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5.1.101 quot
Procedure from library standard.lib (see standard_lib).
- Syntax:
quot (module_expression,module_expression)quot (module_expression,module_expression,int_expression)quot (ideal_expression,ideal_expression)quot (ideal_expression,ideal_expression,int_expression)- Type:
ideal
- Syntax:
quot (module_expression,ideal_expression)- Type:
module
- Purpose:
computes the quotient of the 1st and the 2nd argument. If a 3rd argument ’n’ is given the n-th method is used (n=1...5).
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
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See also: quotient.