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D.15.17.32 multiDegPartition

Procedure from library multigrading.lib (see multigrading_lib).

Usage:
multiDegPartition(def p), p polynomial/vector

Returns:
an ideal/module consisting of multigraded-homogeneous parts of p

Example:
 
LIB "multigrading.lib";
ring r = 0,(x,y,z),dp;
intmat g[2][3]=
1,0,1,
0,1,1;
intmat t[2][1]=
-2,
1;
setBaseMultigrading(g,t);
poly f = x10yz+x8y2z-x4z2+y5+x2y2-z2+x17z3-y6;
multiDegPartition(f);
==> _[1]=x17z3
==> _[2]=x10yz+x8y2z
==> _[3]=-y6
==> _[4]=-x4z2+y5
==> _[5]=x2y2-z2
vector v = xy*gen(1)-x3y2*gen(2)+x4y*gen(3);
intmat B[2][3]=1,-1,-2,0,0,1;
v = setModuleGrading(v,B);
getModuleGrading(v);
==> 1,-1,-2,
==> 0,0,1 
multiDegPartition(v, B);
==> _[1]=x4y*gen(3)-x3y2*gen(2)
==> _[2]=xy*gen(1)