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D.15.14.41 multiDegModulo
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- multiDegModulo(I); I, J are ideals or modules
- Purpose:
- computes the multigraded 'modulo' module of I and J
- Returns:
- module, see 'modulo' command
- Note:
- I and J should have the same multigrading, and their
generators must be multigraded homogeneous
Example:
| | LIB "multigrading.lib";
ring r = 0,(x,y,z),dp;
intmat MM[2][3]=
-1,1,1,
0,1,3;
setBaseMultigrading(MM);
ideal h1 = x, y, z;
ideal h2 = x;
"Multidegrees: "; print(multiDeg(h1));
==> Multidegrees:
==> -1 1 1
==> 0 1 3
// Let's compute modulo(h1, h2):
def K = multiDegModulo(h1, h2); K;
==> K[1]=gen(1)
==> K[2]=y*gen(3)-z*gen(2)
==> K[3]=x*gen(2)
==> K[4]=x*gen(3)
"Module Units Multigrading: "; print( getModuleGrading(K) );
==> Module Units Multigrading:
==> -1 1 1
==> 0 1 3
"Multidegrees: "; print(multiDeg(K));
==> Multidegrees:
==> -1 2 0 0
==> 0 4 1 3
isHomogeneous(K);
==> 1
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