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{
"n": [3, 6, 8],
"m": 108,
"z2": false,
"complexity": 1412,
"multiplications": [
"m1 = (a12 + a16 - a31) * (b13 + b14)",
"m2 = (a12) * (b12 - b23 - b32 - b42 + b52 + b63)",
"m3 = (a13 - a14 - a24 - a25 - a34 - a35) * (-b34 + b41 - b61)",
"m4 = (-a15 - a24 - a25 - a34 - a35) * (b43)",
"m5 = (a15 + a21 + a31) * (b12 + b13 - b32 - b42 + b52)",
"m6 = (-a12 - a13 - a15 - a22 - a23 - a25 - a32 - a33 - a35) * (b11 + b12 + b13 - b31 - b32 - b33 - b34)",
"m7 = (-a13 + a14 + a16 - a32 - a33 - a35) * (b22 + b23 + b41 + b42 + b43 + b44 - b62 - b63)",
"m8 = (-a11 + a12 - a31) * (b12 + b24 - b32 - b42 + b52 - b64)",
"m9 = (a16 - a22 + a36) * (b21 + b23 + b24 - b31 - b33 - b34 - b61 - b64)",
"m10 = (-a14 - a15 - a22 - a24 - a25 - a26 - a34 - a35) * (b41 + b42 + b43 + b44 - b61 - b62 - b63)",
"m11 = (-a12 - a16 - a36) * (b21 + b23 + b24 - b31 - b33 - b34 - b61 - b63 - b64)",
"m12 = (a12 + a16) * (b13 + b14 + b41 + b43 + b44 - b61 - b63 - b64)",
"m13 = (-a13 + a25 - a33) * (b22 + b23 - b32 + b34 + b43 + b44 - b53 - b54 - b62 - b63)",
"m14 = (a14 + a15 + a34 + a35) * (b11 + b12 + b13 - b31 - b32 - b33 - b41 - b42 - b43 - b44 + b51 + b52 + b53)",
"m15 = (a11 + a12 + a13 + a22 + a23 + a25 + a32 + a33 + a35) * (b11 + b12 + b13 - b31 - b33 - b34)",
"m16 = (a12 + a13 + a15 + a22 + a32 + a33 + a35) * (b21 + b22 + b23 - b31 - b32 - b33 - b34 - b61 - b62 - b63)",
"m17 = (a12 + a22 + a23 + a25 + a32 + a33 + a35) * (b22 + b23 - b32 - b62 - b63)",
"m18 = (a11 + a31) * (b11 + b12 + b13 + b14 + b24 - b31 - b32 - b33 - b34 - b41 - b42 - b43 - b44 + b51 + b52 + b53 + b54 - b64)",
"m19 = (a12 - a26 - a36) * (b63)",
"m20 = (a13 + a15 + a33) * (b33 + b34 + b43 + b44 - b53 - b54)",
"m21 = (a11 - a15 - a32 - a33 - a35) * (b31 + b33 + b34)",
"m22 = (a12 + a22 + a32) * (b22 - b32 - b62 - b63)",
"m23 = (-a15 + a23 + a33) * (b22 + b23 - b32 - b33 - b62 - b63)",
"m24 = (-a12 - a14 - a15 - a16 - a22 - a23 - a25 - a32 - a33 - a35) * (b22 + b23 - b62 - b63)",
"m25 = (-a12 - a14 - a15 - a16 - a21 - a22 - a24 - a26 - a31 - a32 - a34 - a36) * (b32 + b42 - b52)",
"m26 = (-a15) * (b12 + b13 - b32 - b33 - b42 + b52 + b53)",
"m27 = (-a11 - a21 - a22 - a26 - a31) * (b41 + b42 + b43 + b44 - b61 - b62 - b63 - b64)",
"m28 = (a11 - a15) * (b11 - b31 - b33 - b34)",
"m29 = (a12 + a13 + a15 + a32 + a33 + a35) * (b21 + b22 + b23 + b41 + b42 + b43 + b44 - b61 - b62 - b63)",
"m30 = (a11 + a12 + a14 + a16 + a22 + a24 + a25 + a26 + a31 + a32 + a34 + a36) * (b32 + b42 - b52 + b61)",
