kap *n1)
4 3 4 2 6 3
+ u3 *( - 40*a11 *b12 *kap *n1*n3 - 40*a11*b12 *kap *n1*n3)
3 2 2 6 2 8 3
+ u3 *v1 *(10*a11 *b12 *kap *n1 + 10*b12 *kap *n1)
3 2 5 2 7 3
+ u3 *v1*( - 30*a11 *b12 *kap *n1*n2 - 30*b12 *kap *n1*n2)
3 2 2 6 2 8 3
+ u3 *v2 *(10*a11 *b12 *kap *n1 + 10*b12 *kap *n1)
3 2 5 2 2 7 3 2
+ u3 *v2*(30*a11 *b12 *kap *n1 + 30*b12 *kap *n1 )
3 2 2 6 2 8 3
+ u3 *v3 *(10*a11 *b12 *kap *n1 + 10*b12 *kap *n1)
3 3 4 2 6 3 3
+ u3 *v3*(20*a11 *b12 *kap *m3*n1 + 20*a11*b12 *kap *m3*n1) + u3 *(
4 2 3 4 2 2
- 40*a11 *b12 *kap*n1 + 40*a11 *b12 *kap*n1*n2
2 4 3 2 2 4 2 3
- 10*a11 *b12 *kap *m3 *n1 - 50*a11 *b12 *kap *n1
2 4 2 2 2 4 2 2
+ 70*a11 *b12 *kap *n1*n2 + 10*a11 *b12 *kap *n1*n3
6 4 2 6 3 3 6 3 2
- 10*b12 *kap *m3 *n1 + 5*b12 *kap *n1 + 30*b12 *kap *n1*n2
6 3 2
+ 10*b12 *kap *n1*n3 )
2 2 4 2 2 6 3 2
+ u3 *v1*( - 30*a11 *b12 *kap *m3*n1 - 30*b12 *kap *m3*n1 )
2 2 4 2 6 3 2
+ u3 *v2*( - 30*a11 *b12 *kap *m3*n1*n2 - 30*b12 *kap *m3*n1*n2) + u3 *(
5 3 5 2 4 2
- 180*a11 *n1 *n3 + 180*a11 *n1*n2 *n3 - 60*a11 *b12*kap*m3*n1 *n2
4 3 3 2 3
- 300*a11 *b12*kap*m3*n2 - 300*a11 *b12 *kap*n1 *n3
3 2 2 2 3 2 2
+ 120*a11 *b12 *kap*n1*n2 *n3 - 60*a11 *b12 *kap *m3*n1 *n2
2 3 2 3 4 2 3
- 300*a11 *b12 *kap *m3*n2 - 90*a11*b12 *kap *n1 *n3
4 2 2 2 4 2 3
- 60*a11*b12 *kap *n1*n2 *n3) + u3*v1 *(60*a11 *b12 *n1
4 2 2 2 4 3 2 4 2
- 60*a11 *b12 *n1*n2 + 90*a11 *b12 *kap*n1 - 90*a11 *b12 *kap*n1*n2
6 2 3 6 2 2 4 3
+ 15*b12 *kap *n1 - 30*b12 *kap *n1*n2 ) + u3*v1*( - 120*a11 *b12*n1 *n2
4 3 2 3 3
+ 120*a11 *b12*n1*n2 - 210*a11 *b12 *kap*n1 *n2
2 3 3 5 2 3 5 2 3
+ 210*a11 *b12 *kap*n1*n2 - 75*b12 *kap *n1 *n2 + 90*b12 *kap *n1*n2 ) +
2 4 2 3 4 2 2 2 4 3
u3*v2 *(60*a11 *b12 *n1 - 60*a11 *b12 *n1*n2 + 90*a11 *b12 *kap*n1
2 4 2 6 2 3 6 2 2
- 90*a11 *b12 *kap*n1*n2 + 15*b12 *kap *n1 - 30*b12 *kap *n1*n2 )
2 3 4 2 3 2 2
+ u3*v2*( - 30*a11 *b12 *kap*n1 + 30*a11 *b12 *kap*n1 *n2
5 2 4 5 2 2 2 2
- 45*b12 *kap *n1 + 30*b12 *kap *n1 *n2 ) + u3*v3 *(
4 2 3 4 2 2 2 4 3
