i1 : wtR = matrix{{5,6,6},{3,6,0}};
2 3
o1 : Matrix ZZ <--- ZZ
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i2 : Rq = ZZ/23[x,y,z,Weights=>entries weightGrevlex(wtR)]; |
i3 : Iq = {x^6+x^3*z-y^3*z^2};
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i4 : (fractions,relicR,icR,wticR) = qthIntegralClosure(wtR,Rq,Iq)
2 2 5 2 4 3 2 2 2 2
o4 = ({y z, x*y z, x + x z, x y + x*y*z, x y , x y z}, {p - p p p + p p ,
0 2 5 6 4 6
------------------------------------------------------------------------
2 2 2 3
p p + p - p p , p p - p p , p p - p p p , p p - p p , p + p - p ,
0 1 0 3 5 0 2 5 6 0 3 4 5 6 0 4 1 6 1 1 5
------------------------------------------------------------------------
2 2
p p - p p , p p - p p , p p - p p + p , p - p p - p , p p - p p
1 2 4 5 1 3 0 5 1 4 2 5 4 2 0 5 3 2 3 1 6
------------------------------------------------------------------------
2 2
- p , p p - p p , p - p p , p p - p p , p - p }, icR, | 10 9 8 7 5 6
6 2 4 3 5 3 2 6 3 4 5 6 4 0 | 6 9 6 3 3 6
------------------------------------------------------------------------
6 |)
0 |
o4 : Sequence
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The presentation is therefore a quotient ring, icR ( with grevlex-over-weight monomial ordering implicit from wticR) modulo the ideal, relicR, of induced relations that define the P-algebra multiplication and possible P-linear dependencies. The fractions returned could be used to define a map from fractions#0 icR to Rq.