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3x5x16_m180_ZT.json
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787 lines (787 loc) · 97.4 KB
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{
"n": [3, 5, 16],
"m": 180,
"z2": false,
"complexity": 1424,
"multiplications": [
"m1 = (a13 - a14 - a15 - a21 + a25) * (b45 - b51)",
"m2 = (a11 - a15 - a31 + a35) * (b43 + b44 - b53 - b54 + b57 - b58)",
"m3 = (a15) * (-b56)",
"m4 = (a31 - a35) * (b12 + b18 + b32 + b38 + b42 + b48)",
"m5 = (a11 - a31 + a35) * (b12 - b17 + b18 - b43 - b44 + b53 + b54 - b57 + b58)",
"m6 = (a31 - a32) * (b12)",
"m7 = (a11) * (-b12 + b13)",
"m8 = (a15 - a25) * (b12 - b13 - b15 - b16 + b22 - b23 - b25 - b26 + b27 - b35 + b52 - b53 - b55 - b56)",
"m9 = (a24) * (b42 - b46)",
"m10 = (a23) * (-b32 + b33)",
"m11 = (a12 - a13 + a22 - a32 + a33) * (b27 + b36)",
"m12 = (a13) * (b17 + b32 + b37 + b47)",
"m13 = (a13 - a34) * (b11 + b31 + b42 - b47 + b48 + b51)",
"m14 = (a12 - a21 + a22 + a31 - a32) * (-b16 + b25)",
"m15 = (a21 - a22 - a31 + a32) * (b25)",
"m16 = (a12 + a22 - a32) * (-b16 - b26 - b36 + b46)",
"m17 = (a13 - a14 - a21 + a24 + a25) * (b42 + b48 - b57)",
"m18 = (a34) * (b31 - b35 + b41 + b42 - b45)",
"m19 = (a11 - a31 + a32) * (b12 + b23 + b24)",
"m20 = (a13 - a14 - a15 - a23 + a24 + a25) * (b17 - b35 + b57)",
"m21 = (a21 - a24 - a25) * (b42 + b48)",
"m22 = (a14 - a24) * (b42 - b46)",
"m23 = (a15 - a25) * (b22 - b23 - b25 - b26 + b27 + b52 - b56)",
"m24 = (a11 - a15 - a21 + a25) * (b12 - b13 - b15 - b16 - b35 - b45)",
"m25 = (a25 - a35) * (-b56)",
"m26 = (a21) * (b12 - b15 - b35 - b55)",
"m27 = (a11 - a14 - a15 - a21 + a24 + a25) * (b17 - b35 - b45)",
"m28 = (a21 - a23 + a33 - a34 - a35) * (-b14 + b42 + b48)",
"m29 = (a22 - a23 - a32 + a33) * (-b24)",
"m30 = (a15 + a24) * (b43 + b44 - b54)",
"m31 = (a21 - a35) * (b12 + b18 + b32 + b38 + b42 + b48 - b51 + b55)",
"m32 = (a21 - a23) * (b17 + b57)",
"m33 = (a23 - a24 - a33 + a34) * (b41 + b42 + b44 - b45 - b54)",
"m34 = (a33 - a34) * (b11 + b31 + b51)",
"m35 = (a11 - a13 + a34) * (b11 + b35 + b45)",
"m36 = (a35) * (b12 - b17 + b18 - b57 + b58)",
"m37 = (a21 - a23 - a35) * (b17 + b32 + b38 + b57)",
"m38 = (a31 - a34 - a35) * (-b14)",
"m39 = (a15 + a21 - a25) * (b12 - b13 - b15 - b16 - b35 - b55)",
"m40 = (a23 - a33 + a34 + a35) * (-b14 - b33 - b34 - b54)",
"m41 = (a12 + a22 - a23 - a32 + a33) * (-b24 - b36)",
"m42 = (a11 - a12 - a22 - a31 + a32) * (-b16 + b23 + b24)",
"m43 = (a12 - a13 - a32 + a33) * (b27)",
