#2e5p2.maple
#
#	This is an attempt to show Shapiro's
#	Conjecture for the case of 2-planes in C^7 satisfying
#	(13)^5 = 6.
#
#	We compute the discriminant, a degree 30 polynomial!
#interface(quiet=true):
with(Ore_algebra):
with(linalg):
with(Groebner):

SmMat := s -> matrix([
		[ 1 , s ,s^2, s^3 , s^4 ,  s^5 ,   s^6],
		[ 0 , 1 ,2*s,3*s^2,4*s^3, 5*s^4, 6*s^5],
		[ 0 , 0 , 1 , 3*s ,6*s^2,10*s^3,15*s^4],
		[ 0 , 0 , 0 ,  1  , 4*s ,10*s^2,20*s^3],
		[ 1 ,x12,x13, x14 ,  0  ,  0   ,   0  ],
		[ 0 , 0 , 0 ,  1  , x25 , x26  ,  x27 ]]):


AA:=op(2,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,2,3,4,5,6])))):
BB:=op(2,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,2,3,4,5,7])))):
CC:=op(2,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,2,3,4,6,7])))):
DD:=op(3,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,2,3,5,6,7])))):
EE:=op(3,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,2,4,5,6,7])))):
FF:=op(3,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[1,3,4,5,6,7])))):
GG:=op(3,factor(det(submatrix(SmMat(s),[1,2,3,4,5,6],[2,3,4,5,6,7])))):
G:=gbasis([AA,BB,CC,DD,EE,FF,GG],
	wdeg([1,2,3,1,2,3],[x12,x13,x14,x25,x26,x27])):

#for i from 1 to nops(G) do indets(G[i]);  od;

equations:=[]:
for P in G do
 equations:=[equations[],P,subs(s=t,P),subs(s=u,P)]:
od:
kernelopts(gcfreq=10000000):
GB:=gbasis(equations,wdeg([1,2,3,1,2,3],[x12,x13,x14,x25,x26,x27])):

#  First 3 equations are linear in some variables:
#sort(GB[1],[x12]);
#sort(GB[2],[x13]);
#sort(GB[3],[x27]);

X27:=solve(GB[3]=0,x27):

GB2:=[]:
for i from 4 to nops(GB) do
GB2:=[GB2[],simplify(subs(x27=X27,GB[i]))]: od:

#for i from 1 to 9 do indets(GB2[i]); od:

with(Groebner):

G:=gbasis(GB2,wdeg([1,2,3],[x25,x26,x14])):

GG:=gbasis(G,wdeg([1,2,7],[x25,x26,x14])):
for i from 1 to 5 do indets(GG[i]); od:

G:=gbasis([GG[1],GG[2],GG[3],GG[4]],wdeg([1,7],[x25,x26])):

Elim:=G[1]:
lprint(Elim):
Disc:=primpart(discrim(Elim,x25)):

lprint(Disc);
time();
quit;