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599 lines (599 loc) · 60.5 KB
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{
"n": [3, 5, 12],
"m": 136,
"z2": false,
"complexity": 988,
"multiplications": [
"m1 = (a23 + a33 - a35) * (-b32 - b36 - b42 - b56)",
"m2 = (a13 - a15 - a23 + a24 + a25) * (b54)",
"m3 = (-a21) * (b12 + b13 + b14 + b16 + b33 + b46 - b56)",
"m4 = (a22) * (b22 + b23 + b24 - b33)",
"m5 = (-a11 - a15) * (-b12)",
"m6 = (a13 - a15) * (b16 + b46 - b56)",
"m7 = (a21 + a23 - a24 + a33 - a34) * (b45 - b55)",
"m8 = (a34) * (-b24 + b34 + b35 + b44 + b45 + b46 + b54)",
"m9 = (a35) * (b22 + b32 + b36 + b42 + b52 + b55 + b56)",
"m10 = (a11 + a12 - a21) * (b11)",
"m11 = (a21 - a23 + a25 - a33 + a35) * (-b33 - b46 + b56)",
"m12 = (a11 + a12 - a21) * (b13 - b33 + b43 - b53)",
"m13 = (a12 - a32 + a33 - a34) * (-b21 + b25 + b31 + b41 - b51)",
"m14 = (-a22 - a33 + a34) * (-b21 + b25 + b41 - b51)",
"m15 = (a14) * (b14 - b31 + b34 - b41 + b44 + b54)",
"m16 = (a11 - a13 + a15 - a31) * (b16 - b36 + b46 - b56)",
"m17 = (a22) * (-b21 + b41 - b51)",
"m18 = (a32 - a35) * (-b22)",
"m19 = (-a11 - a15 + a21) * (b12 + b33 + b53)",
"m20 = (-a13 + a14 - a21) * (b11 - b15 - b45 + b55)",
"m21 = (-a22 - a31 - a32) * (b25)",
"m22 = (-a12 + a32 + a34) * (b24 - b31 - b41)",
"m23 = (-a12 + a32 - a35) * (-b22 - b51)",
"m24 = (a11 + a13 - a14 - a31) * (b11 - b15 - b35 - b45 + b55)",
"m25 = (a22 - a33 + a35) * (b26 + b33)",
"m26 = (a11 - a14 + a23 - a31 + a33) * (b35 + b45)",
"m27 = (a32 + a34) * (-b24)",
"m28 = (-a11 + a14 + a21 - a22 - a24 - a32 - a34) * (-b43)",
"m29 = (-a21) * (b15 + b45 - b55)",
"m30 = (-a22 - a32 - a34) * (-b24 - b43)",
"m31 = (a11 - a14 - a23 + a24 + a25 - a31 - a33 + a34 + a35) * (b46)",
"m32 = (-a31) * (-b13 - b14 - b16 + b23 + b26 + b33 - b43 + b53)",
"m33 = (a13 - a14 + a22 - a23 + a24) * (b41 - b51)",
"m34 = (-a22 - a32 + a35) * (-b22 + b33 + b53)",
"m35 = (-a23) * (-b32 + b34 - b42 + b54)",
"m36 = (a13 - a14 - a23 + a24 + a25) * (-b42 + b51)",
"m37 = (-a23 - a33 + a34) * (-b34 - b35 - b45 - b54)",
"m38 = (-a31) * (-b12 - b15 + b25)",
"m39 = (-a12 - a31) * (-b11 + b25)",
"m40 = (-a23 + a24 + a25) * (b42 - b54)",
"m41 = (-a33 + a35) * (b26 - b32 - b36 - b42 + b54)",
"m42 = (-a11 - a15 + a21 - a22 + a25 - a32 + a35) * (b33 + b53)",
"m43 = (a23 - a24 - a25 + a33 - a35) * (b46 + b54)",
"m44 = (a12 + a13 - a23 - a32 - a34) * (b31 + b41)",
"m45 = (a11 + a15 + a23 - a24 - a25 - a31 + a33 - a34 - a35) * (b55)",
"m46 = (a13 - a15 - a22 - a23 + a25) * (b33)",
"m47 = (a13 - a14) * (-b11 + b15 + b31 - b34 + b42 + b45 - b54 - b55)",
"m48 = (a12 - a32 - a33 + a35) * (-b26)",
"m49 = (-a15) * (-b12 + b32 + b42 - b51 + b52)",
"m50 = (-a11 - a15 + a23 + a31 + a33) * (b36 + b56)",
"m51 = (a13 - a15 - a23) * (-b32 - b42)",
"m52 = (-a23 - a33) * (-b35 + b36 - b45 + b56)",