"m44 = (a33 - a34 - a35) * (b33 + b34)",
"m45 = (a13 - a33) * (b11 + b27 + b31 - b32 + b37 - b38 + b51)",
"m46 = (a21 - a31) * (b11 + b12 - b15 + b18 - b25 + b32 + b38 + b42 + b48)",
"m47 = (a13 - a14 - a15) * (b51)",
"m48 = (a21 - a33 + a34) * (b11 + b35 + b51)",
"m49 = (a13 + a32 - a33) * (b27 - b32)",
"m50 = (a21 - a25) * (b51 - b55)",
"m51 = (a11 - a12 + a21 - a22 - a31 + a32) * (-b16)",
"m52 = (a25 - a35) * (b22 + b28 - b42 - b48 + b51 + b52 - b55 + b58)",
"m53 = (a24) * (-b44 + b54)",
"m54 = (a23 - a33 + a34) * (b31 - b35 + b41 + b42 + b44 - b45 - b54)",
"m55 = (a12) * (b24 - b25 - b26 + b42)",
"m56 = (a11 - a12 - a31 + a32) * (b23 + b24)",
"m57 = (a12 + a14 - a34) * (b21 + b42)",
"m58 = (a12 + a14 - a32 - a34) * (b21)",
"m59 = (a13 - a14) * (b42 - b47 + b48)",
"m60 = (a11 - a14 - a15 - a31 + a34 + a35) * (b43 + b44 + b51)",
"m61 = (a12 + a14) * (b42)",
"m62 = (a32 - a33) * (b32)",
"m63 = (a13 - a14 - a15 - a21 + a24 + a25) * (b17 - b35 - b45 + b57)",
"m64 = (a13 - a14 + a24) * (b17 + b32 - b33 - b36 + b37 + b47)",
"m65 = (a12) * (b23 + b24 - b27 + b28 + b42)",
"m66 = (a12 - a13 + a22 - a23 - a32 + a33) * (-b36)",
"m67 = (a11 - a31 + a34 + a35) * (-b14 - b33 - b34 - b43 - b44)",
"m68 = (a12 - a15 - a22 + a25) * (b22 - b23 - b25 - b26 + b27)",
"m69 = (a12 + a14 + a22 + a24 - a32 - a34) * (-b46)",
"m70 = (a13 - a31 + a35) * (b17 + b32 + b38 + b42 + b48)",
"m71 = (a21 - a31 + a32) * (b12 + b25)",
"m72 = (a14 - a24) * (b17 + b32 - b33 - b36 + b37 + b42 - b43 - b46 + b47)",
"m73 = (a15 + a22 - a25) * (b22 - b23 - b25 - b26 + b27 + b52)",
"m74 = (a13 - a14 - a23 + a24) * (b17 + b32 - b33 - b36 + b37 + b57)",
"m75 = (a11 - a13) * (b35 + b45)",
"m76 = (a12 + a14 + a22 - a32 - a34) * (b21 + b46)",
"m77 = (a11 - a13 - a31 + a33) * (b11 - b33 - b34 + b51)",
"m78 = (a22) * (b21 + b22 + b24 - b25 + b52)",
"m79 = (a22 - a25 - a32 + a35) * (b22 + b28)",
"m80 = (a23 + a32 - a33) * (-b24 + b32)",
"m81 = (a22 - a25 + a35) * (b22 + b28 + b52)",
"m82 = (a11 - a13 - a31 + a34 + a35) * (b33 + b34 - b51)",
"m83 = (a22 - a25) * (b52)",
"m84 = (a32) * (b12 + b21 - b28 + b32)",
"m85 = (a15) * (b43 + b44 - b53 - b54)",
"m86 = (a23 - a33) * (-b14 - b24 - b31 - b34 + b35 - b41 - b42 - b44 + b45)",
"m87 = (a14 - a34) * (b21 - b41 + b42 - b47 + b48 + b51)",
"m88 = (a23 - a24 - a25 - a33 + a34 + a35) * (b42 + b48 + b54)",
"m89 = (a21 - a23 - a31 + a33) * (-b14 + b32 + b38 + b42 + b48)",
