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D.15.17.35 isZeroElement
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- isZeroElement(d, [T]); intvec d, group T
- Purpose:
- For a integer vector 'd' representing the multidegree of some polynomial
or vector this method computes if the multidegree is contained in the grading group
group (either set globally or given as an optional argument), i.e. if it is zero in the multigrading.
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;
intmat tt[2][1]=
1,
-1;
setBaseMultigrading(g,t);
poly a = x10yz;
poly b = x8y2z;
poly c = x4z2;
poly d = y5;
poly e = x2y2;
poly f = z2;
intvec v1 = multiDeg(a) - multiDeg(b);
v1;
==> 2,-1
isZeroElement(v1);
==> 1
isZeroElement(v1, tt);
==> 0
intvec v2 = multiDeg(a) - multiDeg(c);
v2;
==> 5,0
isZeroElement(v2);
==> 0
isZeroElement(v2, tt);
==> 0
intvec v3 = multiDeg(e) - multiDeg(f);
v3;
==> 0,0
isZeroElement(v3);
==> 1
isZeroElement(v3, tt);
==> 1
intvec v4 = multiDeg(c) - multiDeg(d);
v4;
==> 6,-3
isZeroElement(v4);
==> 1
isZeroElement(v4, tt);
==> 0
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