攻防博弈的不同版本和纳什均衡策略

mathe · 发表于 2025-5-24 21:58:21

KeyTo9_Fans 发表于 2025-4-30 22:05
回贴里给出的解是【“轰对轰”可以相互抵消，双方各扣1点能量后，游戏继续（而不是同归于尽，平局）】的版 ...

这个题目对应的方程非常复杂，KeyTo9_Fans这里给出的有64个参数，按他这个表格的顺序可以依次命名为v0,v1,...,v63, 那么我现在可以将所有变量全部表示为v37,v38,v39的组合：

v21=((4*v39^2 + (2*v38 - 10)*v39 + (-v38 + 4))*v37^2 + (16*v39^3 + (8*v38 - 24)*v39^2 + (-12*v38 + 16)*v39 + (4*v38 - 4))*v37 + (-16*v39^4 + 24*v39^3 - 12*v39^2 + (-2*v38^3 + 4*v38^2 - 2*v38 + 2)*v39 + (v38^3 - 2*v38^2 + v38)))/((4*v39^2 + (2*v38 - 14)*v39 + (-v38 + 4))*v37^2 + (24*v39^3 + (16*v38 - 20)*v39^2 + (2*v38^2 - 26*v38 + 12)*v39 + (-4*v38^2 + 12*v38 - 4))*v37 + (-32*v39^4 + (-8*v38 + 48)*v39^3 + (4*v38^2 + 12*v38 - 32)*v39^2 + (-8*v38^2 + 10)*v39 + (-3*v38^3 + 10*v38^2 - 7*v38)))
v19=((4*v39^2 + (2*v38 - 4)*v39)*v37^3 + (-8*v39^4 + (-8*v38 + 12)*v39^3 + (-2*v38^2 + 16*v38 - 20)*v39^2 + (5*v38^2 - 22*v38 + 24)*v39 + (-2*v38^2 + 8*v38 - 8))*v37^2 + ((-16*v38 + 16)*v39^4 + (-16*v38^2 + 40*v38)*v39^3 + (-4*v38^3 + 24*v38^2 - 12*v38 - 44)*v39^2 + (4*v38^3 - 12*v38^2 - 10*v38 + 36)*v39 + (-v38^3 + 2*v38^2 + 4*v38 - 8))*v37 + (32*v39^6 + (64*v38 - 160)*v39^5 + (40*v38^2 - 240*v38 + 312)*v39^4 + (8*v38^3 - 116*v38^2 + 376*v38 - 332)*v39^3 + (-20*v38^3 + 150*v38^2 - 332*v38 + 220)*v39^2 + (-v38^4 + 22*v38^3 - 101*v38^2 + 166*v38 - 88)*v39 + (v38^4 - 9*v38^3 + 28*v38^2 - 36*v38 + 16)))/(4*v37^4 + (-24*v39^2 + (-12*v38 + 12)*v39 + (10*v38 - 4))*v37^3 + (32*v39^4 + (32*v38 + 16)*v39^3 + (8*v38^2 - 24*v38 - 48)*v39^2 + (-16*v38^2 + 28)*v39 + (8*v38^2 - 2*v38 - 4))*v37^2 + (-96*v39^5 + (-80*v38 + 144)*v39^4 + (-8*v38^2 + 136*v38 - 80)*v39^3 + (4*v38^3 + 20*v38^2 - 96*v38 + 24)*v39^2 + (-6*v38^3 - 16*v38^2 + 44*v38 - 12)*v39 + (2*v38^3 + 4*v38^2 - 10*v38 + 4))*v37 + (64*v39^6 + (32*v38 - 128)*v39^5 + (-16*v38^2 - 32*v38 + 80)*v39^4 + (-8*v38^3 + 48*v38^2 - 24*v38)*v39^3 + (16*v38^3 - 52*v38^2 + 40*v38 - 16)*v39^2 + (-10*v38^3 + 24*v38^2 - 16*v38 + 4)*v39 + (2*v38^3 - 4*v38^2 + 2*v38)))
v22=v21/(2*v39 - 1)
v25=((-8*v39 + 4)*v37^4 + (48*v39^3 + (24*v38 - 40)*v39^2 + (-28*v38 + 8)*v39 + 8*v38)*v37^3 + (-64*v39^5 + (-64*v38 - 16)*v39^4 + (-16*v38^2 + 64*v38 + 144)*v39^3 + (36*v38^2 + 16*v38 - 140)*v39^2 + (-20*v38^2 - 40*v38 + 64)*v39 + (3*v38^2 + 12*v38 - 12))*v37^2 + (192*v39^6 + (160*v38 - 416)*v39^5 + (16*v38^2 - 432*v38 + 448)*v39^4 + (-8*v38^3 - 104*v38^2 + 544*v38 - 336)*v39^3 + (4*v38^3 + 152*v38^2 - 384*v38 + 176)*v39^2 + (4*v38^3 - 88*v38^2 + 148*v38 - 56)*v39 + (-2*v38^3 + 18*v38^2 - 24*v38 + 8))*v37 + (-128*v39^7 + (-64*v38 + 384)*v39^6 + (32*v38^2 + 192*v38 - 544)*v39^5 + (16*v38^3 - 80*v38^2 - 240*v38 + 464)*v39^4 + (-48*v38^3 + 120*v38^2 + 128*v38 - 240)*v39^3 + (-4*v38^4 + 60*v38^3 - 112*v38^2 - 8*v38 + 68)*v39^2 + (4*v38^4 - 32*v38^3 + 52*v38^2 - 16*v38 - 8)*v39 + (-v38^4 + 6*v38^3 - 9*v38^2 + 4*v38)))/(4*v37^4 + (-48*v39^2 + (-24*v38 + 48)*v39 + (16*v38 - 16))*v37^3 + (80*v39^4 + (80*v38 - 32)*v39^3 + (20*v38^2 - 96*v38 - 52)*v39^2 + (-40*v38^2 + 68*v38 + 24)*v39 + (19*v38^2 - 28*v38 + 4))*v37^2 + (-192*v39^5 + (-128*v38 + 352)*v39^4 + (16*v38^2 + 256*v38 - 336)*v39^3 + (16*v38^3 + 8*v38^2 - 320*v38 + 296)*v39^2 + (-16*v38^3 - 36*v38^2 + 224*v38 - 176)*v39 + (4*v38^3 + 14*v38^2 - 56*v38 + 40))*v37 + (64*v39^6 - 64*v38*v39^5 + (-112*v38^2 + 384*v38 - 304)*v39^4 + (-32*v38^3 + 336*v38^2 - 736*v38 + 496)*v39^3 + (80*v38^3 - 440*v38^2 + 720*v38 - 388)*v39^2 + (4*v38^4 - 80*v38^3 + 292*v38^2 - 380*v38 + 168)*v39 + (-3*v38^4 + 28*v38^3 - 77*v38^2 + 84*v38 - 32)))
v17=(4*v39*v37^4 + (-8*v39^3 + (-4*v38 + (-16*v19 - 24))*v39^2 + (-8*v19*v38 + (32*v19 + 16))*v39 + (8*v19*v38 - 16*v19))*v37^3 + ((32*v19 + 56)*v39^4 + ((32*v19 + 32)*v38 + (-32*v19 - 12))*v39^3 + ((8*v19 + 2)*v38^2 + (-48*v19 - 40)*v38 + (-48*v19 - 16))*v39^2 + ((-16*v19 - 5)*v38^2 + (24*v19 + 28)*v38 + (64*v19 - 12))*v39 + ((8*v19 + 2)*v38^2 + (-8*v19 - 8)*v38 + (-16*v19 + 8)))*v37^2 + ((-96*v19 - 96)*v39^5 + ((-80*v19 - 32)*v38 + (240*v19 + 96))*v39^4 + ((-8*v19 + 16)*v38^2 + (184*v19 + 32)*v38 + (-192*v19 - 24))*v39^3 + ((4*v19 + 4)*v38^3 + (20*v19 - 24)*v38^2 + (-168*v19 - 24)*v38 + (48*v19 + 32))*v39^2 + ((-6*v19 - 4)*v38^3 + (-16*v19 + 12)*v38^2 + (80*v19 + 16)*v38 - 32)*v39 + ((2*v19 + 1)*v38^3 + (4*v19 - 2)*v38^2 + (-16*v19 - 4)*v38 + 8))*v37 + ((64*v19 + 32)*v39^6 + ((32*v19 - 32)*v38 + (-192*v19 + 32))*v39^5 + ((-16*v19 - 40)*v38^2 + (-64*v19 + 176)*v38 + (208*v19 - 216))*v39^4 + ((-8*v19 - 8)*v38^3 + (48*v19 + 116)*v38^2 + (40*v19 - 328)*v38 + (-96*v19 + 300))*v39^3 + ((16*v19 + 20)*v38^3 + (-52*v19 - 150)*v38^2 + (-8*v19 + 316)*v38 + (16*v19 - 216))*v39^2 + (v38^4 + (-10*v19 - 22)*v38^3 + (24*v19 + 101)*v38^2 - 164*v38 + 88)*v39 + (-v38^4 + (2*v19 + 9)*v38^3 + (-4*v19 - 28)*v38^2 + 36*v38 - 16)))/((4*v39 - 4)*v37^4 + (-8*v39^3 + (-4*v38 - 12)*v39^2 + (6*v38 + 32)*v39 + (-2*v38 - 12))*v37^3 + (48*v39^4 + (24*v38 - 48)*v39^3 + (-48*v38 - 36)*v39^2 + (30*v38 + 48)*v39 + (-6*v38 - 12))*v37^2 + (-96*v39^5 + (-48*v38 + 208)*v39^4 + (120*v38 - 136)*v39^3 + (-108*v38 + 12)*v39^2 + (42*v38 + 16)*v39 + (-6*v38 - 4))*v37 + (64*v39^6 + (32*v38 - 192)*v39^5 + (-96*v38 + 224)*v39^4 + (112*v38 - 128)*v39^3 + (-64*v38 + 36)*v39^2 + (18*v38 - 4)*v39 - 2*v38))
