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533 lines (533 loc) · 58.8 KB
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{
"n": [2, 6, 13],
"m": 122,
"z2": false,
"complexity": 1332,
"multiplications": [
"m1 = (a15 - a25) * (b14 + b23 - b24 + b35 - b52 + b53 - b54 - b55 - b56)",
"m2 = (a13 + a14 + a16) * (b31 - b51)",
"m3 = (a22 + a24) * (b11 + b12 - b31 + b41 + b42)",
"m4 = (a25) * (b54 - b64)",
"m5 = (a11 + a12 - a16 - a25) * (b14 + b35 - b55)",
"m6 = (a21 + a23) * (b31 + b33 + b35 - b36)",
"m7 = (a11 + a12 - a16 - a21 - a22 + a26) * (b14 + b15)",
"m8 = (a12) * (b22 + b23 + b32 + b34 + b35 - b44 + b51 + b53 - b56)",
"m9 = (a21) * (b12 - b13 + b16 + b33 - b36 + b42 + b46 + b56 - b63)",
"m10 = (a11 - a14 - a16) * (b31 + b32 + b34 + b35 - b41 - b42 - b44 - b45)",
"m11 = (a21 + a22 - a25 - a26) * (b14 - b32 - b34 - b43 + b44 - b56 + b63)",
"m12 = (a22 - a26) * (b56 - b66)",
"m13 = (a14 - a24) * (b11 - b21 - b31 + b41)",
"m14 = (a16 + a22 - a26) * (b22 + b26 - b56 + b66)",
"m15 = (a11 + a13 - a21 - a23) * (b13)",
"m16 = (a16) * (b11 + b12 - b31 - b52 + b61 + b62)",
"m17 = (a12 - a15) * (b32 + b34 + b35 + b43 - b44 + b51 + b53 - b63)",
"m18 = (a12 - a16 - a22 + a26) * (b15 - b22 - b26 - b35 + b56 + b65 - b66)",
"m19 = (a12 - a15 + a25) * (b14 + b23 - b24 + b35 + b51 + b53 - b56)",
"m20 = (a12 - a13 - a15 - a16 + a21 + a23) * (b32 + b34 + b43 - b44 + b56 - b63)",
"m21 = (a11 + a12 - a16 - a22 - a24) * (b11 + b12 - b31 - b32 - b34 - b35 + b41 + b42 + b44 + b45)",
"m22 = (a14 + a21 - a24) * (b12 + b42 + b46)",
"m23 = (a23 + a24 + a25 + a26) * (b32 + b34 + b35)",
"m24 = (a11 + a12 - a16 - a22 + a26) * (b15 - b35 + b56 + b65 - b66)",
"m25 = (a13 - a23) * (b13 - b33 + b63)",
"m26 = (a12 - a13 - a15 - a16 - a22 + a23 + a25 + a26) * (b11 + b12 - b21 - b25 + b26 - b31 + b32 + b34 + b35 + b41 + b42 + b43 - b44 + b45 - b63 - b65 + b66)",
"m27 = (a12 - a15 - a22 + a25) * (b14 + b23 - b24 - b32 - b34 - b43 + b44 - b56 + b63)",
"m28 = (a13 + a14 + a16 + a25) * (b32 + b34 + b35 + b51)",
"m29 = (a13 - a21 - a23) * (b13 - b33 + b36 - b56 + b63)",
"m30 = (a13 + a14 + a15 + a16) * (b32 + b34 + b35 - b44 + b51)",
"m31 = (a16 + a25) * (b14 - b32 - b34 + b52 + b64)",
"m32 = (a22) * (b11 + b12 - b21 + b26 - b31 + b41 + b42 - b56 + b66)",
"m33 = (a12 - a13 - a15 - a16 + a23 + a25 + a26) * (b11 + b12 - b21 - b25 + b26 - b31 + b41 + b42 + b45 - b56 - b65 + b66)",
"m34 = (a12 + a14 - a22 - a24) * (b11 + b12 - b21 - b31 + b41 + b42 + b45)",
"m35 = (a11 - a14 - a21 + a24) * (b12)",
"m36 = (a15 + a16) * (b52 + b56)",
