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5.1.101 quotProcedure from library
Example: ring r=181,(x,y,z),(c,ls); ideal id1=maxideal(4); ideal id2=x2+xyz,y2-z3y,z3+y5xz; option(prot); ideal id3=quotient(id1,id2); → [1023:1]4(14)s(13)s(12)s(11)s(10)s(9)s(8)s(7)s(6)s(5)s(4)s(3)s(2)sss → product criterion:12 chain criterion:0 → {3}[1023:3]8(2)s(4)s(5)s9s.s.s.s.s.s → product criterion:0 chain criterion:39 id3; → id3[1]=z2 → id3[2]=yz → id3[3]=y2 → id3[4]=xz → id3[5]=xy → id3[6]=x2 ideal id4=quot(id1,id2,1); → [1023:2]4(14)s(13)s(12)s(11)s(10)s(9)s(8)s(7)s(6)s(5)s(4)s(3)s(2)sss → product criterion:0 chain criterion:0 → (S:3)rtrtrt → {1}[1023:3]4(2)s(4)s(5)s5s.s(3)s(2)sss → product criterion:0 chain criterion:39 → {1}[1023:3]4(5)s(4)s(3)s(2)sss → product criterion:0 chain criterion:9 → [255:3]3(11)s(10)sss(9)s(10)s(8)ss(7)s(8)s(6)s(7)s4(5)----- → product criterion:12 chain criterion:9 → {1}[1023:3]4(2)sss → product criterion:0 chain criterion:12 → [255:3]2(8)s(7)s(6)s3(5)ssssss4----- → product criterion:15 chain criterion:3 id4; → id4[1]=z2 → id4[2]=yz → id4[3]=xz → id4[4]=y2 → id4[5]=xy → id4[6]=x2 ideal id5=quot(id1,id2,2); → [1023:2]4(14)s(13)s(12)s(11)s(10)s(9)s(8)s(7)s(6)s(5)s(4)s(3)s(2)sss → product criterion:0 chain criterion:0 → (S:3)rtrtrt → {1}[1023:3]4(2)sss → product criterion:0 chain criterion:12 → {1}[1023:3]4(5)s(4)s(3)s(2)sss → product criterion:0 chain criterion:9 → [255:3]2(8)s(7)s(6)s3(5)s(4)s(3)s(2)sss → product criterion:15 chain criterion:0 id5; → id5[1]=z2 → id5[2]=yz → id5[3]=xz → id5[4]=y2 → id5[5]=xy → id5[6]=x2 See also: quotient. |
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