# Maple code
# Output: improved lifting square system of equations for the Schubert problem
#
# 48573 78453^2 68574^2 78465^3 47385 = 128 in Fl(2,4,5;8)
#
# Nickolas Hein
# 26 March 2015
#
# This is a proof of concept for computing a non-Grassmannian Schubert problem using a primal-dual formulation in bertini.
# Therefore, precomputations involving linear algebra are omitted.
# This is used as an example in "A lifted square formulation for certifiable Schubert calculus", and it references remarks therein.
#
with(LinearAlgebra):
k:=[2,4,5]:
n:=8:
# Given an instance
#
# (48573)F1 n (78453)F2 n ... n (47385)F9
#
# of the Schubert problem, we choose a basis of the ambient space so that F9 is the coordinate flag.
# Our Stiefel coordinates for (47385)F9 are given by the 5x8 matrix C with columns c[i]:
c[1]:=Matrix(n,1,[[ x1 ],[ x2 ],[ x3 ],[ 1 ],[ 0 ],[ 0 ],[ 0 ],[ 0 ]]):
c[2]:=Matrix(n,1,[[ x4 ],[ x5 ],[ x6 ],[ 0 ],[ x7 ],[ x8 ],[ 1 ],[ 0 ]]):
c[3]:=Matrix(n,1,[[ x9 ],[ x10 ],[ 1 ],[ 0 ],[ 0 ],[ 0 ],[ 0 ],[ 0 ]]):
c[4]:=Matrix(n,1,[[ x11 ],[ x12 ],[ 0 ],[ 0 ],[ x13 ],[ x14 ],[ 0 ],[ 1 ]]):
c[5]:=Matrix(n,1,[[ x15 ],[ x16 ],[ 0 ],[ 0 ],[ 1 ],[ 0 ],[ 0 ],[ 0 ]]):
#
# To restrict to the intersection
#
# X1 := (48573)F1 n (47385)F9
#
# We choose row vectors f_1,...,f_n such that colsp(F1_i) is
# the nullspace of f_{i+1},...,f_n.
#
for i from 1 to 8 do

 f[i]:=RandomMatrix(1,n):
od:
# We now add variables and functions to a file.
# This is part of a bertini input file.
fprintf(file,"variable_group x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;\n"):
fprintf(file,"variable_group y1,y2,y3,y4,y5;\n"): # ...for the condition on F1
fprintf(file,"variable_group z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12;\n\n"):
# ...for the condition on F2 and F3

# bilinear equations described in the paper for the condition on F1
fprintf(file,"function B1,B2,B3,B4,B5,B6,B7,B8,B9,B10;\n"):

# bilinear equations for F2 amd F3
fprintf(file,"function BB1,BB2,BB3,BB4,BB5,BB6,BB7,BB8,BB9,BB10,BB11,BB12,BB13,BB14,BB15,BB16,BB17,BB18;\n"):

# determinants
fprintf(file,"function D1,D2,D3,D4,D5;\n\n"):

# As described in the paper, the lifting coordinates \beta_{k,i} with (k,1)=(1,2),(3,4),(3,2),(5,4), and (5,2) will be denoted by y1,...,y5 respectively.

# The following line prints the ij-th equation from the algorithm given in the paper.
for i from 1 to 4 do

 fprintf(file,"B%a = %a;\n",i,simplify(Multiply(f[i+4],c[1]+y1*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"B%a = %a;\n",i+4,simplify(Multiply(f[i+5],c[3]+y2*c[4]+y3*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"B%a = %a;\n",i+7,simplify(Multiply(f[i+5],c[5]+y4*c[4]+y5*c[2])[1,1])):
od:

# To restrict to the intersection
#
# X2:=X1 n (78453)F2 n (78453)F3.
#
# we choose row vectors f_1,...,f_n such that colsp(F2_i) is
# the nullspace of f_{i+1},...,f_n, and we repeat for F3.
#
for i from 1 to 8 do

 f[i]:=RandomMatrix(1,n):
od:

# We use the z-variables to represent \beta's in the paper.
# The following line prints the ij-th equation from the algorithm given in the paper.
# For F2
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i,simplify(Multiply(f[i+5],c[3]+z1*c[1]+z2*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i+3,simplify(Multiply(f[i+5],c[4]+z3*c[1]+z4*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i+6,simplify(Multiply(f[i+5],c[5]+z5*c[1]+z6*c[2])[1,1])):
od:
# For F3
for i from 1 to 8 do

 f[i]:=RandomMatrix(1,n):
od:
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i+9,simplify(Multiply(f[i+5],c[3]+z7*c[1]+z8*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i+12,simplify(Multiply(f[i+5],c[4]+z9*c[1]+z10*c[2])[1,1])):
od:
for i from 1 to 3 do

 fprintf(file,"BB%a = %a;\n",i+15,simplify(Multiply(f[i+5],c[5]+z11*c[1]+z12*c[2])[1,1])):
od:

# Now we generate the determinantal equations for []F4 and []F5.
# We randomly generate (6-dimensional subspaces of) flags for these Schubert varieties, and we use classical determinantal conditions.
# We place C_2 in a bigger matrix M. (M = [ C_2 | Fi_6 ].)
M:=Matrix(n,n):
for j from 1 to 2 do

 for i from 1 to n do

  M[i,j]:=c[j][i,1]:

 od:
od:
for ii from 1 to 2 do # for each [] condition

 for j from 3 to n do

  for i from 1 to n do

   M[i,j]:=evalf(rand()/10^11):

  od:

 od:

 fprintf(file,"D%a = %a;\n\n",ii,simplify(Determinant(M))):
od:
# Now we generate the determinantal equations for []F6...[]F8.
# We randomly generate (4-dimensional subspaces of) flags for these Schubert varieties, and we use classical determinantal conditions.
# We place C_4 in a bigger matrix M. (M = [ C_4 | Fi_4 ].)
M:=Matrix(n,n):
for j from 1 to 4 do

 for i from 1 to n do

  M[i,j]:=c[j][i,1]:

 od:
od:
for ii from 3 to 5 do # for each [] condition

 for j from 5 to n do

  for i from 1 to n do

   M[i,j]:=evalf(rand()/10^11):

  od:

 od:

 fprintf(file,"D%a = %a;\n\n",ii,simplify(Determinant(M))):
od:
fclose(file):

CONFIG

USEREGENERATION: 1;
TRACKTOLBEFOREEG: 1e-7;
TRACKTOLDURINGEG: 1e-7;
FINALTOL: 1e-11;
SLICETOLBEFOREEG: 1e-7;
SLICETOLDURINGEG: 1e-7;
SLICEFINALTOL: 1e-11;
SECURITYMAXNORM: 1e8;
MAXNORM: 1e8;
PRINTPATHMODULUS: 1000;
SAMPLEFACTOR: 0.1;
NUMSAMPLEPOINTS: 3;
ODEPREDICTOR: 2;
RANDOMSEED: 1000;

END;
INPUT

variable_group x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
variable_group y1,y2,y3,y4,y5;
variable_group z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12;

function B1,B2,B3,B4,B5,B6,B7,B8,B9,B10;
function BB1,BB2,BB3,BB4,BB5,BB6,BB7,BB8,BB9,BB10,BB11,BB12,BB13,BB14,BB15,BB16,BB17,BB18;
function D1,D2,D3,D4,D5;