"m31 = (a14 + a15 - a23 + a24 + a34 + a35) * (b34)",
"m32 = (-a13 - a15 - a33 - a35) * (b21 - b31 - b33 - b34 - b43 - b44 + b53 + b54 - b61)",
"m33 = (a11 + a21 + a31) * (b14 + b41 + b42 + b43 + b44 - b61 - b62 - b63 - b64)",
"m34 = (a12 + a13 + a15 + a21 + a22 + a23 + a32 + a33 + a35) * (b11 + b12 + b13)",
"m35 = (-a13 - a15 - a34 - a35) * (b41 - b61)",
"m36 = (a11 + a22 + a31) * (b24 - b64)",
"m37 = (-a12 - a16 + a34 + a35) * (b41 + b43 + b44 - b61)",
"m38 = (-a12 - a14 - a15 - a16) * (b22 + b23 + b42 - b62 - b63)",
"m39 = (-a14 - a34 - a35) * (b11 + b12 + b13 - b31 - b32 - b33 - b41 - b42 + b51 + b52 + b53)",
"m40 = (a11 - a15 + a31 - a35) * (b31 + b33 + b34 + b41 + b43 + b44 - b51 - b53 - b54 - b61)",
"m41 = (a11 + a25 + a31) * (b11 + b12 + b13 - b31 - b32 - b33 - b34 - b41 - b42 - b43 - b44 + b51 + b52 + b53 + b54)",
"m42 = (-a13 - a15 - a32 - a33 - a35) * (b21 - b31 - b33 - b34 - b61)",
"m43 = (-a12 - a21 - a31) * (b12 - b32 - b42 + b52)",
"m44 = (a14 + a15 + a25 + a34 + a35) * (b11 + b12 + b13 - b31 - b32 - b33 - b41 - b42 - b43 + b51 + b52 + b53)",
"m45 = (-a11 - a12 - a16 - a21 - a31) * (b13 + b14 + b41 + b42 + b43 + b44 - b61 - b62 - b63 - b64)",
"m46 = (a12 + a16 + a32 + a36) * (b21 + b23 + b24 - b31 - b33 - b34 - b61)",
"m47 = (a13 + a15) * (-b33 - b34 + b41 - b61)",
"m48 = (-a12 - a14 - a15 - a16 - a24 - a25 - a34 - a35) * (b42 - b62 - b63)",
"m49 = (-a11 + a15 - a31 - a32 - a34 - a36) * (b61)",
"m50 = (a12 + a13 + a15 + a22 + a24 + a25 + a26 + a32 + a33 + a35) * (b41 + b42 + b43 + b44)",
"m51 = (-a11 + a15 - a31) * (b11 - b31 - b33 - b34 - b41 - b43 - b44 + b51 + b53 + b54)",
"m52 = (-a12 - a14 - a15 - a16 - a22 - a24 - a25 - a26 - a32 - a34 - a35 - a36) * (b32 + b42 - b52 - b62 - b63)",
"m53 = (a14 + a15 + a24 + a25 + a34 + a35) * (-b34 + b41 + b42 + b43 - b61 - b62 - b63)",
"m54 = (-a15 - a25 - a35) * (b22 + b23 - b32 + b43 - b53 - b62 - b63)",
"m55 = (a12 + a16 - a31) * (b17 + b18)",
"m56 = (a12) * (b16 - b27 - b36 - b46 + b56 + b67)",
"m57 = (a13 - a14 - a24 - a25 - a34 - a35) * (-b38 + b45 - b65)",
"m58 = (-a15 - a24 - a25 - a34 - a35) * (b47)",
"m59 = (a15 + a21 + a31) * (b16 + b17 - b36 - b46 + b56)",
"m60 = (-a12 - a13 - a15 - a22 - a23 - a25 - a32 - a33 - a35) * (b15 + b16 + b17 - b35 - b36 - b37 - b38)",
"m61 = (-a13 + a14 + a16 - a32 - a33 - a35) * (b26 + b27 + b45 + b46 + b47 + b48 - b66 - b67)",
"m62 = (-a11 + a12 - a31) * (b16 + b28 - b36 - b46 + b56 - b68)",