60*a11 *b12 *n1 - 60*a11 *b12 *n1*n2 + 90*a11 *b12 *kap*n1
2 4 2 6 2 3 6 2 2
- 90*a11 *b12 *kap*n1*n2 + 15*b12 *kap *n1 - 30*b12 *kap *n1*n2 ) + u3*
4 2 3 4 2 2 4 3 2
( - 60*a11 *kap*m3 *n1 + 60*a11 *kap*m3 *n1*n2 + 60*a11 *n1 *n3
4 2 2 2 2 2 2 3
- 60*a11 *n1*n2 *n3 - 90*a11 *b12 *kap *m3 *n1
2 2 2 2 2 2 2 3 2
+ 90*a11 *b12 *kap *m3 *n1*n2 + 90*a11 *b12 *kap*n1 *n3
2 2 2 2 4 3 2 3
- 90*a11 *b12 *kap*n1*n2 *n3 - 15*b12 *kap *m3 *n1
4 3 2 2 4 2 3 2 4 2 2 2
+ 30*b12 *kap *m3 *n1*n2 + 15*b12 *kap *n1 *n3 - 30*b12 *kap *n1*n2 *n3 )
2 2 4 2 2 2 2
+ v1*(30*a11 *b12 *kap*m3*n1 - 30*a11 *b12 *kap*m3*n1 *n2
4 2 4 4 2 2 2
+ 45*b12 *kap *m3*n1 - 30*b12 *kap *m3*n1 *n2 )
4 2 3
+ 15*v2*b12 *kap *m3*n1 *n2
which is not further factorizable.
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u1*v2*b12 + u1*n1 + u2**2*a11 - u2*v1*b12 + u2*n2 - u3**2*a11 +
u3*n3 + v3*m3$
FI=u1**2*u3**3*(20*a11**4*b12**4*kap**2*n1 + 30*a11**2*b12**6*kap**3*n1 + 10*b12
**8*kap**4*n1) + 15*u1**2*u3*b12**6*kap**3*n1**3 + u1*u2*u3*( - 60*a11**2*b12**4
*kap**2*n1**2*n2 - 60*b12**6*kap**3*n1**2*n2) + u1*u3**3*v2*(20*a11**3*b12**5*
kap**2*n1 + 20*a11*b12**7*kap**3*n1) + u1*u3**3*( - 40*a11**3*b12**4*kap**2*n1**
2 - 40*a11*b12**6*kap**3*n1**2) + u1*u3**2*v3*(30*a11**2*b12**5*kap**2*n1*n2 +
30*b12**7*kap**3*n1*n2) + u1*u3**2*(30*a11**2*b12**4*kap**2*n1**2*n3 + 30*b12**6
*kap**3*n1**2*n3) + u1*u3*v2*( - 60*a11**3*b12**3*kap*n1**3 + 60*a11**3*b12**3*
kap*n1*n2**2 - 90*a11*b12**5*kap**2*n1**3 + 60*a11*b12**5*kap**2*n1*n2**2) + u1*
v1*(60*a11**3*b12**2*kap*m3*n1**3 - 60*a11**3*b12**2*kap*m3*n1*n2**2 + 90*a11*
b12**4*kap**2*m3*n1**3 - 60*a11*b12**4*kap**2*m3*n1*n2**2) - 15*u1*v3*b12**5*kap
**2*n1**3*n2 + u1*(60*a11**3*b12*kap*m3*n1**3*n2 - 60*a11**3*b12*kap*m3*n1*n2**3
- 30*a11**2*b12**2*kap*n1**4*n3 + 30*a11**2*b12**2*kap*n1**2*n2**2*n3 + 60*a11*
b12**3*kap**2*m3*n1**3*n2 - 60*a11*b12**3*kap**2*m3*n1*n2**3 - 45*b12**4*kap**2*
n1**4*n3 + 30*b12**4*kap**2*n1**2*n2**2*n3) + u2**2*u3**3*(20*a11**4*b12**4*kap
