Ideal flag4

p34*p123-p23*p134+p13*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124+p12*p134
p34*p124-p24*p134+p14*p234
p4*p123-p3*p124+p2*p134-p1*p234
p14*p23-p13*p24+p12*p34
p3*p12-p2*p13+p1*p23
p4*p23-p3*p24+p2*p34
p4*p13-p3*p14+p1*p34
p4*p12-p2*p14+p1*p24

MG weight =(1,1,1,0,1,1,0,2,1,1,1,0,1,1)

Ideal degenerate flag4 (initial ideal wrt MG weight)

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


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

s1: vanishing of p3,p4,p13,p23,p14,p24,p34,p124,p134,p234
left with p1,p2,p12,p123, but p12 and p123 not 0

Ideal Schubert
0

Ideal degenerate Schubert
0

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

s2s1: vanishing of p4,p23,p14,p24,p34,p124,p134,p234
left with p1,p2,p3,p12,p13,p123 => p123=/=0


Ideal Schubert
p3*p12-p2*p13


Ideal degenerate Schubert
p3*p12-p2*p13


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

s1s2: vanishing of p3,p4,p14,p24,p34,p124,p134,p234
left with p1,p2,p12,p13,p23,p123, so p123=/=0



Ideal Schubert

p2*p13+p1*p23


Ideal degenerate Schubert

p2*p13


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

s1s3: vanishing of p3,p4,p13,p14,p23,p24,p34,p134,p234
left with p1,p2,p12,p123,p124, so p12 not 0
also, p1 and p2 can not both vanish, same with p123 and p124


Ideal Schubert
0

Ideal degenerate Schubert
0

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

s3s2: vanishing of p2,p3,p4,p23,p24,p34,p134,p234
left p1,p12,p13,p14,p123,p124
p1 not 0, 

Ideal Schubert

p14*p123-p13*p124


Ideal degenerate Schubert

p14*p123-p13*p124


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

s2s3 vanishing of p2,p3,p4,p14,p23,p24,p34,p234
left p1,p12,p13,p123,p124,p134
p1 not 0


Ideal Schubert

p13*p124+p12*p134


Ideal degenerate Schubert
p13*p124


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

s1s2s1 vanishing of p4,p14,p24,p34,p124,p134,p234
left with p1,p2,p3,p12,p13,p23,p123 
so p123 not 0


Ideal Schubert
p3*p12-p2*p13+p1*p23


Ideal degenerate Schubert
p3*p12-p2*p13


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

s2s3s2 vanishing of p2,p3,p4,p23,p24,p34,p234
left with p1,p12,p13,p14,p123,p124,p134
p1 not 0

Ideal Schubert
p14*p123-p13*p124+p12*p134


Ideal degenerate Schubert
p14*p123-p13*p124


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

s1s2s3 vanishing of p3,p4,p14,p24,p34
left with p1,p2,p12,p13,p23,p123,p124,p134,p234


Ideal Schubert
p23*p134+p13*p234
p23*p124+p12*p234
p13*p124+p12*p134
p2*p134-p1*p234
p2*p13+p1*p23


Ideal degenerate Schubert
p13*p234
p23*p124+p12*p234
p13*p124
p2*p13


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

s3s2s1 vanishing of p23,p24,p34,p134,p234
left with p1,p2,p3,p4,p12,p13,p14,p123,p124


Ideal Schubert

p14*p123-p13*p124
p4*p123-p3*p124
p3*p12-p2*p13
p4*p13-p3*p14
p4*p12-p2*p14

Ideal degenerate Schubert

p14*p123-p13*p124
p4*p123-p3*p124
p3*p12-p2*p13
p4*p13-p3*p14
p4*p12-p2*p14

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

s2s1s3 vanishing of p4,p14,p23,p24,p34,p234
left with p1,p2,p3,p12,p13,p123,p124,p134


Ideal Schubert
-p13*p124+p12*p134
-p3*p124+p2*p134
p3*p12-p2*p13


Ideal degenerate Schubert
p13*p124
p3*p124
p3*p12-p2*p13

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

s1s3s2 vanishing of p3,p4,p34,p134,p234

Ideal Schubert

p24*p123-p23*p124
p14*p123-p13*p124
p14*p23-p13*p24
-p2*p13+p1*p23
-p2*p14+p1*p24

