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5.1.75 modulo
Syntax:
modulo ( ideal_expression, ideal_expression )
modulo ( module_expression, module_expression )
Type:
module
Purpose:
modulo(h1,h2)
represents h1∕(h1 ∩h2) (h1 + h2)∕h2
where
h1 and h2
are considered as submodules of the same free module
Rl
(l=1 for ideals). Let
H1, resp. H2,
be
the matrices of size l × k, resp. l × m, having the generators of h1, resp. h2,
as columns.
Then
h1∕(h1 ∩ h2) Rk∕ker(H1)
where
H1 : Rk → Rl∕Im(H2) = Rl∕h2 is the induced map.
modulo(h1,h2) returns generators of
the kernel of this induced map.
Example:
ring r;
ideal h1=x,y,z;
ideal h2=x;
module m=modulo(h1,h2);
print(m);
→ 1,0, 0,0,
→ 0,-z,x,0,
→ 0,y, 0,x
See
syz.
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