"m53 = (-a12) * (-b11 + b21 - b22 - b24)",
"m54 = (a12) * (b13 - b23 - b33 + b43 - b53)",
"m55 = (-a12 - a31) * (-b13 + b23 + b26 + b33 - b43 + b53)",
"m56 = (a13 - a15) * (-b32 - b42 + b54)",
"m57 = (a11 - a14 - a31) * (b14 - b35 - b45 - b46)",
"m58 = (a25) * (b33 - b42 + b52 + b53)",
"m59 = (a11 + a15 - a31) * (b12 + b36 + b55 + b56)",
"m60 = (a13 - a14 - a23) * (-b31 + b34 - b41 + b54)",
"m61 = (-a11 + a14) * (-b14)",
"m62 = (-a24) * (b43 + b44 - b54)",
"m63 = (-a22 - a31 - a32) * (-b23 - b26 - b33 + b43 - b53)",
"m64 = (a13 - a15 - a21) * (-b16 - b33 - b46 + b56)",
"m65 = (a12 + a13 - a14 - a15 - a23 + a24 + a25 - a32 + a35) * (-b51)",
"m66 = (a33 - a34) * (b21 - b25 - b34 - b35 - b41 + b42 + b51 - b54)",
"m67 = (a11 - a14 - a21) * (b14 - b43)",
"m68 = (a23 - a24 - a25 + a33 - a34) * (-b42 - b55)",
"m69 = (a23 + a33 - a35) * (-b38 - b312 - b48 - b512)",
"m70 = (a13 - a15 - a23 + a24 + a25) * (b510)",
"m71 = (-a21) * (b18 + b19 + b110 + b112 + b39 + b412 - b512)",
"m72 = (a22) * (b28 + b29 + b210 - b39)",
"m73 = (-a11 - a15) * (-b18)",
"m74 = (a13 - a15) * (b112 + b412 - b512)",
"m75 = (a21 + a23 - a24 + a33 - a34) * (b411 - b511)",
"m76 = (a34) * (-b210 + b310 + b311 + b410 + b411 + b412 + b510)",
"m77 = (a35) * (b28 + b38 + b312 + b48 + b58 + b511 + b512)",
"m78 = (a11 + a12 - a21) * (b17)",
"m79 = (a21 - a23 + a25 - a33 + a35) * (-b39 - b412 + b512)",
"m80 = (a11 + a12 - a21) * (b19 - b39 + b49 - b59)",
"m81 = (a12 - a32 + a33 - a34) * (-b27 + b211 + b37 + b47 - b57)",
"m82 = (-a22 - a33 + a34) * (-b27 + b211 + b47 - b57)",
"m83 = (a14) * (b110 - b37 + b310 - b47 + b410 + b510)",
"m84 = (a11 - a13 + a15 - a31) * (b112 - b312 + b412 - b512)",
"m85 = (a22) * (-b27 + b47 - b57)",
"m86 = (a32 - a35) * (-b28)",
"m87 = (-a11 - a15 + a21) * (b18 + b39 + b59)",
"m88 = (-a13 + a14 - a21) * (b17 - b111 - b411 + b511)",
"m89 = (-a22 - a31 - a32) * (b211)",
"m90 = (-a12 + a32 + a34) * (b210 - b37 - b47)",
"m91 = (-a12 + a32 - a35) * (-b28 - b57)",
"m92 = (a11 + a13 - a14 - a31) * (b17 - b111 - b311 - b411 + b511)",
"m93 = (a22 - a33 + a35) * (b212 + b39)",
"m94 = (a11 - a14 + a23 - a31 + a33) * (b311 + b411)",
"m95 = (a32 + a34) * (-b210)",
"m96 = (-a11 + a14 + a21 - a22 - a24 - a32 - a34) * (-b49)",
"m97 = (-a21) * (b111 + b411 - b511)",
"m98 = (-a22 - a32 - a34) * (-b210 - b49)",
"m99 = (a11 - a14 - a23 + a24 + a25 - a31 - a33 + a34 + a35) * (b412)",
"m100 = (-a31) * (-b19 - b110 - b112 + b29 + b212 + b39 - b49 + b59)",
"m101 = (a13 - a14 + a22 - a23 + a24) * (b47 - b57)",
"m102 = (-a22 - a32 + a35) * (-b28 + b39 + b59)",
"m103 = (-a23) * (-b38 + b310 - b48 + b510)",
"m104 = (a13 - a14 - a23 + a24 + a25) * (-b48 + b57)",
"m105 = (-a23 - a33 + a34) * (-b310 - b311 - b411 - b510)",
"m106 = (-a31) * (-b18 - b111 + b211)",
"m107 = (-a12 - a31) * (-b17 + b211)",
