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7.8.7 modulo (letterplace)
Syntax:
Syntax:
modulo ( ideal_expression, ideal_expression )
modulo ( module_expression, module_expression )
Type:
- module
Purpose:
- computes the kernel of the bimodule homomorphism from the free bimodule (determined
in basering) to its factor-bimodule modulo the second argument. The first argument
determines the homomorphism via images of the canonical free bimodule generators.
If option(returnSB) is set, a Groebner basis is returned, otherwise a generating set.
Example:
| LIB "freegb.lib";
ring r = 0,(x,y,z),dp;
ring R = freeAlgebra(r,7,2); // free bimodule of rank 2
ideal I = x*y*z - z*y*x;
I = twostd(I); I;
==> I[1]=z*y*x-x*y*z
modulo(y,twostd(0)); // shows the canonical generator of the kernel
==> _[1]=ncgen(1)*y*gen(1)-y*ncgen(1)*gen(1)
// which can be interpreted as (1 otimes y - y otimes 1)
module M = modulo(y, I);
print(M); // as we see (z E y - y E z) generates the kernel
==> ncgen(1)*y-y*ncgen(1),z*ncgen(1)*x-x*ncgen(1)*z
// of bimodule homomorphism sending E to y
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See
ideal;
lift (letterplace);
liftstd (letterplace);
module;
ncgen;
option;
syz (letterplace).
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