B1 = 1e-2*(-41*x1-41*y1*x4+24*x2+24*y1*x5+65*x3+65*y1*x6+1-42*y1*x7-82*y1*x8+59*y1);
B2 = 1e-2*(53*x1+53*y1*x4+61*x2+61*y1*x5-70*x3-70*y1*x6+22-81*y1*x7-99*y1*x8-2*y1);
B3 = 1e-2*(-54*x1-54*y1*x4-88*x2-88*y1*x5-90*x3-90*y1*x6-66-11*y1*x7+35*y1*x8+61*y1);
B4 = 1e-2*(72*x1+72*y1*x4+22*x2+22*y1*x5-34*x3-34*y1*x6+69+55*y1*x7-12*y1*x8+98*y1);
B5 = 1e-2*(53*x9+53*y2*x11+53*y3*x4+61*x10+61*y2*x12+61*y3*x5-70-70*y3*x6-81*y2*x13-81*y3*x7-99*y2*x14-99*y3*x8-2*y3-98*y2);
B6 = 1e-2*(-54*x9-54*y2*x11-54*y3*x4-88*x10-88*y2*x12-88*y3*x5-90-90*y3*x6-11*y2*x13-11*y3*x7+35*y2*x14+35*y3*x8+61*y3+96*y2);
B7 = 1e-2*(72*x9+72*y2*x11+72*y3*x4+22*x10+22*y2*x12+22*y3*x5-34-34*y3*x6+55*y2*x13+55*y3*x7-12*y2*x14-12*y3*x8+98*y3+56*y2);
B8 = 1e-2*(53*x15+53*y4*x11+53*y5*x4+61*x16+61*y4*x12+61*y5*x5-70*y5*x6-81-81*y4*x13-81*y5*x7-99*y4*x14-99*y5*x8-2*y5-98*y4);
B9 = 1e-2*(-54*x15-54*y4*x11-54*y5*x4-88*x16-88*y4*x12-88*y5*x5-90*y5*x6-11-11*y4*x13-11*y5*x7+35*y4*x14+35*y5*x8+61*y5+96*y4);
B10 = 1e-2*(72*x15+72*y4*x11+72*y5*x4+22*x16+22*y4*x12+22*y5*x5-34*y5*x6+55+55*y4*x13+55*y5*x7-12*y4*x14-12*y5*x8+98*y5+56*y4);
BB1 = 1e-2*(11*x9+11*z1*x1+11*z2*x4+24*x10+24*z1*x2+24*z2*x5-96-96*z1*x3-96*z2*x6-90*z1+70*z2*x7+72*z2*x8-78*z2);
BB2 = 1e-2*(3*x9+3*z1*x1+3*z2*x4-17*x10-17*z1*x2-17*z2*x5-44-44*z1*x3-44*z2*x6-19*z1-47*z2*x7+66*z2*x8+67*z2);
BB3 = 1e-2*(51*x9+51*z1*x1+51*z2*x4+15*x10+15*z1*x2+15*z2*x5+44+44*z1*x3+44*z2*x6+12*z1+69*z2*x7-59*z2*x8-29*z2);
BB4 = 1e-2*(11*x11+11*z3*x1+11*z4*x4+24*x12+24*z3*x2+24*z4*x5-96*z3*x3-96*z4*x6-90*z3+70*x13+70*z4*x7+72*x14+72*z4*x8-78*z4-13);
BB5 = 1e-2*(3*x11+3*z3*x1+3*z4*x4-17*x12-17*z3*x2-17*z4*x5-44*z3*x3-44*z4*x6-19*z3-47*x13-47*z4*x7+66*x14+66*z4*x8+67*z4+85);
BB6 = 1e-2*(51*x11+51*z3*x1+51*z4*x4+15*x12+15*z3*x2+15*z4*x5+44*z3*x3+44*z4*x6+12*z3+69*x13+69*z4*x7-59*x14-59*z4*x8-29*z4+68);