**2*n1 + 30*a11**2*b12**6*kap**3*n1 + 10*b12**8*kap**4*n1) + u2**2*u3*(30*a11**2
*b12**4*kap**2*n1**3 - 30*a11**2*b12**4*kap**2*n1*n2**2 + 45*b12**6*kap**3*n1**3
- 30*b12**6*kap**3*n1*n2**2) + u2*u3**3*v1*( - 20*a11**3*b12**5*kap**2*n1 - 20*
a11*b12**7*kap**3*n1) + u2*u3**3*( - 40*a11**3*b12**4*kap**2*n1*n2 - 40*a11*b12
**6*kap**3*n1*n2) + u2*u3**2*v3*( - 30*a11**2*b12**5*kap**2*n1**2 - 30*b12**7*
kap**3*n1**2) + u2*u3**2*(30*a11**2*b12**4*kap**2*n1*n2*n3 + 30*b12**6*kap**3*n1
*n2*n3) + u2*u3*v1*(60*a11**3*b12**3*kap*n1**3 - 60*a11**3*b12**3*kap*n1*n2**2 +
90*a11*b12**5*kap**2*n1**3 - 60*a11*b12**5*kap**2*n1*n2**2) + u2*v2*(60*a11**3*
b12**2*kap*m3*n1**3 - 60*a11**3*b12**2*kap*m3*n1*n2**2 - 120*a11**2*b12**3*kap*
n1**2*n2*n3 + 90*a11*b12**4*kap**2*m3*n1**3 - 60*a11*b12**4*kap**2*m3*n1*n2**2 -
120*b12**5*kap**2*n1**2*n2*n3) + u2*v3*(30*a11**2*b12**3*kap*n1**4 - 30*a11**2*
b12**3*kap*n1**2*n2**2 + 45*b12**5*kap**2*n1**4 - 30*b12**5*kap**2*n1**2*n2**2)
+ u2*(120*a11**4*n1**3*n2*n3 - 120*a11**4*n1*n2**3*n3 + 330*a11**2*b12**2*kap*n1
**3*n2*n3 - 210*a11**2*b12**2*kap*n1*n2**3*n3 + 195*b12**4*kap**2*n1**3*n2*n3 -
90*b12**4*kap**2*n1*n2**3*n3) + u3**5*(40*a11**4*b12**4*kap**2*n1 + 38*a11**2*
b12**6*kap**3*n1 - 2*b12**8*kap**4*n1) + u3**4*( - 40*a11**3*b12**4*kap**2*n1*n3
- 40*a11*b12**6*kap**3*n1*n3) + u3**3*v1**2*(10*a11**2*b12**6*kap**2*n1 + 10*
b12**8*kap**3*n1) + u3**3*v1*( - 30*a11**2*b12**5*kap**2*n1*n2 - 30*b12**7*kap**
3*n1*n2) + u3**3*v2**2*(10*a11**2*b12**6*kap**2*n1 + 10*b12**8*kap**3*n1) + u3**
3*v2*(30*a11**2*b12**5*kap**2*n1**2 + 30*b12**7*kap**3*n1**2) + u3**3*v3**2*(10*
a11**2*b12**6*kap**2*n1 + 10*b12**8*kap**3*n1) + u3**3*v3*(20*a11**3*b12**4*kap
**2*m3*n1 + 20*a11*b12**6*kap**3*m3*n1) + u3**3*( - 40*a11**4*b12**2*kap*n1**3 +
40*a11**4*b12**2*kap*n1*n2**2 - 10*a11**2*b12**4*kap**3*m3**2*n1 - 50*a11**2*
b12**4*kap**2*n1**3 + 70*a11**2*b12**4*kap**2*n1*n2**2 + 10*a11**2*b12**4*kap**2
*n1*n3**2 - 10*b12**6*kap**4*m3**2*n1 + 5*b12**6*kap**3*n1**3 + 30*b12**6*kap**3