"m37 = (a13 + a14 + a16 - a21 - a23) * (b31 + b32 + b34 + b35 + b43 - b44)",
"m38 = (a13) * (b32 + b36)",
"m39 = (a11 + a12 - a16) * (b11 + b12 - b31 - b32 - b34 - b35 + b41 + b42 + b44 + b45 + b55 - b56 - b65 + b66)",
"m40 = (a22) * (b14 - b24 - b25 - b32 - b34 + b44 + b45 - b65)",
"m41 = (a12 - a13 - a15 - a16) * (b32 + b34 - b44)",
"m42 = (a13 + a15 + a16 - a23 - a25 - a26) * (b11 + b12 - b21 - b25 + b26 - b31 + b41 + b42 + b45 - b65 + b66)",
"m43 = (a12) * (b11 + b12 - b21 + b22 - b25 + b26 - b31 + b41 + b42 + b45 - b56 - b65 + b66)",
"m44 = (a11 + a12 - a15 - a16) * (b35 - b55)",
"m45 = (a23 + a25 + a26) * (b32)",
"m46 = (a14) * (b46)",
"m47 = (a16 - a21 + a24) * (b11 + b12 - b31 + b61)",
"m48 = (a21 - a24 - a26) * (b32 + b34 + b35 + b43 - b44 + b61)",
"m49 = (a21 - a24) * (b11 + b12 - b31 + b42 + b46 + b61)",
"m50 = (a11) * (b15 - b16 - b35 + b56 + b65 - b66)",
"m51 = (a14 - a22 - a24) * (b11 + b12 - b21 - b31 + b41 + b42)",
"m52 = (a16 - a26) * (b14 + b22 + b26 - b32 - b34 - b56 + b62 + b64 + b66)",
"m53 = (a12 - a13 - a15 - a16 - a22 - a24) * (b32 + b34 + b35 - b44)",
"m54 = (a13 + a14 + a16 - a23 - a24 - a26) * (b43 - b44)",
"m55 = (a25 + a26) * (b14 - b34 + b64)",
"m56 = (a13 - a23 - a25 - a26) * (b32 + b56)",
"m57 = (-a13 - a14) * (-b28 - b211 + b212 - b48 - b411 + b412)",
"m58 = (a11) * (-b19 + b110 + b29 - b210 + b49 - b410 - b59 + b510 - b69 + b610)",
"m59 = (a16) * (b28 + b211 - b212 + b58 + b511 - b512 + b68 + b611 - b612)",
"m60 = (a11 + a12 - a13 - a15 - a25 + a26) * (b213 + b57 - b58 + b59)",
"m61 = (a24) * (-b17 + b18 - b210 - b37 + b38 - b39 - b312 + b47 - b57 + b512 - b67 + b612)",
"m62 = (-a11 + a15) * (-b59 + b510)",
"m63 = (a21 + a22 - a24 - a25) * (b18 - b210 + b38 - b39 - b312 + b512 + b612)",
"m64 = (a11 + a21) * (b18 + b19 + b111 + b113 - b28 - b210 - b211 + b212 - b410 + b59 + b512 + b513 + b612 + b613)",
"m65 = (-a11 + a13 + a14 + a15 - a21 + a23 + a24 + a25) * (-b47 + b48 - b410 - b412 + b413)",
"m66 = (a21 + a22 - a23 - a26) * (-b17 + b18 + b113 - b210 + b213 - b410 + b59 + b513 - b67 + b612 + b613)",
"m67 = (a14 + a24) * (-b28 - b211 + b212 - b47 - b49 - b411 + b412)",
"m68 = (a11 + a12) * (-b29 - b39)",
"m69 = (a11 - a15 + a21 - a25) * (-b213 - b47 + b48 - b412 + b413 - b59 + b512 - b513 + b67 - b613)",
"m70 = (-a26) * (-b17 + b18 - b110 + b113 - b57 + b58 - b510 + b513 - b67 + b68 - b610 + b613)",
"m71 = (a23 + a25 - a26) * (-b17 + b18 + b113 - b210 + b213 - b37 + b38 - b39 - b312 + b313 + b47 - b48 + b412 - b413 + b59 + b513 - b67 + b612 + b613)",
