IN THIS FILE:

Macaulay2 output of applying “primaryDecomposition” to the ideals of degenerate Schubert varieties.

****************************************

R=QQ[p1,p2,p3,p4,p12,p13,p14,p23,p24,p34,p123,p124,p134,p234]

*************************

s2s1=ideal(
p3*p12-p2*p13
)
*************************

s1s2=ideal(
p2*p13
)

*************************

s3s2=ideal(
p13*p124-p14*p123)

{ideal(
p14*p123-p13*p124)}

*************************

s2s3=ideal(
p13*p124
)
{
ideal(p13),
ideal(p124)
}

*************************

s1s2s1=ideal(
p3*p12-p2*p13
)

{ideal(
p3*p12-p2*p13)}

*************************

s2s3s2=ideal(
p13*p124-p14*p123
)

{ideal(
p14*p123-p13*p124)}

*************************

s1s2s3=ideal(
-p13*p234,
p23*p124-p12*p234,
p13*p124,
-p2*p13
)

{ideal(
p13,
p23*p124-p12*p234), 

ideal(
p234,
p124,
p2)}
*************************

s3s2s1=ideal(
p13*p124-p14*p123,
p3*p124-p4*p123,
p3*p12-p2*p13,
-p3*p14+p4*p13,
-p2*p14+p4*p12
)

{ideal(
p14*p123-p13*p124,
p4*p123-p3*p124,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13)}
*************************

s2s1s3=ideal(
p13*p124,
p3*p124,
p3*p12-p2*p13
)

{ideal(
p124,
p3*p12-p2*p13), 

ideal(
p13,
p3)}
*************************

s1s3s2=ideal(
p24*p123-p23*p124,
p14*p123-p13*p124,
p14*p23-p13*p24,
-p2*p13+p1*p23,
-p2*p14+p1*p24
)
{ideal(
p24*p123-p23*p124,
p14*p123-p13*p124,
p14*p23-p13*p24,
p2*p14-p1*p24,
p2*p13-p1*p23)}

*************************
s2s1s3s2=ideal(
-p34*p123,
p23*p124-p24*p123,
p13*p124-p14*p123,
-p34*p124,
p3*p124,
-p34*p12+p24*p13-p14*p23,
p3*p12-p2*p13,
-p3*p24+p2*p34,
-p3*p14,
-p2*p14
)

{ideal(
p34,
p14,
p13,
p3,
p24*p123-p23*p124), 

ideal(
p34,
p3,
p2,
p24*p123-p23*p124,
p14*p123-p13*p124,
p14*p23-p13*p24), 

ideal(
p124,
p123,
p3,
p2,
p14*p23-p13*p24+p12*p34), 

ideal(
p124,
p123,
p14,
p13*p24-p12*p34,
p3*p24-p2*p34,
p3*p12-p2*p13),

ideal(
p124,
p34,
p24,
p14,
p3*p12-p2*p13)}

*************************
       
s3s1s2s1=ideal(
p23*p124-p24*p123,
p13*p124-p14*p123,
p3*p124-p4*p123,
+p24*p13-p14*p23,
p3*p12-p2*p13,
-p3*p24+p4*p23,
-p3*p14+p4*p13,
-p2*p14+p4*p12
)
{ideal(
p24*p123-p23*p124,
p14*p123-p13*p124,
p4*p123-p3*p124,
p14*p23-p13*p24,
p4*p23-p3*p24,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13)}

*************************

s1s2s1s3=ideal(
-p13*p234,
p23*p124-p12*p234,
p13*p124,
p3*p124,
p3*p12-p2*p13
)

{ideal(
p124,
p13,
p12), 

ideal(
p13,
p3,
p23*p124-p12*p234
), 

ideal(
p234,
p124,
p3*p12-p2*p13)}
*************************

s1s2s3s2=ideal(
-p13*p234,
p23*p124-p12*p234,
-p24*p123,
p13*p124-p14*p123,
-p14*p234,
+p24*p13-p14*p23,
-p2*p13,
-p2*p14
)