Ideal degenerate Schubert

p24*p123-p23*p124
p14*p123-p13*p124
p14*p23-p13*p24
p2*p13
p2*p14

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

s2s1s3s2 vanishing of p4,p234
left with p1,p2,p3,p12,p13,p23,p14,p24,p34,p123,p124,p134

Ideal Schubert
p34*p123-p23*p134
p24*p123-p23*p124
p14*p123-p13*p124+p12*p134
p34*p124-p24*p134
-p3*p124+p2*p134
p14*p23-p13*p24+p12*p34
p3*p12-p2*p13+p1*p23
-p3*p24+p2*p34
-p3*p14+p1*p34
-p2*p14+p1*p24

Ideal degenerate Schubert
p34*p123       
p24*p123-p23*p124
p14*p123-p13*p124
p34*p124        
-p3*p124
p14*p23-p13*p24+p12*p34
p3*p12-p2*p13
-p3*p24+p2*p34
-p3*p14
-p2*p14


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

s3s1s2s1 vanishing of p34,p134,p234
left with p1,p2,p3,p4,p12,p13,p23,p14,p24,p123,p124


Ideal Schubert

p24*p123-p23*p124
p14*p123-p13*p124
p4*p123-p3*p124
p14*p23-p13*p24
p3*p12-p2*p13+p1*p23
p4*p23-p3*p24
p4*p13-p3*p14
p4*p12-p2*p14+p1*p24

Ideal degenerate Schubert

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


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

s1s2s1s3 vanishing of p4,p14,p24,p34
left with p1,p2,p3,p12,p13,p23,p123,p124,p134,p234

Ideal Schubert
-p23*p134+p13*p234
-p23*p124+p12*p234
-p13*p124+p12*p134
-p3*p124+p2*p134-p1*p234
p3*p12-p2*p13+p1*p23

Ideal degenerate Schubert
p13*p234
-p23*p124+p12*p234
p13*p124
p3*p124
p3*p12-p2*p13

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

s1s2s3s2 vanishing of p3,p4,p34
left with p1,p2,p12,p13,p23,p14,p24,p123,p124,p134,p234

Ideal Schubert
-p23*p134+p13*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124+p12*p134
-p24*p134+p14*p234
+p2*p134-p1*p234
p14*p23-p13*p24
-p2*p13+p1*p23
-p2*p14+p1*p24

Ideal degenerate Schubert
p13*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124
p14*p234
p14*p23-p13*p24
p2*p13
p2*p14

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

s2s3s2s1 vanishing of p23,p24,p34,p234
left with p1,p2,p3,p4,p12,p13,p14,p123,p124,p134

Ideal Schubert

p14*p123-p13*p124+p12*p134
p4*p123-p3*p124+p2*p134
p3*p12-p2*p13
p4*p13-p3*p14
p4*p12-p2*p14

Ideal degenerate Schubert

p14*p123-p13*p124
p4*p123-p3*p124
p3*p12-p2*p13
p4*p13-p3*p14
p4*p12-p2*p14

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

s2s3s1s2s3 vanishing of p4
left with p1,p2,p3,p12,p13,p23,p14,p24,p34,p123,p124,p134,p234

Ideal degenerate Schubert
-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



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

s1s3s2s1s3 vanishing of p34

Ideal degenerate Schubert
-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



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

s2s3s1s2s1 vanishing of p234

Ideal degenerate Schubert
-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

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

s1s2s1s3s2s1 (full flag variety)

Ideal Schubert
p34*p123-p23*p134+p13*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124+p12*p134
p34*p124-p24*p134+p14*p234
p4*p123-p3*p124+p2*p134-p1*p234
p14*p23-p13*p24+p12*p34
p3*p12-p2*p13+p1*p23
p4*p23-p3*p24+p2*p34
p4*p13-p3*p14+p1*p34
p4*p12-p2*p14+p1*p24


Ideal degenerate Schubert
p34*p123+p13*p234
p24*p123-p23*p124+p12*p234
p14*p123-p13*p124
p34*p124+p14*p234
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