v53=(4*v37^4 + (-16*v39^2 + (-8*v38 - 8)*v39 + (4*v38 + 8))*v37^3 + (16*v39^4 + (16*v38 + 48)*v39^3 + (4*v38^2 + 16*v38 - 52)*v39^2 + (-4*v38^2 - 36*v38 + 16)*v39 + (-v38^2 + 16*v38 - 4))*v37^2 + (-64*v39^5 + (-64*v38 + 48)*v39^4 + (-16*v38^2 + 88*v38 + 24)*v39^3 + (36*v38^2 - 28*v38 - 48)*v39^2 + (2*v38^3 - 22*v38^2 - 16*v38 + 32)*v39 + (-v38^3 + 4*v38^2 + 8*v38 - 8))*v37 + (64*v39^6 + (64*v38 - 160)*v39^5 + (16*v38^2 - 176*v38 + 192)*v39^4 + (-56*v38^2 + 208*v38 - 136)*v39^3 + (-4*v38^3 + 64*v38^2 - 124*v38 + 52)*v39^2 + (4*v38^3 - 30*v38^2 + 36*v38 - 8)*v39 + (-v38^3 + 5*v38^2 - 4*v38)))/((16*v39^4 + (24*v38 - 64)*v39^3 + (12*v38^2 - 72*v38 + 96)*v39^2 + (2*v38^3 - 24*v38^2 + 72*v38 - 64)*v39 + (-2*v38^3 + 12*v38^2 - 24*v38 + 16))*v37 + ((16*v38 - 16)*v39^4 + (24*v38^2 - 88*v38 + 64)*v39^3 + (12*v38^3 - 84*v38^2 + 168*v38 - 96)*v39^2 + (2*v38^4 - 26*v38^3 + 96*v38^2 - 136*v38 + 64)*v39 + (-2*v38^4 + 14*v38^3 - 36*v38^2 + 40*v38 - 16)))
v33=(16*v37^5 + (-80*v39^2 - 40*v38*v39 + 40*v38)*v37^4 + (96*v39^4 + (96*v38 + 112)*v39^3 + (24*v38^2 - 112*v38 - 80)*v39^2 + (-84*v38^2 - 32*v38 + 80)*v39 + (28*v38^2 + 48*v38 - 48))*v37^3 + (-256*v39^5 + (-96*v38 + 224)*v39^4 + (96*v38^2 + 432*v38 + (16*v53 - 368))*v39^3 + (40*v38^3 + 72*v38^2 + (24*v53 - 528)*v38 + (-48*v53 + 304))*v39^2 + (-44*v38^3 + (12*v53 - 156)*v38^2 + (-48*v53 + 288)*v38 + (48*v53 - 80))*v39 + (2*v53*v38^3 + (-12*v53 + 84)*v38^2 + (24*v53 - 96)*v38 + (-16*v53 + 16)))*v37^2 + (64*v39^6 + (-384*v38 + 224)*v39^5 + (-384*v38^2 + 768*v38 - 224)*v39^4 + (-64*v38^3 + 672*v38^2 + (32*v53 - 640)*v38 + (-32*v53 - 48))*v39^3 + (12*v38^4 + 176*v38^3 + (48*v53 - 552)*v38^2 + (-144*v53 + 240)*v38 + (96*v53 + 144))*v39^2 + (2*v38^4 + (24*v53 - 136)*v38^3 + (-120*v53 + 180)*v38^2 + (192*v53 + 64)*v38 + (-96*v53 - 112))*v39 + ((4*v53 - 4)*v38^4 + (-28*v53 + 32)*v38^3 + (72*v53 - 12)*v38^2 + (-80*v53 - 48)*v38 + (32*v53 + 32)))*v37 + (128*v39^7 + (384*v38 - 704)*v39^6 + (192*v38^2 - 1184*v38 + 1312)*v39^5 + (-32*v38^3 - 512*v38^2 + 1760*v38 - 1376)*v39^4 + (-24*v38^4 + (16*v53 + 736)*v38^2 + (-32*v53 - 1616)*v38 + (16*v53 + 944))*v39^3 + (28*v38^4 + (24*v53 + 72)*v38^3 + (-96*v53 - 600)*v38^2 + (120*v53 + 912)*v38 + (-48*v53 - 416))*v39^2 + (2*v38^5 + (12*v53 - 10)*v38^4 + (-72*v53 - 76)*v38^3 + (156*v53 + 284)*v38^2 + (-144*v53 - 312)*v38 + (48*v53 + 112))*v39 + (2*v53*v38^5 + (-16*v53 - 4)*v38^4 + (50*v53 + 32)*v38^3 + (-76*v53 - 68)*v38^2 + (56*v53 + 56)*v38 + (-16*v53 - 16))))/(12*v37^5 + (-48*v39^2 + (-24*v38 - 16)*v39 + (28*v38 + 4))*v37^4 + (48*v39^4 + (48*v38 + 112)*v39^3 + (12*v38^2 - 32*v38 - 92)*v39^2 + (-44*v38^2 - 92*v38 + 104)*v39 + (13*v38^2 + 60*v38 - 52))*v37^3 + (-160*v39^5 + (-96*v38 + 160)*v39^4 + (24*v38^2 + 408*v38 - 288)*v39^3 + (16*v38^3 + 144*v38^2 - 468*v38 + 196)*v39^2 + (-10*v38^3 - 204*v38^2 + 276*v38 - 40)*v39 + (-9*v38^3 + 93*v38^2 - 96*v38 + 12))*v37^2 + (64*v39^6 + (-192*v38 - 32)*v39^5 + (-240*v38^2 + 224*v38 + 304)*v39^4 + (-64*v38^3 + 384*v38^2 + 96*v38 - 592)*v39^3 + (152*v38^3 - 216*v38^2 - 408*v38 + 524)*v39^2 + (10*v38^4 - 104*v38^3 - 12*v38^2 + 364*v38 - 264)*v39 + (-5*v38^4 + 22*v38^3 + 27*v38^2 - 100*v38 + 56))*v37 + (128*v39^7 + (384*v38 - 704)*v39^6 + (288*v38^2 - 1440*v38 + 1472)*v39^5 + (64*v38^3 - 992*v38^2 + 2560*v38 - 1792)*v39^4 + (-264*v38^3 + 1560*v38^2 - 2664*v38 + 1408)*v39^3 + (-20*v38^4 + 380*v38^3 - 1332*v38^2 + 1676*v38 - 708)*v39^2 + (30*v38^4 - 254*v38^3 + 628*v38^2 - 620*v38 + 216)*v39 + (v38^5 - 15*v38^4 + 71*v38^3 - 133*v38^2 + 108*v38 - 32)))
v26=((4*v39^2 + (2*v38 + (4*v25 - 8))*v39 + ((2*v25 - 2)*v38 + (-4*v25 + 4)))*v37 + ((4*v38 - 4*v25)*v39^2 + (2*v38^2 - 6*v38 + 4*v25)*v39 + ((v25 - 1)*v38^2 + (-2*v25 + 2)*v38)))/(2*v37^2 + (-4*v39^2 + (-2*v38 - 2)*v39 + (v38 + 2))*v37 + (8*v39^3 + (4*v38 - 8)*v39^2 + (-4*v38 + 2)*v39 + v38))
v30=(4*v37^3 + (-8*v39^2 - 4*v38*v39 + (8*v38 - 4))*v37^2 + (8*v39^3 + (-8*v38 - 4)*v39^2 + (-6*v38^2 - 4*v38 + 16)*v39 + (3*v38^2 + 4*v38 - 8))*v37 + (16*v39^4 + (32*v38 - 56)*v39^3 + (12*v38^2 - 60*v38 + 60)*v39^2 + (-18*v38^2 + 48*v38 - 32)*v39 + (-v38^3 + 9*v38^2 - 16*v38 + 8)))/(4*v37^3 + (-8*v39^2 + (-4*v38 - 4)*v39 + 6*v38)*v37^2 + (16*v39^3 - 8*v39^2 + (-4*v38^2 - 8*v38 + 8)*v39 + (2*v38^2 + 4*v38 - 4))*v37 + ((16*v38 - 16)*v39^3 + (8*v38^2 - 24*v38 + 16)*v39^2 + (-8*v38^2 + 12*v38 - 4)*v39 + (2*v38^2 - 2*v38)))
v35=((-2*v33 + 2)*v37^2 + ((4*v33 - 4)*v39^2 + ((2*v33 - 2)*v38 + (2*v33 + 2))*v39 + ((-v33 + 3)*v38 + (-2*v33 - 2)))*v37 + ((-8*v33 + 8)*v39^3 + ((-4*v33 + 4)*v38 + (12*v33 - 12))*v39^2 + ((8*v33 - 4)*v38 + (-10*v33 + 6))*v39 + ((v33 + 1)*v38^2 + (-5*v33 - 1)*v38 + 4*v33)))/((4*v39 + (2*v38 - 4))*v37 + ((4*v38 - 4)*v39 + (2*v38^2 - 6*v38 + 4)))
v42=(v37 + (v38 - 1))/((2*v39 + 1)*v37 + ((2*v38 - 4)*v39 + 1))
v41=(v37 + (-2*v39 + 1))*v42/(v37+v38-1)
v46=(-4*v39*v41 + 4*v39*v42)/(4*v42)
v55=-(-2*v41*v46 + (v41 + v42))/(2*v41 - 2*v42)
v59=(2*v55 - v46)/(2*v55 + (-2*v46 + 1))
v62=1/(2*v59+1)
v57=-(4*v59^2 - 6*v59 + 2)