BB7 = 1e-2*(11*x15+11*z5*x1+11*z6*x4+24*x16+24*z5*x2+24*z6*x5-96*z5*x3-96*z6*x6-90*z5+70+70*z6*x7+72*z6*x8-78*z6);
BB8 = 1e-2*(3*x15+3*z5*x1+3*z6*x4-17*x16-17*z5*x2-17*z6*x5-44*z5*x3-44*z6*x6-19*z5-47-47*z6*x7+66*z6*x8+67*z6);
BB9 = 1e-2*(51*x15+51*z5*x1+51*z6*x4+15*x16+15*z5*x2+15*z6*x5+44*z5*x3+44*z6*x6+12*z5+69+69*z6*x7-59*z6*x8-29*z6);
BB10 = 1e-2*(-92*x9-92*z7*x1-92*z8*x4-98*x10-98*z7*x2-98*z8*x5+45+45*z7*x3+45*z8*x6-77*z8*x7+9*z8*x8-59*z8);
BB11 = 1e-2*(98*x9+98*z7*x1+98*z8*x4-46*x10-46*z7*x2-46*z8*x5+1+z7*x3+z8*x6+3*z7-3*z8*x7-46*z8*x8+79*z8);
BB12 = 1e-2*(-10*x9-10*z7*x1-10*z8*x4-7*x10-7*z7*x2-7*z8*x5+12+12*z7*x3+12*z8*x6-92*z7+87*z8*x7-29*z8*x8+10*z8);
BB13 = 1e-2*(-92*x11-92*z9*x1-92*z10*x4-98*x12-98*z9*x2-98*z10*x5+45*z9*x3+45*z10*x6-45-77*x13-77*z10*x7+9*x14+9*z10*x8-59*z10);
BB14 = 1e-2*(98*x11+98*z9*x1+98*z10*x4-46*x12-46*z9*x2-46*z10*x5+z9*x3+z10*x6+3*z9-3*x13-3*z10*x7-46*x14-46*z10*x8+79*z10+76);
BB15 = 1e-2*(-10*x11-10*z9*x1-10*z10*x4-7*x12-7*z9*x2-7*z10*x5+12*z9*x3+12*z10*x6-92*z9+87*x13+87*z10*x7-29*x14-29*z10*x8+10*z10-53);
BB16 = 1e-2*(-92*x15-92*z11*x1-92*z12*x4-98*x16-98*z11*x2-98*z12*x5+45*z11*x3+45*z12*x6-77-77*z12*x7+9*z12*x8-59*z12);
BB17 = 1e-2*(98*x15+98*z11*x1+98*z12*x4-46*x16-46*z11*x2-46*z12*x5+z11*x3+z12*x6+3*z11-3-3*z12*x7-46*z12*x8+79*z12);
BB18 = 1e-2*(-10*x15-10*z11*x1-10*z12*x4-7*x16-7*z11*x2-7*z12*x5+12*z11*x3+12*z12*x6-92*z11+87+87*z12*x7-29*z12*x8+10*z12);
D1 = 1e-5*(-30179.00176*x1*x5+33870.02348*x1*x6+4254.152030*x1*x7-8413.571272*x1*x8+17321.83103*x1+30179.00176*x2*x4-69768.18322*x2*x6-83393.49048*x2*x7-25848.41057*x2*x8-51699.06456*x2-33870.02348*x3*x4+69768.18322*x3*x5+83758.07174*x3*x7+48460.37815*x3*x8+17977.26220*x3+22633.87950*x4-101501.9179*x5+61590.76040*x6-48235.97623*x7-47683.59887*x8+19485.35860);