"m72 = (a22) * (b18 - b112 - b28 + b212)",
"m73 = (a11 - a13 - a16 + a24) * (-b412 + b512 + b67)",
"m74 = (-a11 + a13 + a14 + a15) * (b17 - b113 - b27 + b410 - b59 - b513 + b67 - b613)",
"m75 = (-a11 - a26) * (b110 - b210 - b410 + b510 - b69 + b610)",
"m76 = (a11 - a13 - a16 - a23) * (-b39 + b310 - b312 + b512 + b612)",
"m77 = (-a11 + a22) * (b112 + b29 - b210 + b512 + b612)",
"m78 = (a11 + a12 - a14 - a15 + a21 + a22 - a24 - a25) * (-b28 - b211 + b212)",
"m79 = (a11 + a12 - a13 + a24 + a25) * (-b17 + b113 - b410 - b57 + b513 - b67 + b613)",
"m80 = (-a21 - a24) * (b113 - b410 + b59 + b513 + b613)",
"m81 = (a13 + a23) * (-b210 - b39 - b312 + b512 + b612)",
"m82 = (-a12 - a22) * (b29 - b210 + b212)",
"m83 = (a21 + a22 - a23 - a24 - a25) * (-b17 + b18 + b113 - b210 + b38 - b39 - b312 - b410 + b59 + b513 - b67 + b612 + b613)",
"m84 = (-a21 + a23 + a24 + a26) * (-b47 + b48 - b410 - b412 + b413 + b512 + b67)",
"m85 = (a23 + a24) * (-b17 + b18 + b113 - b210 - b37 + b38 - b39 - b312 - b410 + b59 + b512 + b513 + b612 + b613)",
"m86 = (-a11 - a12 + a13 - a26) * (b17 - b18 - b113 + b210 + b410 + b57 - b58 - b513 + b67 - b68 - b613)",
"m87 = (a11 + a12 - a13 - a15 + a21 + a22 - a23 - a25) * (b213)",
"m88 = (-a11 + a16) * (b39 - b310 + b312 - b512 - b69 + b610 - b612)",
"m89 = (-a15 + a16 - a25 + a26) * (-b28 - b211 + b212 - b58 - b511 + b512 - b67 + b613)",
"m90 = (a11 - a13 - a16 - a22) * (-b17 + b18 + b113 + b27 - b28 - b410 + b59 + b513 - b67 + b612 + b613)",
"m91 = (a13) * (-b18 - b28 + b210 - b211 + b212 + b39 + b311 - b48 - b411 + b412 - b58 - b511 - b612)",
"m92 = (a13 - a24) * (-b17 + b18 + b113 - b28 - b210 - b211 + b212 - b37 + b38 - b39 - b312 - b48 - b410 - b411 + b412 + b59 + b512 + b513 + b612 + b613)",
"m93 = (a11 + a12 - a13 - a23) * (-b210 - b39)",
"m94 = (a23) * (-b39 + b310)",
"m95 = (-a11 - a12 + a13 + a15 - a24) * (b48 - b412 - b57 - b59 + b512)",
"m96 = (a11 - a13 - a14 - a16) * (-b412 + b512)",
"m97 = (-a24 - a25) * (-b17 + b113 - b410 - b57 + b59 + b513 - b67 + b613)",
"m98 = (a14 + a15 + a24 + a25) * (b410)",
"m99 = (a16 + a26) * (-b69)",
"m100 = (a25 - a26) * (-b17 + b18 + b113 - b210 + b213 - b37 + b38 - b39 - b312 + b313 + b47 - b48 + b412 - b413 + b57 - b58 + b59 + b510 - b67 + b612 + b613)",
"m101 = (a11 - a15 - a25 + a26) * (-b213 - b47 + b48 - b410 - b412 + b413 - b59 + b510 + b512 - b513 + b67 - b613)",
"m102 = (-a13 - a21 - a22 + a24 + a25) * (b18 - b28 - b210 - b211 + b212 + b38 - b39 - b312 + b512 + b612)",
"m103 = (-a11 - a12 + a13) * (b18 - b210 - b39 + b58 + b68)",