"m90 = (a11 - a31) * (b12 + b13 + b14 - b17 + b18 + b23 + b24 + b33 + b34 + b53 + b54 - b57 + b58)",
"m91 = (a13 - a14 - a15 - a21 + a25) * (b413 - b59)",
"m92 = (a11 - a15 - a31 + a35) * (b411 + b412 - b511 - b512 + b515 - b516)",
"m93 = (a15) * (-b514)",
"m94 = (a31 - a35) * (b110 + b116 + b310 + b316 + b410 + b416)",
"m95 = (a11 - a31 + a35) * (b110 - b115 + b116 - b411 - b412 + b511 + b512 - b515 + b516)",
"m96 = (a31 - a32) * (b110)",
"m97 = (a11) * (-b110 + b111)",
"m98 = (a15 - a25) * (b110 - b111 - b113 - b114 + b210 - b211 - b213 - b214 + b215 - b313 + b510 - b511 - b513 - b514)",
"m99 = (a24) * (b410 - b414)",
"m100 = (a23) * (-b310 + b311)",
"m101 = (a12 - a13 + a22 - a32 + a33) * (b215 + b314)",
"m102 = (a13) * (b115 + b310 + b315 + b415)",
"m103 = (a13 - a34) * (b19 + b39 + b410 - b415 + b416 + b59)",
"m104 = (a12 - a21 + a22 + a31 - a32) * (-b114 + b213)",
"m105 = (a21 - a22 - a31 + a32) * (b213)",
"m106 = (a12 + a22 - a32) * (-b114 - b214 - b314 + b414)",
"m107 = (a13 - a14 - a21 + a24 + a25) * (b410 + b416 - b515)",
"m108 = (a34) * (b39 - b313 + b49 + b410 - b413)",
"m109 = (a11 - a31 + a32) * (b110 + b211 + b212)",
"m110 = (a13 - a14 - a15 - a23 + a24 + a25) * (b115 - b313 + b515)",
"m111 = (a21 - a24 - a25) * (b410 + b416)",
"m112 = (a14 - a24) * (b410 - b414)",
"m113 = (a15 - a25) * (b210 - b211 - b213 - b214 + b215 + b510 - b514)",
"m114 = (a11 - a15 - a21 + a25) * (b110 - b111 - b113 - b114 - b313 - b413)",
"m115 = (a25 - a35) * (-b514)",
"m116 = (a21) * (b110 - b113 - b313 - b513)",
"m117 = (a11 - a14 - a15 - a21 + a24 + a25) * (b115 - b313 - b413)",
"m118 = (a21 - a23 + a33 - a34 - a35) * (-b112 + b410 + b416)",
"m119 = (a22 - a23 - a32 + a33) * (-b212)",
"m120 = (a15 + a24) * (b411 + b412 - b512)",
"m121 = (a21 - a35) * (b110 + b116 + b310 + b316 + b410 + b416 - b59 + b513)",
"m122 = (a21 - a23) * (b115 + b515)",
"m123 = (a23 - a24 - a33 + a34) * (b49 + b410 + b412 - b413 - b512)",
"m124 = (a33 - a34) * (b19 + b39 + b59)",
"m125 = (a11 - a13 + a34) * (b19 + b313 + b413)",
"m126 = (a35) * (b110 - b115 + b116 - b515 + b516)",
"m127 = (a21 - a23 - a35) * (b115 + b310 + b316 + b515)",
"m128 = (a31 - a34 - a35) * (-b112)",
"m129 = (a15 + a21 - a25) * (b110 - b111 - b113 - b114 - b313 - b513)",
"m130 = (a23 - a33 + a34 + a35) * (-b112 - b311 - b312 - b512)",
"m131 = (a12 + a22 - a23 - a32 + a33) * (-b212 - b314)",
"m132 = (a11 - a12 - a22 - a31 + a32) * (-b114 + b211 + b212)",
"m133 = (a12 - a13 - a32 + a33) * (b215)",
"m134 = (a33 - a34 - a35) * (b311 + b312)",