v54=(2-2*v55)/(2-2*v59)
v63=1/2
v61=v62
v60=1-v61-v62
v58=2-2*v59
v56=1-v57-v58
v52=1-v53-v54
v51=1
v50=0
v49=0
v48=1
v47=1-v59
v45=v58/2
v44=1-v45-v46
v43=1/2
v40=1-v41-v42
v36=1-v37-v38
v34=0
v32=1-v33
v31=1-v55
v29=1-v55
v28=1-v29-v30
v27=1-v39
v24=1-v25-v26
v23=1/2
v20=1-v21-v22
v18=0
v16=1-v17
v15=1-v51
v14=2/3
v13=0
v12=1/3
v11=1-v35
v10=v33
v9=0
v8=1-v10
v7=1-v19
v6=2-2*v19
v5=0
v4=1-v6
v3=1/2
v2=0
v1=0
v0=1

但是v37,v38,v39的表达式非常复杂

mathe · 发表于 2025-5-24 22:46:10

KeyTo9_Fans 发表于 2025-4-30 22:05
回贴里给出的解是【“轰对轰”可以相互抵消，双方各扣1点能量后，游戏继续（而不是同归于尽，平局）】的版 ...

Singular的数值解:

[6]:
[1]:
1
[2]:
0
[3]:
0
[4]:
0.5
[5]:
0.5322164753917473785730130135837516764153
[6]:
0
[7]:
0.4677835246082526214269869864162483235847
[8]:
0.2338917623041263107134934932081241617924
[9]:
0.5435599392114846833945392592447825794875
[10]:
0
[11]:
0.4564400607885153166054607407552174205125
[12]:
0.1067575702040283885142929385064802401963
[13]:
0.3333333333333333333333333333333333333333
[14]:
0
[15]:
0.6666666666666666666666666666666666666667
[16]:
0
[17]:
0.6767027602640444037698408890552034157298
[18]:
0.3232972397359555962301591109447965842702
[19]:
0
[20]:
0.7661082376958736892865065067918758382076
[21]:
0.2890991910655504452694973388386245833886
[22]:
0.1677023090143674924812794066684739089692
[23]:
0.5431984999200820622492232544929015076422
[24]:
0.5
[25]:
0.229723376779308992354268786751867182406
[26]:
0.1484504857764892184708816136855450780036
[27]:
0.6218261374442017891748495995625877395904
[28]:
0.345634414455267594632411852533035565922
[29]:
0.2960166353232403562260597893149840700427
[30]:
0.1964044119198634755202773300619960957683
[31]:
0.507578952756896168253662880623019834189
[32]:
0.1964044119198634755202773300619960957683
[33]:
0.5435599392114846833945392592447825794875
[34]:
0.4564400607885153166054607407552174205125
[35]:
0
[36]:
0.8932424297959716114857070614935197598037
[37]:
0.235080991685955290728811793040237656087
[38]:
0.2272600907872339989668723236668473384232
[39]:
0.5376589175268107103043158832929150054898
[40]:
0.654365585544732405367588147466964434078
[41]:
0.1865110237728683122925916452336539105152
[42]:
0.2093678467839996568771268907180845244511
[43]:
0.6041211294431320308302814640482615650337
[44]:
0.5
[45]:
0.2456982845434307717922939735167945759736
[46]:
0.3267169971550315044857450841469151865197
[47]:
0.4275847183015377237219609423362902375067
[48]:
0.3267169971550315044857450841469151865197
[49]:
1
[50]:
0
[51]:
0
[52]:
1
[53]:
0.172208189184588117717598023423322049212
[54]:
0.2266464353678437119922203717975587385607
[55]:
0.6011453754475681702901816047791192122273
[56]:
0.8035955880801365244797226699380039042317
[57]:
0.1201079962998774388409560385447331389395
[58]:
0.2264580093900595521875537931614364880211
[59]:
0.6534339943100630089714901682938303730394
[60]:
0.6732830028449684955142549158530848134803
[61]:
0.1476907126624975141627392922523725624813
[62]:
0.4261546436687512429186303538738137187593
[63]:
0.4261546436687512429186303538738137187593
[64]:
0.5

mathe · 发表于 2025-5-25 08:39:48

根据KeyTo9_Fans的结果给出的对应的Singular代码

LIB "primdec.lib";
LIB "solve.lib";
ring r=0,(v(0..63)),dp;
//VID(0,0,XI)+VID(0,0,HO)+VID(0,0,FA)=1
poly f0=v(0)+v(1)+v(2)-1;
//VID(0,1,XI)+VID(0,1,HO)+VID(0,1,FA)=1
poly f1=v(4)+v(5)+v(6)-1;
//VID(0,2,XI)+VID(0,2,HO)+VID(0,2,FA)=1
poly f2=v(8)+v(9)+v(10)-1;
//VID(0,3,XI)+VID(0,3,HO)+VID(0,3,FA)=1
poly f3=v(12)+v(13)+v(14)-1;
//VID(1,0,XI)+VID(1,0,HO)+VID(1,0,FA)=1
poly f4=v(16)+v(17)+v(18)-1;
//VID(1,1,XI)+VID(1,1,HO)+VID(1,1,FA)=1
poly f5=v(20)+v(21)+v(22)-1;
//VID(1,2,XI)+VID(1,2,HO)+VID(1,2,FA)=1
poly f6=v(24)+v(25)+v(26)-1;
//VID(1,3,XI)+VID(1,3,HO)+VID(1,3,FA)=1
poly f7=v(28)+v(29)+v(30)-1;
//VID(2,0,XI)+VID(2,0,HO)+VID(2,0,FA)=1
poly f8=v(32)+v(33)+v(34)-1;
//VID(2,1,XI)+VID(2,1,HO)+VID(2,1,FA)=1
poly f9=v(36)+v(37)+v(38)-1;
//VID(2,2,XI)+VID(2,2,HO)+VID(2,2,FA)=1
poly f10=v(40)+v(41)+v(42)-1;
//VID(2,3,XI)+VID(2,3,HO)+VID(2,3,FA)=1
poly f11=v(44)+v(45)+v(46)-1;
//VID(3,0,XI)+VID(3,0,HO)+VID(3,0,FA)=1
poly f12=v(48)+v(49)+v(50)-1;
//VID(3,1,XI)+VID(3,1,HO)+VID(3,1,FA)=1
poly f13=v(52)+v(53)+v(54)-1;
//VID(3,2,XI)+VID(3,2,HO)+VID(3,2,FA)=1
poly f14=v(56)+v(57)+v(58)-1;
//VID(3,3,XI)+VID(3,3,HO)+VID(3,3,FA)=1
poly f15=v(60)+v(61)+v(62)-1;
poly f16=2*v(3)-1;
poly f17=2*v(23)-1;
poly f18=2*v(43)-1;
poly f19=2*v(63)-1;
poly f20=v(19)+v(7)-1;
poly f21=v(35)+v(11)-1;
poly f22=v(39)+v(27)-1;
poly f23=v(51)+v(15)-1;
poly f24=v(55)+v(31)-1;
poly f25=v(59)+v(47)-1;
poly f26=v(2);
poly f27=v(18);
poly f28=v(34);
poly f29=v(50);
poly f30=v(1);
poly f31=v(5);
poly f32=v(9);
poly f33=v(13);
poly f34=v(0)-1;
poly f35=v(48)-1;
//VID(0,0,MT)
poly f36=v(0)*v(0)*v(23)+v(0)*v(2)*v(19)+v(2)*v(0)*v(7)+v(2)*v(2)*v(3)-v(3);
//VID(0,1,MT)
poly f37=v(4)*v(16)*v(27)+v(4)*v(18)*v(23)+v(6)*v(16)*v(11)+v(6)*v(17)*v(3)+v(6)*v(18)*v(7)-v(7);
//VID(0,2,MT)
poly f38=v(8)*v(32)*v(31)+v(8)*v(34)*v(27)+v(10)*v(32)*v(15)+v(10)*v(33)*v(7)+v(10)*v(34)*v(11)-v(11);
//VID(0,3,MT)
poly f39=0+v(12)*v(50)*v(31)+v(14)*v(49)*v(11)+v(14)*v(50)*v(15)-v(15);
//VID(1,0,MT)
