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D.5.5.7 invariantsProcedure from library
Example: LIB "hnoether.lib"; ring exring=0,(x,y),dp; list hne=develop(y4+2x3y2+x6+x5y); list INV=invariants(hne); INV[1]; // the characteristic exponents → 4,6,7 INV[2]; // the generators of the semigroup of values → 4,6,13 INV[3],INV[4]; // the Puiseux pairs in packed form → 3,7 2,2 INV[5] / 2; // the delta-invariant → 8 INV[6]; // the sequence of multiplicities → 4,2,2,1,1 // To display the invariants more 'nicely': displayInvariants(hne); → characteristic exponents : 4,6,7 → generators of semigroup : 4,6,13 → Puiseux pairs : (3,2)(7,2) → degree of the conductor : 16 → delta invariant : 8 → sequence of multiplicities: 4,2,2,1,1 ///////////////////////////// INV=invariants((x2-y3)*(x3-y5)); INV[1][1]; // the characteristic exponents of the first branch → 2,3 INV[2][6]; // the sequence of multiplicities of the second branch → 3,2,1,1 print(INV[size(INV)][1]); // the contact matrix of the branches → 0 3 → 3 0 print(INV[size(INV)][2]); // the intersection numbers of the branches → 0 9 → 9 0 INV[size(INV)][3]; // the delta invariant of the curve → 14 See also: develop; displayInvariants; intersection; multsequence. |
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