"m104 = (a11 + a14) * (b49 - b410)",
"m105 = (-a11 + a13 + a14 + a15 + a22) * (b17 - b113 - b27 + b410 - b59 + b512 - b513 + b67 - b613)",
"m106 = (a26) * (b28 + b211 - b212 + b58 + b511 - b512 + b68 + b611 - b612)",
"m107 = (a13 - a25 + a26) * (-b17 + b18 + b113 + b28 - b210 + b211 - b212 + b213 - b37 + b38 - b39 - b312 + b313 + b47 - b48 + b412 - b413 + b58 + b59 + b511 - b512 + b513 - b67 + b612 + b613)",
"m108 = (-a11 + a13 + a16 - a21 + a23 + a26) * (-b67 + b612)",
"m109 = (-a11 + a13 + a14 + a15 + a25 - a26) * (-b47 + b48 - b410 - b412 + b413 + b512)",
"m110 = (-a11 - a12 + a13 + a14 + a15) * (-b17 + b113 + b27 - b28 - b211 + b212 - b48 - b410 + b412 + b59 - b512 + b513 - b67 + b613)",
"m111 = (a13 + a23) * (b213 + b38 + b311 - b312 + b313 + b47 - b48 + b410 + b412 - b413 - b512 - b67)",
"m112 = (a11 + a12 - a13 - a16) * (b17 - b18 - b113 - b27 + b28 + b410 - b59 - b513 + b67 - b68 - b613)",
"m113 = (-a11 - a21) * (b19 + b112 + b113 - b210 - b410 + b59 + b512 + b513 + b612 + b613)",
"m114 = (-a11 + a13 + a16) * (-b17 + b18 + b113 + b27 - b28 - b39 + b310 - b312 - b410 + b412 + b59 + b513 - b67 + b612 + b613)",
"m115 = (-a11 + a24) * (b113 + b49 - b410 + b513 + b613)",
"m116 = (-a21 + a26) * (b110 - b210 + b213 + b47 - b48 + b412 - b413 + b59 - b512 + b513 - b67 + b613)",
"m117 = (a11 - a15 - a24 - a25) * (b410 - b59)",
"m118 = (-a11 - a12 + a13 - a21 - a22 + a23) * (b210)",
"m119 = (-a21 - a22) * (-b112 - b512 - b612)",
"m120 = (a13 + a15 - a16) * (-b28 - b211 + b212 - b58 - b511 + b512)",
"m121 = (a11) * (b18 + b111 - b112 - b28 - b211 + b212)",
"m122 = (-a11 - a12 + a13 + a15) * (b48 - b412 - b58 + b512)"
],
"elements": [
"c11 = m2 + m3 + m10 + m21 - m22 + m30 - m34 - m35 + m46 + m47 + m49 + m51 + m53",
"c12 = m16 + m22 - m33 + m35 + m36 - m42 + m43 + m45 - m46 - m47 - m49 + m56",
"c13 = -m2 + m6 + m8 + m15 - m17 + m20 - m29 - m30 + m33 + m37 + m38 - m41 + m42 - m43 - m45 - m56",
"c14 = -m1 + m4 + m5 + m8 - m19 + m28 - m30 + m31 + m33 - m36 - m41 + m42 - m43 - m44 - m45 - m56",
"c15 = -m3 + m12 + m14 - m18 - m21 + m24 + m34 + m39 + m41 - m43 + m44 - m51 - m53",
"c16 = m12 + m14 - m18 + m24 + m33 + m38 + m42 - m43 - m45 + m46 - m50 - m56",
"c17 = -m57 - m61 - m63 - m67 - m73 - m74 - m78 - m79 - m92 - m95 + m96 - m97 - m98 - m102 - m104 - m110 - m115 - m117",
"c18 = -m63 - m74 - m76 - m78 - m81 - m93 - m94 + m96 - m102 - m103 - m110 + m112 - m114 - m122",
"c19 = -m58 - m68 - m70 - m75 + m79 - m86 + m97 + m98 - m99 - m103 + m104 + m117",