"m108 = (-a23 + a24 + a25) * (b48 - b510)",
"m109 = (-a33 + a35) * (b212 - b38 - b312 - b48 + b510)",
"m110 = (-a11 - a15 + a21 - a22 + a25 - a32 + a35) * (b39 + b59)",
"m111 = (a23 - a24 - a25 + a33 - a35) * (b412 + b510)",
"m112 = (a12 + a13 - a23 - a32 - a34) * (b37 + b47)",
"m113 = (a11 + a15 + a23 - a24 - a25 - a31 + a33 - a34 - a35) * (b511)",
"m114 = (a13 - a15 - a22 - a23 + a25) * (b39)",
"m115 = (a13 - a14) * (-b17 + b111 + b37 - b310 + b48 + b411 - b510 - b511)",
"m116 = (a12 - a32 - a33 + a35) * (-b212)",
"m117 = (-a15) * (-b18 + b38 + b48 - b57 + b58)",
"m118 = (-a11 - a15 + a23 + a31 + a33) * (b312 + b512)",
"m119 = (a13 - a15 - a23) * (-b38 - b48)",
"m120 = (-a23 - a33) * (-b311 + b312 - b411 + b512)",
"m121 = (-a12) * (-b17 + b27 - b28 - b210)",
"m122 = (a12) * (b19 - b29 - b39 + b49 - b59)",
"m123 = (-a12 - a31) * (-b19 + b29 + b212 + b39 - b49 + b59)",
"m124 = (a13 - a15) * (-b38 - b48 + b510)",
"m125 = (a11 - a14 - a31) * (b110 - b311 - b411 - b412)",
"m126 = (a25) * (b39 - b48 + b58 + b59)",
"m127 = (a11 + a15 - a31) * (b18 + b312 + b511 + b512)",
"m128 = (a13 - a14 - a23) * (-b37 + b310 - b47 + b510)",
"m129 = (-a11 + a14) * (-b110)",
"m130 = (-a24) * (b49 + b410 - b510)",
"m131 = (-a22 - a31 - a32) * (-b29 - b212 - b39 + b49 - b59)",
"m132 = (a13 - a15 - a21) * (-b112 - b39 - b412 + b512)",
"m133 = (a12 + a13 - a14 - a15 - a23 + a24 + a25 - a32 + a35) * (-b57)",
"m134 = (a33 - a34) * (b27 - b211 - b310 - b311 - b47 + b48 + b57 - b510)",
"m135 = (a11 - a14 - a21) * (b110 - b49)",
"m136 = (a23 - a24 - a25 + a33 - a34) * (-b48 - b511)"
],
"elements": [
"c11 = m2 + m10 - m18 - m20 - m22 + m23 - m27 - m29 - m35 + m36 + m40 + m44 + m47 + m51 - m53 - m56 + m60 + m65",
"c12 = m2 + m5 - m18 + m23 + m36 + m40 - m49 - m56 + m65",
"c13 = -m3 - m5 - m6 + m12 - m19 - m54 - m61 - m64 + m67",
"c14 = m15 - m22 - m27 - m35 + m44 + m51 - m56 + m60 + m61",
"c15 = -m5 + m10 - m20 - m24 - m26 - m29 + m38 - m39 + m50 + m52 + m59",
"c16 = m6 + m16 + m26 + m32 - m50 - m52 + m54 - m55 + m57 - m61",
"c17 = m70 + m78 - m86 - m88 - m90 + m91 - m95 - m97 - m103 + m104 + m108 + m112 + m115 + m119 - m121 - m124 + m128 + m133",
"c18 = m70 + m73 - m86 + m91 + m104 + m108 - m117 - m124 + m133",
"c19 = -m71 - m73 - m74 + m80 - m87 - m122 - m129 - m132 + m135",
"c110 = m83 - m90 - m95 - m103 + m112 + m119 - m124 + m128 + m129",
"c111 = -m73 + m78 - m88 - m92 - m94 - m97 + m106 - m107 + m118 + m120 + m127",
"c112 = m74 + m84 + m94 + m100 - m118 - m120 + m122 - m123 + m125 - m129",
"c21 = m2 - m17 - m20 - m29 + m33 - m35 + m36 + m40 + m47 + m51 - m56 + m60",
"c22 = m2 + m5 + m18 + m19 + m34 + m40 - m42 + m51 - m56 + m58",
"c23 = -m3 + m4 - m5 - m6 - m18 - m19 - m27 + m28 - m30 - m34 + m42 - m46 - m61 - m64 + m67",
"c24 = m2 + m27 - m28 + m30 - m35 + m51 - m56 + m61 - m62 - m67",