poly f40=v(16)*v(4)*v(39)+v(16)*v(6)*v(35)+v(17)*v(4)+v(17)*v(6)*v(3)+v(18)*v(4)*v(23)+v(18)*v(6)*v(19)-v(19);
//VID(1,1,MT)
poly f41=v(20)*v(20)*v(43)+v(20)*v(22)*v(39)+v(21)*v(20)+v(21)*v(21)*v(3)+v(21)*v(22)*v(7)+v(22)*v(20)*v(27)+v(22)*v(21)*v(19)+v(22)*v(22)*v(23)-v(23);
//VID(1,2,MT)
poly f42=v(24)*v(36)*v(47)+v(24)*v(38)*v(43)+v(25)*v(36)+v(25)*v(37)*v(7)+v(25)*v(38)*v(11)+v(26)*v(36)*v(31)+v(26)*v(37)*v(23)+v(26)*v(38)*v(27)-v(27);
//VID(1,3,MT)
poly f43=0+v(28)*v(54)*v(47)+v(29)*v(52)+v(29)*v(53)*v(11)+v(29)*v(54)*v(15)+v(30)*v(53)*v(27)+v(30)*v(54)*v(31)-v(31);
//VID(2,0,MT)
poly f44=v(32)*v(8)*v(55)+v(32)*v(10)*v(51)+v(33)*v(8)+v(33)*v(10)*v(19)+v(34)*v(8)*v(39)+v(34)*v(10)*v(35)-v(35);
//VID(2,1,MT)
poly f45=v(36)*v(24)*v(59)+v(36)*v(26)*v(55)+v(37)*v(24)+v(37)*v(25)*v(19)+v(37)*v(26)*v(23)+v(38)*v(24)*v(43)+v(38)*v(25)*v(35)+v(38)*v(26)*v(39)-v(39);
//VID(2,2,MT)
poly f46=v(40)*v(40)*v(63)+v(40)*v(42)*v(59)+v(41)*v(40)+v(41)*v(41)*v(23)+v(41)*v(42)*v(27)+v(42)*v(40)*v(47)+v(42)*v(41)*v(39)+v(42)*v(42)*v(43)-v(43);
//VID(2,3,MT)
poly f47=0+v(44)*v(58)*v(63)+v(45)*v(56)+v(45)*v(57)*v(27)+v(45)*v(58)*v(31)+v(46)*v(57)*v(43)+v(46)*v(58)*v(47)-v(47);
//VID(3,0,MT)
poly f48=v(48)*v(12)+v(48)*v(14)+v(49)*v(12)+v(49)*v(14)*v(35)+v(50)*v(12)*v(55)+v(50)*v(14)*v(51)-v(51);
//VID(3,1,MT)
poly f49=v(52)*v(28)+v(52)*v(30)+v(53)*v(28)+v(53)*v(29)*v(35)+v(53)*v(30)*v(39)+v(54)*v(28)*v(59)+v(54)*v(29)*v(51)+v(54)*v(30)*v(55)-v(55);
//VID(3,2,MT)
poly f50=v(56)*v(44)+v(56)*v(46)+v(57)*v(44)+v(57)*v(45)*v(39)+v(57)*v(46)*v(43)+v(58)*v(44)*v(63)+v(58)*v(45)*v(55)+v(58)*v(46)*v(59)-v(59);
//VID(3,3,MT)
poly f51=v(60)*v(60)*1/2+v(60)*v(62)+v(61)*v(60)+v(61)*v(61)*v(43)+v(61)*v(62)*v(47)+v(62)*v(61)*v(59)+v(62)*v(62)*v(63)-v(63);
//extra equation by sim
//XI[0,1]=FA[0,1]
poly f52=v(16)*v(27)+v(18)*v(23)-(v(16)*v(11)+v(18)*v(7)+v(17)*v(3));
//XI[0,2]=FA[0,2]
poly f53=v(32)*v(31)+v(34)*v(27)-(v(32)*v(15)+v(34)*v(11)+v(33)*v(7));
//XI[0,3]=FA[0,3]
poly f54=v(48)*0+v(50)*v(31)-(v(48)*0+v(50)*v(15)+v(49)*v(11));
//XI[0,3]=HO[0,3]
poly f55=v(48)*0+v(50)*v(31);
//FA[0,3]=HO[0,3]
poly f56=v(48)*0+v(50)*v(15)+v(49)*v(11);
//XI[1,0]=HO[1,0]
poly f57=v(4)*v(39)+v(6)*v(35)-(v(4)+v(6)*v(3));
//XI[1,1]=FA[1,1]
poly f58=v(20)*v(43)+v(22)*v(39)-(v(20)*v(27)+v(22)*v(23)+v(21)*v(19));
//XI[1,1]=HO[1,1]
poly f59=v(20)*v(43)+v(22)*v(39)-(v(20)+v(22)*v(7)+v(21)*v(3));
//FA[1,1]=HO[1,1]
poly f60=v(20)*v(27)+v(22)*v(23)+v(21)*v(19)-(v(20)+v(22)*v(7)+v(21)*v(3));
//XI[1,2]=FA[1,2]
poly f61=v(36)*v(47)+v(38)*v(43)-(v(36)*v(31)+v(38)*v(27)+v(37)*v(23));
