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2x3x13_m65_ZT.json
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305 lines (305 loc) · 20.9 KB
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{
"n": [2, 3, 13],
"m": 65,
"z2": false,
"complexity": 382,
"multiplications": [
"m1 = (a21) * (b11 - b13 - b21)",
"m2 = (a12) * (b12 - b22 + b23)",
"m3 = (a13) * (b13 + b32 - b33)",
"m4 = (a23) * (b23 + b31 - b33)",
"m5 = (a11 + a12) * (b12)",
"m6 = (a11 + a13) * (b13)",
"m7 = (a11 - a21) * (b11 - b12 - b31)",
"m8 = (a12 + a21) * (b12 - b21)",
"m9 = (a21 + a22) * (b21)",
"m10 = (a12 - a22) * (b21 - b22 + b32)",
"m11 = (a22 + a23) * (b23)",
"m12 = (a11 + a13 - a21) * (b13 - b31)",
"m13 = (a12 - a22 - a23) * (b23 - b32)",
"m14 = (a12 + a13 - a22 - a23) * (b32)",
"m15 = (a11 + a13 - a21 - a23) * (b31)",
"m16 = (a21 + a22) * (b24 - b210)",
"m17 = (a11 + a12) * (b15 - b18)",
"m18 = (a12 - a13 - a22 + a23) * (b18 - b210 + b37 - b38)",
"m19 = (a13) * (b18 - b113 - b28 - b38 - b39 - b312 + b313)",
"m20 = (a11 - a21 - a23) * (b110 - b210 + b39 - b310)",
"m21 = (a21 + a23) * (b110 - b210)",
"m22 = (a11 - a21) * (b17 - b19 + b110 - b111 + b112 - b210 + b39 - b310 + b311)",
"m23 = (a23) * (b213 + b311 - b313)",
"m24 = (a21) * (b14 - b16 - b24)",
"m25 = (a12) * (b15 - b112 - b25 + b26 + b212 - b213)",
"m26 = (a13) * (b113 + b312 - b313)",
"m27 = (a23) * (b26 + b213 + b34 - b36 + b311 - b313)",
"m28 = (a11 + a12) * (b18 - b112 + b29)",
"m29 = (a11 + a13) * (b16 - b113)",
"m30 = (a11 - a21) * (b14 - b15 + b17 - b19 + b110 - b111 + b112 - b210 - b34 + b39 - b310 + b311)",
"m31 = (a12 + a21) * (b15 + b112 - b24 - b211)",
"m32 = (a21 + a22) * (b17 - b24 + b210)",
"m33 = (a12 - a22) * (b211 - b212 + b312)",
"m34 = (a22 + a23) * (b26 - b213)",
"m35 = (a11 + a13 - a21) * (b16 - b113 - b34 + b311)",
"m36 = (a12 - a22 - a23) * (b26 + b213 - b35 - b312)",
"m37 = (a12 + a13 - a22 - a23) * (b35 - b312)",
"m38 = (a11 + a13 - a21 - a23) * (b311)",
"m39 = (a11) * (b19 - b29)",
"m40 = (a13) * (b16 - b113 + b35 - b36 - b39 - b312 + b313)",
"m41 = (a12 - a13 + a21 + a23) * (b18 - b210)",
"m42 = (a12 - a22) * (b24 - b25 + b35)",
"m43 = (a11 + a22) * (b17 - b29)",
"m44 = (a11 + a12) * (b112)",
"m45 = (a22) * (b17 - b27)",
"m46 = (a11 + a13 - a21 - a23) * (b18 - b210 + b34 + b39 - b310)",
"m47 = (a21 + a22) * (b24 - b211)",
"m48 = (a12 - a13) * (b18 - b28)",
"m49 = (a23) * (b37)",
"m50 = (a12 - a13 - a22) * (b18 - b28 + b37 - b38)",
"m51 = (a21) * (b111 - b113 - b211)",
"m52 = (a12) * (b15 - b25 + b26)",
"m53 = (a13) * (b113 + b39 + b312 - b313)",
"m54 = (a23) * (b110 - b210 + b213 - b37 - b310 + b311 - b313)",
"m55 = (a11 + a12) * (b15 - b18 - b29)",
"m56 = (a11 + a13) * (b113)",
"m57 = (a11 - a21) * (b111 - b112 - b311)",
"m58 = (a12 + a21) * (b112 - b211)",
"m59 = (a21 + a22) * (b17 + b210)",
"m60 = (a12 - a22) * (b18 - b24 + b25 + b27 - b28 - b29 - b211 + b212 - b35 + b37 - b38 - b312)",
"m61 = (a22 + a23) * (b213)",
"m62 = (a11 + a13 - a21) * (b113 - b311)",
"m63 = (a12 - a22 - a23) * (b213 - b312)",
"m64 = (a12 + a13 - a22 - a23) * (b312)",
"m65 = (a11 + a13 - a21 - a23) * (b18 - b210 + b39 - b310 - b311)"
],
"elements": [
"c11 = m1 + m5 + m6 + m7 - m8 - m12",
"c12 = -m2 + m5 + m11 + m13 + m14",
"c13 = -m3 + m6 + m11 + m13 + m14",
"c14 = -m22 + m24 + m28 + m29 + m30 - m31 - m35 + m44 + m55 + m56 + m58 - m62",
"c15 = m28 + m34 + m36 + m37 + m44 - m52 + m55 + m61 - m63 + m64",
"c16 = m29 + m34 + m36 + m37 - m40 - m53 + m56 + m61 - m63 + m64",
"c17 = m17 - m19 + m33 + m42 + m43 - m45 - m50 - m53 - m55 + m60",
"c18 = -m17 - m19 + m28 + m44 - m48 - m53 + m55",
"c19 = m17 - m26 + m39 + m53 - m55",