"m135 = (a13 - a33) * (b19 + b215 + b39 - b310 + b315 - b316 + b59)",
"m136 = (a21 - a31) * (b19 + b110 - b113 + b116 - b213 + b310 + b316 + b410 + b416)",
"m137 = (a13 - a14 - a15) * (b59)",
"m138 = (a21 - a33 + a34) * (b19 + b313 + b59)",
"m139 = (a13 + a32 - a33) * (b215 - b310)",
"m140 = (a21 - a25) * (b59 - b513)",
"m141 = (a11 - a12 + a21 - a22 - a31 + a32) * (-b114)",
"m142 = (a25 - a35) * (b210 + b216 - b410 - b416 + b59 + b510 - b513 + b516)",
"m143 = (a24) * (-b412 + b512)",
"m144 = (a23 - a33 + a34) * (b39 - b313 + b49 + b410 + b412 - b413 - b512)",
"m145 = (a12) * (b212 - b213 - b214 + b410)",
"m146 = (a11 - a12 - a31 + a32) * (b211 + b212)",
"m147 = (a12 + a14 - a34) * (b29 + b410)",
"m148 = (a12 + a14 - a32 - a34) * (b29)",
"m149 = (a13 - a14) * (b410 - b415 + b416)",
"m150 = (a11 - a14 - a15 - a31 + a34 + a35) * (b411 + b412 + b59)",
"m151 = (a12 + a14) * (b410)",
"m152 = (a32 - a33) * (b310)",
"m153 = (a13 - a14 - a15 - a21 + a24 + a25) * (b115 - b313 - b413 + b515)",
"m154 = (a13 - a14 + a24) * (b115 + b310 - b311 - b314 + b315 + b415)",
"m155 = (a12) * (b211 + b212 - b215 + b216 + b410)",
"m156 = (a12 - a13 + a22 - a23 - a32 + a33) * (-b314)",
"m157 = (a11 - a31 + a34 + a35) * (-b112 - b311 - b312 - b411 - b412)",
"m158 = (a12 - a15 - a22 + a25) * (b210 - b211 - b213 - b214 + b215)",
"m159 = (a12 + a14 + a22 + a24 - a32 - a34) * (-b414)",
"m160 = (a13 - a31 + a35) * (b115 + b310 + b316 + b410 + b416)",
"m161 = (a21 - a31 + a32) * (b110 + b213)",
"m162 = (a14 - a24) * (b115 + b310 - b311 - b314 + b315 + b410 - b411 - b414 + b415)",
"m163 = (a15 + a22 - a25) * (b210 - b211 - b213 - b214 + b215 + b510)",
"m164 = (a13 - a14 - a23 + a24) * (b115 + b310 - b311 - b314 + b315 + b515)",
"m165 = (a11 - a13) * (b313 + b413)",
"m166 = (a12 + a14 + a22 - a32 - a34) * (b29 + b414)",
"m167 = (a11 - a13 - a31 + a33) * (b19 - b311 - b312 + b59)",
"m168 = (a22) * (b29 + b210 + b212 - b213 + b510)",
"m169 = (a22 - a25 - a32 + a35) * (b210 + b216)",
"m170 = (a23 + a32 - a33) * (-b212 + b310)",
"m171 = (a22 - a25 + a35) * (b210 + b216 + b510)",
"m172 = (a11 - a13 - a31 + a34 + a35) * (b311 + b312 - b59)",
"m173 = (a22 - a25) * (b510)",
"m174 = (a32) * (b110 + b29 - b216 + b310)",
"m175 = (a15) * (b411 + b412 - b511 - b512)",
"m176 = (a23 - a33) * (-b112 - b212 - b39 - b312 + b313 - b49 - b410 - b412 + b413)",
"m177 = (a14 - a34) * (b29 - b49 + b410 - b415 + b416 + b59)",
"m178 = (a23 - a24 - a25 - a33 + a34 + a35) * (b410 + b416 + b512)",
