If
i is a multi-degree, then the result is the submodule generated by all elements of degree exactly
i, together with all generators of
M whose first degree is higher than the first entry in
i.
i1 : R = ZZ/101[a..c];
|
i2 : truncate(2,R^1)
o2 = image | a2 ab ac b2 bc c2 |
1
o2 : R-module, submodule of R
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i3 : truncate(2, ideal(a,b,c^3)/ideal(a^2,b^2,c^4))
o3 = subquotient (| ab ac bc c3 |, | a2 b2 c4 |)
1
o3 : R-module, subquotient of R
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i4 : truncate(2,ideal(a,b*c,c^7))
2 7
o4 = ideal (a , a*b, a*c, b*c, c )
o4 : Ideal of R
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The base may be ZZ, or another polynomial ring. In this case, the generators may not be minimal.
i5 : A = ZZ[x,y,z];
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i6 : truncate(2,ideal(3*x,5*y,15))
2 2 2
o6 = ideal (3x , 3x*y, 3x*z, 5x*y, 5y , 5y*z, 15z )
o6 : Ideal of A
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i7 : truncate(2,comodule ideal(3*x,5*y,15))
o7 = subquotient (| x2 xy xz y2 yz z2 |, | 3x 5y 15 |)
1
o7 : A-module, subquotient of A
|
i8 : L = ZZ/691[x,y,z];
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i9 : B = L[s,t];
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i10 : truncate(2,ideal(3*x*s,5*y*t^2,s*t))
2 2
o10 = ideal (3x*s , 5y*t , s*t)
o10 : Ideal of B
|
i11 : truncate(2,comodule ideal(3*x,5*y,15))
o11 = subquotient (0, | 3x 5y 15 |)
1
o11 : L-module, subquotient of L
|
The following includes the generator of degree {8,20}.
i12 : S = ZZ/101[x,y,z,Degrees=>{{1,3},{1,4},{1,-1}}];
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i13 : truncate({7,24}, S^1 ++ S^{{-8,-20}})
o13 = image {0, 0} | x4y3 |
{8, 20} | 0 |
2
o13 : S-module, submodule of S
|