"c110 = -m17 + m20 + m21 - m26 + m28 - m38 - m41 + m44 + m53 + m55 - m65",
"c111 = m44 + m51 + m56 + m57 - m58 - m62",
"c112 = m25 + m44 - m52 + m61 + m63 + m64",
"c113 = -m26 + m56 + m61 + m63 + m64",
"c21 = m1 + m6 + m9 - m12 - m15",
"c22 = -m2 + m8 + m9 + m10 + m11 + m13",
"c23 = -m4 + m6 + m11 - m12 - m15",
"c24 = m24 + m29 - m32 - m35 + m38 - m46 + m56 + m59 - m62 + m65",
"c25 = m31 - m32 + m34 + m36 + m42 - m52 - m58 + m59 + m61 - m63",
"c26 = m23 - m27 + m29 + m34 - m35 + m38 - m46 + m56 + m61 - m62 + m65",
"c27 = m16 + m32 - m45 + m49",
"c28 = -m16 - m18 - m32 + m41 - m48 + m49 + m50 + m59",
"c29 = m16 - m20 + m22 + m23 + m32 + m39 - m43 - m49 - m54 + m57",
"c210 = -m16 + m21 + m23 - m32 - m49 - m54 + m59",
"c211 = -m32 - m38 - m47 + m51 + m56 + m59 - m62",
"c212 = m25 - m32 + m33 - m47 - m52 + m58 + m59 + m61 + m63",
"c213 = -m23 - m38 + m56 + m61 - m62"
],
"u": [
[0, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1],
[1, 1, 0, 0, 0, 0],
[1, 0, 1, 0, 0, 0],
[1, 0, 0, -1, 0, 0],
[0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 1, 0],
[0, 1, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 1],
[1, 0, 1, -1, 0, 0],
[0, 1, 0, 0, -1, -1],
[0, 1, 1, 0, -1, -1],
[1, 0, 1, -1, 0, -1],
[0, 0, 0, 1, 1, 0],
[1, 1, 0, 0, 0, 0],
[0, 1, -1, 0, -1, 1],
[0, 0, 1, 0, 0, 0],
[1, 0, 0, -1, 0, -1],
[0, 0, 0, 1, 0, 1],
[1, 0, 0, -1, 0, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1],
[1, 1, 0, 0, 0, 0],
[1, 0, 1, 0, 0, 0],
[1, 0, 0, -1, 0, 0],
[0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 1, 0],
[0, 1, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 1],
[1, 0, 1, -1, 0, 0],
[0, 1, 0, 0, -1, -1],
[0, 1, 1, 0, -1, -1],
[1, 0, 1, -1, 0, -1],
[1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 1, -1, 1, 0, 1],
[0, 1, 0, 0, -1, 0],
[1, 0, 0, 0, 1, 0],
[1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0],
[1, 0, 1, -1, 0, -1],
[0, 0, 0, 1, 1, 0],
[0, 1, -1, 0, 0, 0],
[0, 0, 0, 0, 0, 1],
[0, 1, -1, 0, -1, 0],
[0, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1],
[1, 1, 0, 0, 0, 0],
[1, 0, 1, 0, 0, 0],
[1, 0, 0, -1, 0, 0],
[0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 1, 0],
[0, 1, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 1],
[1, 0, 1, -1, 0, 0],
[0, 1, 0, 0, -1, -1],
[0, 1, 1, 0, -1, -1],
[1, 0, 1, -1, 0, -1]
],
"v": [
[1, 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, 0, 0, 0, 0, 0, 0],
[0, 1, 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, 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, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 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, 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, 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, 0, 0, 0, 0, 0, -1, 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, -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, 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, 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, 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, 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, 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, -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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 1, 0, -1, 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, 1, -1, 1, 0, 0],
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],
"invariant_f": "2x^3y^2z + 2x^2y^3z + 2x^3yz^2 + 78x^2y^2z^2 + 2xy^3z^2 + 2x^2yz^3 + 2xy^2z^3 + 12x^3yz + 6x^2y^2z + 12xy^3z + 6x^2yz^2 + 6xy^2z^2 + 12xyz^3 + 40x^2yz + 40xy^2z + 40xyz^2 + 126xyz",
"invariant_g": "w^116 + w^84 + w^78",
"type": "13X^2Y^2Z^2 + 2XY^3Z^2 + 6XY^3Z + 3XY^2Z^2 + 19XY^2Z + XYZ^2 + 21XYZ"
}