"c25 = -m2 - m7 - m14 - m17 - m29 + m35 + m37 - m40 - m51 + m56 + m66 + m68",
"c26 = -m1 - m2 + m6 + m11 + m25 - m41 - m43 + m46 - m51 + m56 + m64",
"c27 = m70 - m85 - m88 - m97 + m101 - m103 + m104 + m108 + m115 + m119 - m124 + m128",
"c28 = m70 + m73 + m86 + m87 + m102 + m108 - m110 + m119 - m124 + m126",
"c29 = -m71 + m72 - m73 - m74 - m86 - m87 - m95 + m96 - m98 - m102 + m110 - m114 - m129 - m132 + m135",
"c210 = m70 + m95 - m96 + m98 - m103 + m119 - m124 + m129 - m130 - m135",
"c211 = -m70 - m75 - m82 - m85 - m97 + m103 + m105 - m108 - m119 + m124 + m134 + m136",
"c212 = -m69 - m70 + m74 + m79 + m93 - m109 - m111 + m114 - m119 + m124 + m132",
"c31 = m13 + m14 + m17 - m18 - m21 - m22 + m23 - m27 + m39 - m53",
"c32 = -m1 - m2 + m5 + m9 - m18 - m40 + m45 - m50 - m51 + m56 - m59 + m68",
"c33 = -m4 + m18 - m25 + m27 + m30 + m34 - m48 - m54 + m55 + m63",
"c34 = -m2 + m8 - m26 - m27 - m31 + m35 + m37 - m43 - m51 + m56 - m57 + m61",
"c35 = m2 - m5 + m14 + m17 - m21 - m35 - m37 + m38 + m40 - m45 + m50 + m51 + m52 - m56 + m59 - m66 - m68",
"c36 = m1 + m2 + m26 + m31 + m32 + m41 + m43 + m48 + m51 - m52 + m54 - m55 - m56 + m57 - m61",
"c37 = m81 + m82 + m85 - m86 - m89 - m90 + m91 - m95 + m107 - m121",
"c38 = -m69 - m70 + m73 + m77 - m86 - m108 + m113 - m118 - m119 + m124 - m127 + m136",
"c39 = -m72 + m86 - m93 + m95 + m98 + m102 - m116 - m122 + m123 + m131",
"c310 = -m70 + m76 - m94 - m95 - m99 + m103 + m105 - m111 - m119 + m124 - m125 + m129",
"c311 = m70 - m73 + m82 + m85 - m89 - m103 - m105 + m106 + m108 - m113 + m118 + m119 + m120 - m124 + m127 - m134 - m136",
"c312 = m69 + m70 + m94 + m99 + m100 + m109 + m111 + m116 + m119 - m120 + m122 - m123 - m124 + m125 - m129"
],
"u": [
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1],
[0, 0, 1, 0, -1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 1, -1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, -1, 0, 1],
[1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0],
[0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0],
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1],
[-1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0],
[0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0],
[0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1],
[1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1],
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],
"invariant_f": "8x^3y^2z^2 + 8x^2y^3z^2 + 8x^2y^2z^3 + 8x^4yz + 14x^3y^2z + 14x^2y^3z + 8xy^4z + 14x^3yz^2 + 216x^2y^2z^2 + 14xy^3z^2 + 14x^2yz^3 + 14xy^2z^3 + 8xyz^4 + 60x^3yz + 16x^2y^2z + 60xy^3z + 16x^2yz^2 + 16xy^2z^2 + 60xyz^3 + 64x^2yz + 64xy^2z + 64xyz^2 + 48xyz",
"invariant_g": "w^242 + w^236 + w^216",
"type": "4X^2Y^3Z^2 + 4XY^4Z + 4X^3YZ^2 + 36X^2Y^2Z^2 + 4X^2YZ^3 + 6XY^2Z^3 + 12X^3YZ + 8X^2Y^2Z + 10XY^3Z + 8XYZ^3 + 16X^2YZ + 16XY^2Z + 8XYZ"
}