*n1*n2**2 + 10*b12**6*kap**3*n1*n3**2) + u3**2*v1*( - 30*a11**2*b12**4*kap**2*m3
*n1**2 - 30*b12**6*kap**3*m3*n1**2) + u3**2*v2*( - 30*a11**2*b12**4*kap**2*m3*n1
*n2 - 30*b12**6*kap**3*m3*n1*n2) + u3**2*( - 180*a11**5*n1**3*n3 + 180*a11**5*n1
*n2**2*n3 - 60*a11**4*b12*kap*m3*n1**2*n2 - 300*a11**4*b12*kap*m3*n2**3 - 300*
a11**3*b12**2*kap*n1**3*n3 + 120*a11**3*b12**2*kap*n1*n2**2*n3 - 60*a11**2*b12**
3*kap**2*m3*n1**2*n2 - 300*a11**2*b12**3*kap**2*m3*n2**3 - 90*a11*b12**4*kap**2*
n1**3*n3 - 60*a11*b12**4*kap**2*n1*n2**2*n3) + u3*v1**2*(60*a11**4*b12**2*n1**3
- 60*a11**4*b12**2*n1*n2**2 + 90*a11**2*b12**4*kap*n1**3 - 90*a11**2*b12**4*kap*
n1*n2**2 + 15*b12**6*kap**2*n1**3 - 30*b12**6*kap**2*n1*n2**2) + u3*v1*( - 120*
a11**4*b12*n1**3*n2 + 120*a11**4*b12*n1*n2**3 - 210*a11**2*b12**3*kap*n1**3*n2 +
210*a11**2*b12**3*kap*n1*n2**3 - 75*b12**5*kap**2*n1**3*n2 + 90*b12**5*kap**2*
n1*n2**3) + u3*v2**2*(60*a11**4*b12**2*n1**3 - 60*a11**4*b12**2*n1*n2**2 + 90*
a11**2*b12**4*kap*n1**3 - 90*a11**2*b12**4*kap*n1*n2**2 + 15*b12**6*kap**2*n1**3
- 30*b12**6*kap**2*n1*n2**2) + u3*v2*( - 30*a11**2*b12**3*kap*n1**4 + 30*a11**2
*b12**3*kap*n1**2*n2**2 - 45*b12**5*kap**2*n1**4 + 30*b12**5*kap**2*n1**2*n2**2)
+ u3*v3**2*(60*a11**4*b12**2*n1**3 - 60*a11**4*b12**2*n1*n2**2 + 90*a11**2*b12
**4*kap*n1**3 - 90*a11**2*b12**4*kap*n1*n2**2 + 15*b12**6*kap**2*n1**3 - 30*b12
**6*kap**2*n1*n2**2) + u3*( - 60*a11**4*kap*m3**2*n1**3 + 60*a11**4*kap*m3**2*n1
*n2**2 + 60*a11**4*n1**3*n3**2 - 60*a11**4*n1*n2**2*n3**2 - 90*a11**2*b12**2*kap
**2*m3**2*n1**3 + 90*a11**2*b12**2*kap**2*m3**2*n1*n2**2 + 90*a11**2*b12**2*kap*
n1**3*n3**2 - 90*a11**2*b12**2*kap*n1*n2**2*n3**2 - 15*b12**4*kap**3*m3**2*n1**3
+ 30*b12**4*kap**3*m3**2*n1*n2**2 + 15*b12**4*kap**2*n1**3*n3**2 - 30*b12**4*
kap**2*n1*n2**2*n3**2) + v1*(30*a11**2*b12**2*kap*m3*n1**4 - 30*a11**2*b12**2*
kap*m3*n1**2*n2**2 + 45*b12**4*kap**2*m3*n1**4 - 30*b12**4*kap**2*m3*n1**2*n2**2
) + 15*v2*b12**4*kap**2*m3*n1**3*n2$