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5.1.103 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
==> map[1023:1]{6:6}...
==> {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
==> map[1023:1]{6:6}...
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
==> map[1023:1]{6:6}...
id5;
==> id5[1]=z2
==> id5[2]=yz
==> id5[3]=xz
==> id5[4]=y2
==> id5[5]=xy
==> id5[6]=x2
quotient


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