This seminormalizes a reduced ring and outputs the map from the original ring to the seminormalization .
i1 : R = QQ[x,y]/ideal(x^3 - y^2); |
i2 : L = seminormalize(R)
QQ[Yy , Yy , Yy ]
0 1 2
o2 = {---------------------------------------,
2 2
(Yy - Yy , Yy Yy - Yy , Yy - Yy Yy )
2 1 1 2 0 1 0 2
------------------------------------------------------------------------
QQ[Yy , Yy , Yy ]
0 1 2
map(---------------------------------------,R,{Yy , Yy }),
2 2 1 0
(Yy - Yy , Yy Yy - Yy , Yy - Yy Yy )
2 1 1 2 0 1 0 2
------------------------------------------------------------------------
QQ[Yy00000RE1, xRE1, yRE1]
map(--------------------------------------------------------------------
2 2
(Yy00000RE1*yRE1 - xRE1 , Yy00000RE1*xRE1 - yRE1, Yy00000RE1 - xRE1
------------------------------------------------------------------------
QQ[Yy , Yy , Yy ]
0 1 2
-,---------------------------------------,{yRE1, xRE1, Yy00000RE1})}
2 2
) (Yy - Yy , Yy Yy - Yy , Yy - Yy Yy )
2 1 1 2 0 1 0 2
o2 : List
|
i3 : L#0
QQ[Yy , Yy , Yy ]
0 1 2
o3 = ---------------------------------------
2 2
(Yy - Yy , Yy Yy - Yy , Yy - Yy Yy )
2 1 1 2 0 1 0 2
o3 : QuotientRing
|
The previous example seminormalized a non-seminormal ring. Let’s try a seminormal ring.
i4 : R = QQ[x,y,z]/ideal(x^2*y-z^2); |
i5 : L = seminormalize(R)
QQ[Yy , Yy , Yy ] QQ[Yy , Yy , Yy ]
0 1 2 0 1 2
o5 = {-----------------, map(-----------------,R,{Yy , Yy , Yy }),
2 2 2 2 1 2 0
Yy Yy - Yy Yy Yy - Yy
1 2 0 1 2 0
------------------------------------------------------------------------
QQ[Yy00000RE1, xRE1, yRE1, zRE1]
map(--------------------------------------------------------------------
2
(Yy00000RE1*zRE1 - xRE1*yRE1, Yy00000RE1*xRE1 - zRE1, Yy00000RE1 -
------------------------------------------------------------------------
QQ[Yy , Yy , Yy ]
0 1 2
-----,-----------------,{zRE1, xRE1, yRE1})}
2 2
yRE1) Yy Yy - Yy
1 2 0
o5 : List
|
i6 : L#0
QQ[Yy , Yy , Yy ]
0 1 2
o6 = -----------------
2 2
Yy Yy - Yy
1 2 0
o6 : QuotientRing
|