"m63 = (a16 - a22 + a36) * (b25 + b27 + b28 - b35 - b37 - b38 - b65 - b68)",
"m64 = (-a14 - a15 - a22 - a24 - a25 - a26 - a34 - a35) * (b45 + b46 + b47 + b48 - b65 - b66 - b67)",
"m65 = (-a12 - a16 - a36) * (b25 + b27 + b28 - b35 - b37 - b38 - b65 - b67 - b68)",
"m66 = (a12 + a16) * (b17 + b18 + b45 + b47 + b48 - b65 - b67 - b68)",
"m67 = (-a13 + a25 - a33) * (b26 + b27 - b36 + b38 + b47 + b48 - b57 - b58 - b66 - b67)",
"m68 = (a14 + a15 + a34 + a35) * (b15 + b16 + b17 - b35 - b36 - b37 - b45 - b46 - b47 - b48 + b55 + b56 + b57)",
"m69 = (a11 + a12 + a13 + a22 + a23 + a25 + a32 + a33 + a35) * (b15 + b16 + b17 - b35 - b37 - b38)",
"m70 = (a12 + a13 + a15 + a22 + a32 + a33 + a35) * (b25 + b26 + b27 - b35 - b36 - b37 - b38 - b65 - b66 - b67)",
"m71 = (a12 + a22 + a23 + a25 + a32 + a33 + a35) * (b26 + b27 - b36 - b66 - b67)",
"m72 = (a11 + a31) * (b15 + b16 + b17 + b18 + b28 - b35 - b36 - b37 - b38 - b45 - b46 - b47 - b48 + b55 + b56 + b57 + b58 - b68)",
"m73 = (a12 - a26 - a36) * (b67)",
"m74 = (a13 + a15 + a33) * (b37 + b38 + b47 + b48 - b57 - b58)",
"m75 = (a11 - a15 - a32 - a33 - a35) * (b35 + b37 + b38)",
"m76 = (a12 + a22 + a32) * (b26 - b36 - b66 - b67)",
"m77 = (-a15 + a23 + a33) * (b26 + b27 - b36 - b37 - b66 - b67)",
"m78 = (-a12 - a14 - a15 - a16 - a22 - a23 - a25 - a32 - a33 - a35) * (b26 + b27 - b66 - b67)",
"m79 = (-a12 - a14 - a15 - a16 - a21 - a22 - a24 - a26 - a31 - a32 - a34 - a36) * (b36 + b46 - b56)",
"m80 = (-a15) * (b16 + b17 - b36 - b37 - b46 + b56 + b57)",
"m81 = (-a11 - a21 - a22 - a26 - a31) * (b45 + b46 + b47 + b48 - b65 - b66 - b67 - b68)",
"m82 = (a11 - a15) * (b15 - b35 - b37 - b38)",
"m83 = (a12 + a13 + a15 + a32 + a33 + a35) * (b25 + b26 + b27 + b45 + b46 + b47 + b48 - b65 - b66 - b67)",
"m84 = (a11 + a12 + a14 + a16 + a22 + a24 + a25 + a26 + a31 + a32 + a34 + a36) * (b36 + b46 - b56 + b65)",
"m85 = (a14 + a15 - a23 + a24 + a34 + a35) * (b38)",
"m86 = (-a13 - a15 - a33 - a35) * (b25 - b35 - b37 - b38 - b47 - b48 + b57 + b58 - b65)",
"m87 = (a11 + a21 + a31) * (b18 + b45 + b46 + b47 + b48 - b65 - b66 - b67 - b68)",
"m88 = (a12 + a13 + a15 + a21 + a22 + a23 + a32 + a33 + a35) * (b15 + b16 + b17)",
"m89 = (-a13 - a15 - a34 - a35) * (b45 - b65)",
"m90 = (a11 + a22 + a31) * (b28 - b68)",
"m91 = (-a12 - a16 + a34 + a35) * (b45 + b47 + b48 - b65)",
"m92 = (-a12 - a14 - a15 - a16) * (b26 + b27 + b46 - b66 - b67)",
"m93 = (-a14 - a34 - a35) * (b15 + b16 + b17 - b35 - b36 - b37 - b45 - b46 + b55 + b56 + b57)",
