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7.2.6.1 resolution declarations (plural)
- Syntax:
resolution name = resolution_expression ;
- Purpose:
- defines a resolution.
- Default:
- none
- Example:
| | ring r=0,(x,y,z),dp;
matrix D[3][3];
D[1,2]=z;
def R=nc_algebra(1,D); // it is a Heisenberg algebra
setring R;
ideal i=z2+z,x+y;
resolution re=nres(i,0);
re;
==> 1 2 1
==> R <-- R <-- R
==>
==> 0 1 2
==> resolution not minimized yet
==>
list l = re;
l;
==> [1]:
==> _[1]=z2+z
==> _[2]=x+y
==> [2]:
==> _[1]=z2*gen(2)-x*gen(1)-y*gen(1)+z*gen(2)
==> [3]:
==> _[1]=0
print(matrix(l[2]));
==> -x-y,
==> z2+z
print(module(transpose(matrix(l[2]))*transpose(matrix(l[1])))); // check that product is zero
==> 0
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