D2 = 1e-5*(22528.87741*x1*x5-20919.84203*x1*x6+73251.33856*x1*x7+10388.44738*x1*x8-9073.031330*x1-22528.87741*x2*x4+24206.04740*x2*x6-92280.30705*x2*x7+2147.634954*x2*x8+7170.824820*x2+20919.84203*x3*x4-24206.04740*x3*x5+6984.993890*x3*x7-13156.06762*x3*x8+3089.799068*x3-11235.32049*x4+7577.227890*x5+5035.683252*x6-21383.96540*x7+4565.029934*x8+524.5751080);

D3 = 1e-3*(298.2653354*x1*x6*x10*x14+98.22778689*x1*x6*x10*x13+298.2653354*x3*x8*x10*x11-298.2653354*x3*x8*x9*x12+98.22778689*x3*x7*x10*x11-98.22778689*x3*x7*x9*x12+298.2653354*x3*x5*x9*x14-298.2653354*x3*x4*x10*x14-98.22778689*x3*x4*x10*x13-144.8135281*x3*x8*x9*x13+144.8135281*x3*x7*x9*x14-1640.649452*x3*x8*x10*x13+1640.649452*x3*x7*x10*x14+98.22778689*x3*x5*x9*x13+28.15216670*x2*x8*x9*x13-28.15216670*x2*x7*x9*x14-298.2653354*x2*x6*x9*x14-98.22778689*x2*x6*x9*x13+28.15216670*x1*x7*x10*x14-98.22778689*x1*x5*x13+508.1956018*x1+1097.282116*x2+497.0253498*x4-551.8802590*x5-1136.503460*x7+5664.227250*x8+274.6277710*x9-1296.068173*x10+317.5371444*x11+928.8531570*x12-474.7317269*x13+2492.783636*x14+342.1166295*x3*x9*x14-319.6734073*x1*x6*x10+9.695145240*x5*x9*x13+2569.089823*x5*x14-510.0435407*x5*x13+3066.145822*x10*x14+319.6734073*x1*x5-135.3246289*x1*x7-882.1911023*x1*x8-319.6734073*x2*x4+881.2285440*x2*x7-2663.524051*x2*x8+551.8802590*x6*x10-63.40345930*x1*x7*x10-28.15216670*x1*x8*x10*x13-497.3267209*x10*x13+510.0435407*x6*x10*x13-2569.089823*x6*x10*x14+308.1120564*x7*x10*x14-308.1120564*x8*x10*x13-416.1975435*x7*x10+510.0435407*x7*x12+55.76742540*x7*x14+1763.002250*x8*x10-2569.089823*x8*x12-55.76742540*x8*x13+355.6607306*x9*x14-38.12872738*x9*x13-48.35835910*x4*x13+216.6248689*x4*x14-17.85742520*x7*x9+48.35835910*x7*x11+369.3463770*x8*x9-216.6248689*x8*x11-497.0253498*x6*x9+48.35835910*x6*x9*x13-216.6248689*x6*x9*x14+28.15273454*x7*x9*x14-28.15273454*x8*x9*x13+190.6865195*x4*x10-9.695145240*x4*x10*x13-100.0973066*x4*x10*x14-190.6865195*x5*x9-258.0483060*x9*x12+258.0483060*x10*x11+100.0973066*x5*x9*x14-9.695145240*x7*x9*x12+9.695145240*x7*x10*x11-100.0973066*x8*x9*x12+100.0973066*x8*x10*x11-298.2653354*x1*x5*x14+246.5391478*x6*x9*x12-246.5391478*x6*x10*x11-246.5391478*x4*x12+246.5391478*x5*x11-2583.387072+371.6052832*x1*x10-47.84852480*x1*x12-135.9007177*x1*x13-342.1166295*x1*x14-371.6052832*x2*x9+47.84852480*x2*x11-469.0696070*x2*x13-625.1240100*x2*x14-508.1956018*x3*x9-1097.282116*x3*x10+98.22778689*x1*x7*x12-144.8135281*x1*x7*x14-100.9037790*x1*x8*x10+298.2653354*x1*x8*x12+144.8135281*x1*x8*x13-104.6949853*x1*x10*x13-331.6161909*x1*x10*x14+98.22778689*x2*x4*x13+298.2653354*x2*x4*x14+319.6734073*x2*x6*x9+63.40345930*x2*x7*x9-98.22778689*x2*x7*x11-1640.649452*x2*x7*x14+100.9037790*x2*x8*x9-298.2653354*x2*x8*x11+1640.649452*x2*x8*x13+104.6949853*x2*x9*x13+331.6161909*x2*x9*x14+625.1240100*x3*x10*x14+469.0696070*x3*x10*x13-881.2285440*x3*x7*x10+2663.524051*x3*x8*x10+135.9007177*x3*x9*x13+135.3246289*x3*x7*x9+882.1911023*x3*x8*x9+319.6734073*x3*x4*x10-319.6734073*x3*x5*x9+47.84852480*x3*x9*x12-47.84852480*x3*x10*x11);