"m94 = (a11 - a15 + a31 - a35) * (b35 + b37 + b38 + b45 + b47 + b48 - b55 - b57 - b58 - b65)",
"m95 = (a11 + a25 + a31) * (b15 + b16 + b17 - b35 - b36 - b37 - b38 - b45 - b46 - b47 - b48 + b55 + b56 + b57 + b58)",
"m96 = (-a13 - a15 - a32 - a33 - a35) * (b25 - b35 - b37 - b38 - b65)",
"m97 = (-a12 - a21 - a31) * (b16 - b36 - b46 + b56)",
"m98 = (a14 + a15 + a25 + a34 + a35) * (b15 + b16 + b17 - b35 - b36 - b37 - b45 - b46 - b47 + b55 + b56 + b57)",
"m99 = (-a11 - a12 - a16 - a21 - a31) * (b17 + b18 + b45 + b46 + b47 + b48 - b65 - b66 - b67 - b68)",
"m100 = (a12 + a16 + a32 + a36) * (b25 + b27 + b28 - b35 - b37 - b38 - b65)",
"m101 = (a13 + a15) * (-b37 - b38 + b45 - b65)",
"m102 = (-a12 - a14 - a15 - a16 - a24 - a25 - a34 - a35) * (b46 - b66 - b67)",
"m103 = (-a11 + a15 - a31 - a32 - a34 - a36) * (b65)",
"m104 = (a12 + a13 + a15 + a22 + a24 + a25 + a26 + a32 + a33 + a35) * (b45 + b46 + b47 + b48)",
"m105 = (-a11 + a15 - a31) * (b15 - b35 - b37 - b38 - b45 - b47 - b48 + b55 + b57 + b58)",
"m106 = (-a12 - a14 - a15 - a16 - a22 - a24 - a25 - a26 - a32 - a34 - a35 - a36) * (b36 + b46 - b56 - b66 - b67)",
"m107 = (a14 + a15 + a24 + a25 + a34 + a35) * (-b38 + b45 + b46 + b47 - b65 - b66 - b67)",
"m108 = (-a15 - a25 - a35) * (b26 + b27 - b36 + b47 - b57 - b66 - b67)"
],
"elements": [
"c11 = m7 + m14 + m21 + m26 + m28 + m29 + m35 + m37 + m38 + m39 + m42 + m47",
"c12 = m2 + m5 + m6 + m12 + m15 + m17 + m24 - m28 + m33 - m38 + m43 + m45",
"c13 = -m2 + m3 + m4 - m5 - m12 - m26 - m33 - m43 - m45 - m47 + m48 + m53",
"c14 = m1 - m3 - m4 + m5 + m8 - m14 + m18 + m33 - m35 - m37 - m39 + m43 + m45 - m48 + m51 - m53",
"c15 = m61 + m68 + m75 + m80 + m82 + m83 + m89 + m91 + m92 + m93 + m96 + m101",
"c16 = m56 + m59 + m60 + m66 + m69 + m71 + m78 - m82 + m87 - m92 + m97 + m99",
"c17 = -m56 + m57 + m58 - m59 - m66 - m80 - m87 - m97 - m99 - m101 + m102 + m107",
"c18 = m55 - m57 - m58 + m59 + m62 - m68 + m72 + m87 - m89 - m91 - m93 + m97 + m99 - m102 + m105 - m107",
"c21 = -m3 - m5 - m7 + m13 - m14 - m15 + m16 - m17 + m20 + m23 + m25 - m26 + m28 - m29 + m30 + m31 + m34 - m37 - m38 - m39 + m41 + m47 + m49 + m51",
"c22 = -m2 + m5 + m6 + m7 + m8 + m9 + m10 + m11 + m12 + m15 + m16 + m19 - m25 - m28 - m30 + m33 + m36 + m37 + m38 + m42 + m45 - m48 - m49 + m50",
"c23 = m2 + m3 - m8 - m9 - m11 - m12 - m13 - m16 + m17 - m19 - m20 - m23 + m26 - m33 - m36 + m39 - m41 - m42 + m44 - m45 - m47 + m48 - m51 + m53",
"c24 = -m10 + m14 - m18 + m27 - m31 + m33 + m36 + m41 - m44 - m53",
