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3.13 modulo
Syntax:
modulo ( ideal_expression, ideal_expression )
modulo ( module_expression, module_expression )
Type:
- module
Purpose:
modulo(h1,h2)
represents
where
and are considered as submodules of the same free module
(l=1 for ideals). Let
, resp. ,be the matrices of size , resp. , having the
generators of , resp. ,as columns.
Then
where
is the induced map.
modulo(h1,h2) returns generators of
the kernel of this induced map.
Example:
| LIB "ncalg.lib";
def A = sl2();
setring A;
option(redSB);
option(redTail);
ideal I = e2,f2,h2-1;
I = twostd(I);
I;
==> I[1]=h2-1
==> I[2]=fh-f
==> I[3]=eh+e
==> I[4]=f2
==> I[5]=2ef-h-1
==> I[6]=e2
ideal E = std(e);
ideal T = modulo(E,I);
T = NF(std(I+T),I);
T = std(T);
T;
==> T[1]=h-1
==> T[2]=e
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See
syz.
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