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7.3.14 modulo (plural)

Syntax:
modulo ( ideal_expression, ideal_expression )
modulo ( module_expression, module_expression )
Type:
module
Purpose:
modulo(h1,h2) represents 154#154, where 155#155 and 156#156are considered as submodules of the same free module 157#157(l=1 for ideals).
Let 158#158 (resp. 159#159) be the matrix of size 160#160 (resp. 161#161), having the generators of 155#155 (resp. 156#156)as columns.
Then 162#162, where 163#163is the induced map given by 158#158.
modulo(h1,h2) returns generators of the kernel of this induced map.

Note: If, for at least one of
155#155 or 156#156,the attribute isHomog is st, then modulo(h1,h2) also sets this attribute (if the weights are compatible).

Example:
 
LIB "ncalg.lib";
def A = makeUsl2();
setring A; // this algebra is U(sl_2)
option(redSB);
option(redTail);
ideal H2 = e2,f2,h2-1;
H2 = twostd(H2);
print(matrix(H2)); // print H2 in a compact form
==> h2-1,fh-f,eh+e,f2,2ef-h-1,e2
ideal H1 = std(e);
ideal T = modulo(H1,H2);
T = NF(std(H2+T),H2);
T = std(T);
T;
==> T[1]=h-1
==> T[2]=e
See also syz (plural).


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