//XI[1,2]=HO[1,2]
poly f62=v(36)*v(47)+v(38)*v(43)-(v(36)+v(38)*v(11)+v(37)*v(7));
//FA[1,2]=HO[1,2]
poly f63=v(36)*v(31)+v(38)*v(27)+v(37)*v(23)-(v(36)+v(38)*v(11)+v(37)*v(7));
//XI[1,3]=FA[1,3]
poly f64=v(52)*0+v(54)*v(47)-(v(52)*0+v(54)*v(31)+v(53)*v(27));
//XI[1,3]=HO[1,3]
poly f65=v(52)*0+v(54)*v(47)-(v(52)+v(54)*v(15)+v(53)*v(11));
//FA[1,3]=HO[1,3]
poly f66=v(52)*0+v(54)*v(31)+v(53)*v(27)-(v(52)+v(54)*v(15)+v(53)*v(11));
//XI[2,0]=HO[2,0]
poly f67=v(8)*v(55)+v(10)*v(51)-(v(8)+v(10)*v(19));
//XI[2,1]=FA[2,1]
poly f68=v(24)*v(59)+v(26)*v(55)-(v(24)*v(43)+v(26)*v(39)+v(25)*v(35));
//XI[2,1]=HO[2,1]
poly f69=v(24)*v(59)+v(26)*v(55)-(v(24)+v(26)*v(23)+v(25)*v(19));
//FA[2,1]=HO[2,1]
poly f70=v(24)*v(43)+v(26)*v(39)+v(25)*v(35)-(v(24)+v(26)*v(23)+v(25)*v(19));
//XI[2,2]=FA[2,2]
poly f71=v(40)*v(63)+v(42)*v(59)-(v(40)*v(47)+v(42)*v(43)+v(41)*v(39));
//XI[2,2]=HO[2,2]
poly f72=v(40)*v(63)+v(42)*v(59)-(v(40)+v(42)*v(27)+v(41)*v(23));
//FA[2,2]=HO[2,2]
poly f73=v(40)*v(47)+v(42)*v(43)+v(41)*v(39)-(v(40)+v(42)*v(27)+v(41)*v(23));
//XI[2,3]=FA[2,3]
poly f74=v(56)*0+v(58)*v(63)-(v(56)*0+v(58)*v(47)+v(57)*v(43));
//XI[2,3]=HO[2,3]
poly f75=v(56)*0+v(58)*v(63)-(v(56)+v(58)*v(31)+v(57)*v(27));
//FA[2,3]=HO[2,3]
poly f76=v(56)*0+v(58)*v(47)+v(57)*v(43)-(v(56)+v(58)*v(31)+v(57)*v(27));
//XI[3,1]=FA[3,1]
poly f77=v(28)*1+v(30)*1-(v(28)*v(59)+v(30)*v(55)+v(29)*v(51));
//XI[3,1]=HO[3,1]
poly f78=v(28)*1+v(30)*1-(v(28)+v(30)*v(39)+v(29)*v(35));
//FA[3,1]=HO[3,1]
poly f79=v(28)*v(59)+v(30)*v(55)+v(29)*v(51)-(v(28)+v(30)*v(39)+v(29)*v(35));
//XI[3,2]=FA[3,2]
poly f80=v(44)*1+v(46)*1-(v(44)*v(63)+v(46)*v(59)+v(45)*v(55));
//XI[3,2]=HO[3,2]
poly f81=v(44)*1+v(46)*1-(v(44)+v(46)*v(43)+v(45)*v(39));
//FA[3,2]=HO[3,2]
poly f82=v(44)*v(63)+v(46)*v(59)+v(45)*v(55)-(v(44)+v(46)*v(43)+v(45)*v(39));
//XI[3,3]=FA[3,3]
poly f83=v(60)*1/2+v(62)*1-(v(60)*0+v(62)*v(63)+v(61)*v(59));
//XI[3,3]=HO[3,3]
poly f84=v(60)*1/2+v(62)*1-(v(60)+v(62)*v(47)+v(61)*v(43));
//FA[3,3]=HO[3,3]
poly f85=v(60)*0+v(62)*v(63)+v(61)*v(59)-(v(60)+v(62)*v(47)+v(61)*v(43));
poly f86=3*v(12)-1;
ideal ii=f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18,f19,f20,f21,f22,f23,f24,f25,f26,f27,f28,f29,f30,f31,f32,f33,f34,f35,f36,f37,f38,f39,f40,f41,f42,f43,f44,f45,f46,f47,f48,f49,f50,f51,f52,f53,f54,f55,f56,f57,f58,f59,f60,f61,f62,f63,f64,f65,f66,f67,f68,f69,f70,f71,f72,f73,f74,f75,f76,f77,f78,f79,f80,f81,f82,f83,f84,f85,f86;
ideal i0=std(ii);
dim(i0);i0;
def AC=solve(i0,40,0);

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