"c25 = -m57 - m59 - m61 + m67 - m68 - m69 + m70 - m71 + m74 + m77 + m79 - m80 + m82 - m83 + m84 + m85 + m88 - m91 - m92 - m93 + m95 + m101 + m103 + m105",
"c26 = -m56 + m59 + m60 + m61 + m62 + m63 + m64 + m65 + m66 + m69 + m70 + m73 - m79 - m82 - m84 + m87 + m90 + m91 + m92 + m96 + m99 - m102 - m103 + m104",
"c27 = m56 + m57 - m62 - m63 - m65 - m66 - m67 - m70 + m71 - m73 - m74 - m77 + m80 - m87 - m90 + m93 - m95 - m96 + m98 - m99 - m101 + m102 - m105 + m107",
"c28 = -m64 + m68 - m72 + m81 - m85 + m87 + m90 + m95 - m98 - m107",
"c31 = -m20 - m21 - m28 + m32 - m35 + m40 - m42 - m47 - m49 - m51",
"c32 = -m5 - m6 - m7 - m8 - m9 - m10 - m11 - m12 - m15 - m16 - m17 + m22 - m24 + m28 + m30 - m33 - m36 - m37 - m42 - m43 - m45 + m49 - m50 + m52",
"c33 = -m3 - m4 + m5 + m8 + m9 + m11 + m12 + m13 + m16 + m20 - m22 + m33 + m36 - m39 + m41 + m42 + m43 - m44 + m45 + m47 - m48 + m51 - m53 + m54",
"c34 = -m1 + m3 + m4 - m5 - m8 - m9 - m13 - m16 + m22 - m32 - m33 + m35 - m36 + m37 + m39 - m41 - m43 + m44 - m45 + m46 + m48 - m51 + m53 - m54",
"c35 = -m74 - m75 - m82 + m86 - m89 + m94 - m96 - m101 - m103 - m105",
"c36 = -m59 - m60 - m61 - m62 - m63 - m64 - m65 - m66 - m69 - m70 - m71 + m76 - m78 + m82 + m84 - m87 - m90 - m91 - m96 - m97 - m99 + m103 - m104 + m106",
"c37 = -m57 - m58 + m59 + m62 + m63 + m65 + m66 + m67 + m70 + m74 - m76 + m87 + m90 - m93 + m95 + m96 + m97 - m98 + m99 + m101 - m102 + m105 - m107 + m108",
"c38 = -m55 + m57 + m58 - m59 - m62 - m63 - m67 - m70 + m76 - m86 - m87 + m89 - m90 + m91 + m93 - m95 - m97 + m98 - m99 + m100 + m102 - m105 + m107 - m108"
],
"u": [
[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 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, 1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0],
[0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0],
[0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, 0],
[0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0],
[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, -1, -1, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0, -1, -1, 0],
[0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, -1, -1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1, -1, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, 1, 0, -1],
[0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1]
],
"invariant_f": "216x^2y^2z^2 + 144x^2yz + 144xy^2z + 144xyz^2",
"invariant_g": "2w^180 + w^144",
"type": "36X^2Y^2Z^2 + 36X^2YZ + 36XY^2Z"
}