"c110 = m62 - m70 - m75 - m76 + m79 - m81 - m86 + m88 - m93 - m94 + m97 + m98 - m99 - m103 + m117",
"c111 = m57 + m59 + m68 - m72 - m77 - m82 - m90 + m91 + m103 + m105 + m110 - m112 - m120 + m121 + m122",
"c112 = m68 - m72 - m74 - m76 - m77 - m81 - m82 - m90 - m93 - m94 + m96 + m105 - m114",
"c113 = -m57 + m60 - m61 + m62 - m67 - m73 + m89 - m92 - m95 + m96 + m100 + m101 - m104 + m107 + m109 - m115 + m120 + m122",
"c21 = m2 + m3 - m13 - m22 - m23 + m28 - m37 + m46 - m48 + m49 + m51 + m54",
"c22 = m13 + m14 + m16 + m22 + m31 - m32 + m45 - m46 - m47 - m49 - m51 - m52 - m55",
"c23 = -m2 + m6 - m17 + m19 + m20 + m23 + m25 - m26 - m27 - m28 - m29 - m32 + m33 + m37 + m38 - m40 - m41 - m45 + m53 - m54 - m56",
"c24 = m4 + m11 + m20 + m23 - m26 - m32 + m33 - m40 - m41 - m45 + m53 + m55",
"c25 = -m3 + m5 - m7 - m11 + m12 - m20 - m21 + m24 + m26 + m32 - m33 + m39 + m41 - m53",
"c26 = m9 + m12 - m13 - m22 + m25 - m29 + m32 + m38 - m45 + m46 + m51 - m56",
"c27 = m61 + m63 - m65 + m74 - m80 - m83 + m84 - m85 + m97 - m105 + m109",
"c28 = m60 + m63 - m65 + m66 - m73 + m74 + m76 - m79 - m83 + m84 + m86 - m87 + m90 + m93 + m94 - m95 + m103 - m105 + m108 + m109 + m114 - m118 + m122",
"c29 = m58 + m70 + m75 + m77 - m79 + m80 + m86 + m93 - m97 + m103 - m113 + m115 - m118 - m119",
"c210 = -m62 + m69 + m70 - m79 + m86 + m93 + m94 - m97 - m101 + m103 - m116 - m117 - m118",
"c211 = -m60 + m64 - m66 - m71 + m72 + m79 + m83 + m85 - m86 + m87 - m91 + m92 - m93 + m95 + m102 - m103 + m106 - m107 + m111 + m113 + m118 + m119 - m121 - m122",
"c212 = -m65 + m72 - m73 + m74 + m76 + m84 + m90 + m94 - m105 + m108 + m109 + m114 + m119",
"c213 = -m60 + m61 - m62 + m69 + m71 - m80 + m84 - m85 + m87 + m95 - m100 - m101 - m117 - m122"
],
"u": [
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0],
[0, 0, 1, 1, 0, 1, 0, 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, 1, 0],
[1, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0],
[1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, -1],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1],
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],
"invariant_f": "2x^6y^2z^2 + 2x^2y^6z^2 + 2x^2y^2z^6 + 2x^5y^2z^2 + 2x^2y^5z^2 + 2x^2y^2z^5 + 4x^6yz + 4xy^6z + 14x^4y^2z^2 + 14x^2y^4z^2 + 14x^2y^2z^4 + 4xyz^6 + 16x^5yz + 16xy^5z + 16xyz^5 + 28x^4yz + 28xy^4z + 150x^2y^2z^2 + 28xyz^4 + 32x^3yz + 32xy^3z + 32xyz^3 + 14x^2yz + 14xy^2z + 14xyz^2 + 246xyz",
"invariant_g": "w^300 + 2w^156",
"type": "X^2Y^6Z^2 + X^2Y^5Z^2 + 2XY^6Z + 7X^2Y^4Z^2 + 8XY^5Z + 14XY^4Z + 25X^2Y^2Z^2 + 16XY^3Z + 7XY^2Z + 41XYZ"
}