"m179 = (a21 - a23 - a31 + a33) * (-b112 + b310 + b316 + b410 + b416)",
"m180 = (a11 - a31) * (b110 + b111 + b112 - b115 + b116 + b211 + b212 + b311 + b312 + b511 + b512 - b515 + b516)"
],
"elements": [
"c11 = m13 + m18 + m35 - m47 + m57 - m59 - m61 - m75 - m87",
"c12 = m6 + m19 - m43 - m49 - m55 - m56 + m61 - m62 + m68 + m73 - m83",
"c13 = m6 + m7 + m12 + m19 + m22 - m29 + m30 + m41 + m53 - m56 - m64 - m66 - m72 - m85",
"c14 = -m12 - m22 + m29 - m30 - m38 - m41 + m47 - m53 - m60 + m64 + m66 - m67 + m72 - m82",
"c15 = -m1 - m7 + m14 + m15 - m24 - m39 - m47 + m50 + m51 - m75",
"c16 = -m3 - m9 - m14 - m15 - m22 + m29 - m41 - m51 - m55 + m61 + m66",
"c17 = m12 - m17 - m21 + m27 + m43 + m49 + m59 + m62 - m63 + m75",
"c18 = m2 + m4 + m5 - m6 - m17 - m19 - m21 + m27 + m43 + m49 + m56 - m61 + m62 - m63 + m65 + m70 + m75 + m85",
"c19 = m103 + m108 + m125 - m137 + m147 - m149 - m151 - m165 - m177",
"c110 = m96 + m109 - m133 - m139 - m145 - m146 + m151 - m152 + m158 + m163 - m173",
"c111 = m96 + m97 + m102 + m109 + m112 - m119 + m120 + m131 + m143 - m146 - m154 - m156 - m162 - m175",
"c112 = -m102 - m112 + m119 - m120 - m128 - m131 + m137 - m143 - m150 + m154 + m156 - m157 + m162 - m172",
"c113 = -m91 - m97 + m104 + m105 - m114 - m129 - m137 + m140 + m141 - m165",
"c114 = -m93 - m99 - m104 - m105 - m112 + m119 - m131 - m141 - m145 + m151 + m156",
"c115 = m102 - m107 - m111 + m117 + m133 + m139 + m149 + m152 - m153 + m165",
"c116 = m92 + m94 + m95 - m96 - m107 - m109 - m111 + m117 + m133 + m139 + m146 - m151 + m152 - m153 + m155 + m160 + m165 + m175",
"c21 = -m1 - m9 + m20 - m32 - m33 + m34 - m47 + m48 + m53 + m54 - m58 - m63 + m69 + m76",
"c22 = m6 + m9 - m15 + m29 + m58 - m62 - m69 + m71 - m76 + m78 + m80 - m83",
"c23 = m8 + m10 - m23 + m26 + m29 + m30 - m39 - m42 + m51 + m53 + m56 - m62 + m80 - m85",
"c24 = -m10 + m21 - m28 - m29 - m40 + m44 - m53 + m62 - m80 - m88",
"c25 = -m1 + m6 - m15 + m20 - m26 - m32 - m47 + m50 - m63 + m71",
"c26 = -m3 + m11 + m23 + m42 - m43 - m51 - m56 + m58 + m66 - m69 - m73 - m76 + m78",
"c27 = m10 + m11 - m17 - m21 + m32 - m43 + m59 + m64 + m66 - m74",
"c28 = -m6 - m9 + m15 - m21 - m29 + m31 + m32 + m36 - m37 + m50 + m52 - m58 + m62 + m69 - m71 + m76 - m78 - m80 + m81",
"c29 = -m91 - m99 + m110 - m122 - m123 + m124 - m137 + m138 + m143 + m144 - m148 - m153 + m159 + m166",
"c210 = m96 + m99 - m105 + m119 + m148 - m152 - m159 + m161 - m166 + m168 + m170 - m173",