{ideal(
p123,
p14,
p13,
p23*p124-p12*p234
), 

ideal(
p24,
p14,
p13,
p23*p124-p12*p234
), 

ideal(
p234,
p24,
p23,
p2,
p14*p123-p13*p124), 

ideal(
p234,
p124,
p24,
p14,
p2), 

ideal(
p234,
p124,
p123,
p2,
p14*p23-p13*p24),

ideal(
p234,
p123,
p23,
p13,
p2)}
*************************

s2s3s2s1=ideal(
p13*p124-p14*p123,
p3*p124-p4*p123,
p3*p12-p2*p13,
-p3*p14+p4*p13,
-p2*p14+p4*p12
)
 {ideal(
p14*p123-p13*p124,
p4*p123-p3*p124,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13)}

*************************

s2s3s1s2s3=ideal(
-p13*p234,
-p34*p123,
p23*p124-p12*p234,
-p24*p123,
p13*p124-p14*p123,
-p34*p124-p14*p234,
p3*p124,
-p34*p12+p24*p13-p14*p23,
p3*p12-p2*p13,
-p3*p24+p2*p34,
-p3*p14,
-p2*p14
)
{ideal(
p123,
p34,
p14,
p13,
p3,
p23*p124-p12*p234
), 

ideal(
p123,
p13,
p3,
p2,
p34*p124+p14*p234,
p23*p124-p12*p234,
p14*p23+p12*p34),

ideal(
p234,
p34,
p24,
p23,
p3,
p2,
p14*p123-p13*p124), 

ideal(
p234,
p124,
p123,
p3,
p2,
p14*p23-p13*p24+p12*p34), 

ideal(
p234,
p124,
p123,
p14,
p13*p24-p12*p34,
p3*p24-p2*p34,
p3*p12-p2*p13), 

ideal(
p234,
p124,
p34,
p24,
p14,
p3*p12-p2*p13),

ideal(
p124,
p123,
p14,
p13,
p12,
p3*p24-p2*p34), 

ideal(
p124,
p34,
p24,
p14,
p13,
p12), 

ideal(
p34,
p24,
p14,
p13,
p3,
p23*p124-p12*p234
)}
*************************

s1s3s2s1s3=ideal(
-p13*p234,
p23*p124-p12*p234,
-p24*p123,
p13*p124-p14*p123,
-p14*p234,
p3*p124-p4*p123,
+p24*p13-p14*p23,
p3*p12-p2*p13,
-p3*p24+p4*p23,
-p3*p14+p4*p13,
-p2*p14+p4*p12
)

{ideal(
p24,
p23,
p14,
p13,
p12,
p4*p123-p3*p124), 

ideal(
p24,
p14,
p13,
p4,
p3,
p23*p124-p12*p234), 

ideal(
p123,
p14,
p13,
p4,
p3,
p23*p124-p12*p234), 

ideal(
p234,
p124,
p24,
p14,
p4,
p3*p12-p2*p13),

ideal(
p124,
p24,
p14,
p13,
p12,
p4), 

ideal(
p234,
p123,
p23,
p13,
p3,
p4*p12-p2*p14),

ideal(
p123,
p23,
p14,
p13,
p12,
p3), 

ideal(
p234,
p124,
p123,
p14*p23-p13*p24,
p4*p23-p3*p24,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13),

ideal(
p124,
p123,
p14,
p13,
p12,
p4*p23-p3*p24), 

ideal(
p234,
p24,
p23,
p14*p123-p13*p124,
p4*p123-p3*p124,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13)}
*************************

s2s3s1s2s1=ideal(
-p34*p123,
p23*p124-p24*p123,
p13*p124-p14*p123,
-p34*p124,
p3*p124-p4*p123,
-p34*p12+p24*p13-p14*p23,
p3*p12-p2*p13,
-p3*p24+p2*p34+p4*p23,
-p3*p14+p4*p13,
-p2*p14+p4*p12
)
{ideal(
p124,
p123,
p14*p23-p13*p24+p12*p34,
p4*p23-p3*p24+p2*p34,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13), 

ideal(
p34,
p24*p123-p23*p124,
p14*p123-p13*p124,
p4*p123-p3*p124,
p14*p23-p13*p24,
p4*p23-p3*p24,
p4*p13-p3*p14,
p4*p12-p2*p14,
p3*p12-p2*p13)}

*************************
121321

p34*p123+p13*p234
p34*p124+p14*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124
p4*p123-p3*p124
p14*p23-p13*p24+p12*p34
p3*p12-p2*p13
p4*p23-p3*p24+p2*p34
p4*p13-p3*p14
p4*p12-p2*p14