"c211 = m98 + m100 - m113 + m116 + m119 + m120 - m129 - m132 + m141 + m143 + m146 - m152 + m170 - m175",
"c212 = -m100 + m111 - m118 - m119 - m130 + m134 - m143 + m152 - m170 - m178",
"c213 = -m91 + m96 - m105 + m110 - m116 - m122 - m137 + m140 - m153 + m161",
"c214 = -m93 + m101 + m113 + m132 - m133 - m141 - m146 + m148 + m156 - m159 - m163 - m166 + m168",
"c215 = m100 + m101 - m107 - m111 + m122 - m133 + m149 + m154 + m156 - m164",
"c216 = -m96 - m99 + m105 - m111 - m119 + m121 + m122 + m126 - m127 + m140 + m142 - m148 + m152 + m159 - m161 + m166 - m168 - m170 + m171",
"c31 = m18 + m34 + m35 - m44 + m57 - m58 - m61 - m75 - m77 - m82",
"c32 = m6 - m57 + m58 + m61 - m62 - m79 + m81 - m83 + m84",
"c33 = m5 + m6 + m7 + m10 + m18 + m19 - m36 + m40 - m54 - m62 - m67 + m80 - m86 - m90",
"c34 = -m10 - m18 - m38 - m40 + m44 + m54 + m62 - m80 + m86",
"c35 = m4 + m6 - m26 - m31 + m35 - m44 + m46 - m48 + m71 - m75 - m77 - m82",
"c36 = -m3 - m9 + m11 - m14 - m15 + m16 - m22 + m23 + m25 + m29 - m41 + m42 - m43 - m51 - m55 - m56 + m58 + m61 + m66 - m73 - m76 + m78",
"c37 = m12 + m13 - m28 + m32 - m34 - m37 + m38 - m45 + m49 + m62 - m70 + m89",
"c38 = m4 - m6 - m28 + m32 + m36 - m37 + m38 + m57 - m58 - m61 + m62 - m84 + m89",
"c39 = m108 + m124 + m125 - m134 + m147 - m148 - m151 - m165 - m167 - m172",
"c310 = m96 - m147 + m148 + m151 - m152 - m169 + m171 - m173 + m174",
"c311 = m95 + m96 + m97 + m100 + m108 + m109 - m126 + m130 - m144 - m152 - m157 + m170 - m176 - m180",
"c312 = -m100 - m108 - m128 - m130 + m134 + m144 + m152 - m170 + m176",
"c313 = m94 + m96 - m116 - m121 + m125 - m134 + m136 - m138 + m161 - m165 - m167 - m172",
"c314 = -m93 - m99 + m101 - m104 - m105 + m106 - m112 + m113 + m115 + m119 - m131 + m132 - m133 - m141 - m145 - m146 + m148 + m151 + m156 - m163 - m166 + m168",
"c315 = m102 + m103 - m118 + m122 - m124 - m127 + m128 - m135 + m139 + m152 - m160 + m179",
"c316 = m94 - m96 - m118 + m122 + m126 - m127 + m128 + m147 - m148 - m151 + m152 - m174 + m179"
],
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[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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
],
"invariant_f": "8x^3y^2z^2 + 8x^2y^3z^2 + 8x^2y^2z^3 + 336x^2y^2z^2 + 52x^3yz + 28x^2y^2z + 52xy^3z + 28x^2yz^2 + 28xy^2z^2 + 52xyz^3 + 124x^2yz + 124xy^2z + 124xyz^2 + 108xyz",
"invariant_g": "w^318 + w^308 + w^240",
"type": "4X^2Y^3Z^2 + 56X^2Y^2Z^2 + 10XY^3Z + 14XY^2Z^2 + 16XYZ^3 + 30XY^2Z + 32XYZ^2 + 18XYZ"
}