D4 = 1e-4*(339.1734230*x1*x6*x10*x14+1741.058260*x1*x6*x10*x13+339.1734230*x3*x8*x10*x11-339.1734230*x3*x8*x9*x12+1741.058260*x3*x7*x10*x11-1741.058260*x3*x7*x9*x12+339.1734230*x3*x5*x9*x14-339.1734230*x3*x4*x10*x14-1741.058260*x3*x4*x10*x13-566.9003122*x3*x8*x9*x13+566.9003122*x3*x7*x9*x14+1425.993377*x3*x8*x10*x13-1425.993377*x3*x7*x10*x14+1741.058260*x3*x5*x9*x13+1667.930669*x2*x8*x9*x13-1667.930669*x2*x7*x9*x14-339.1734230*x2*x6*x9*x14-1741.058260*x2*x6*x9*x13+1667.930669*x1*x7*x10*x14-1741.058260*x1*x5*x13+99.07337110*x1-1426.568467*x2-124.6795439*x4+2535.415446*x5-1720.662966*x7-1058.631291*x8-217.1665526*x9-1141.293608*x10-76.89499660*x11-750.5899722*x12+275.4720249*x13+361.0414708*x14-291.6840570*x3*x9*x14-286.2861049*x1*x6*x10+2223.774697*x5*x9*x13+471.5931004*x5*x14-2315.472086*x5*x13-307.4440228*x10*x14+286.2861049*x1*x5-358.0457201*x1*x7-162.9671336*x1*x8-286.2861049*x2*x4+3330.079159*x2*x7+883.2079174*x2*x8-2535.415446*x6*x10+3615.808212*x1*x7*x10-1667.930669*x1*x8*x10*x13+877.8708318*x10*x13+2315.472086*x6*x10*x13-471.5931004*x6*x10*x14+396.8614522*x7*x10*x14-396.8614522*x8*x10*x13+555.3847521*x7*x10+2315.472086*x7*x12-1286.843935*x7*x14+321.4433215*x8*x10-471.5931004*x8*x12+1286.843935*x8*x13-172.7992899*x9*x14-17.87863390*x9*x13-650.6540830*x4*x13-493.5573687*x4*x14+1808.585882*x7*x9+650.6540830*x7*x11+1113.721572*x8*x9+493.5573687*x8*x11+124.6795439*x6*x9+650.6540830*x6*x9*x13+493.5573687*x6*x9*x14+1347.401476*x7*x9*x14-1347.401476*x8*x9*x13+2705.214087*x4*x10-2223.774697*x4*x10*x13+645.9984080*x4*x10*x14-2705.214087*x5*x9+293.7626691*x9*x12-293.7626691*x10*x11-645.9984080*x5*x9*x14-2223.774697*x7*x9*x12+2223.774697*x7*x10*x11+645.9984080*x8*x9*x12-645.9984080*x8*x10*x11-339.1734230*x1*x5*x14-1126.525330*x6*x9*x12+1126.525330*x6*x10*x11+1126.525330*x4*x12-1126.525330*x5*x11-1650.975829*x1*x10-718.5997844*x1*x12+296.2039174*x1*x13+291.6840570*x1*x14+1650.975829*x2*x9+718.5997844*x2*x11+316.9718956*x2*x13-526.8118304*x2*x14-99.07337110*x3*x9+1426.568467*x3*x10+1741.058260*x1*x7*x12-566.9003122*x1*x7*x14+978.6527337*x1*x8*x10+339.1734230*x1*x8*x12+566.9003122*x1*x8*x13+964.5110228*x1*x10*x13-500.5220873*x1*x10*x14+1741.058260*x2*x4*x13+339.1734230*x2*x4*x14+286.2861049*x2*x6*x9-3615.808212*x2*x7*x9-1741.058260*x2*x7*x11+1425.993377*x2*x7*x14-978.6527337*x2*x8*x9-339.1734230*x2*x8*x11-1425.993377*x2*x8*x13-964.5110228*x2*x9*x13+500.5220873*x2*x9*x14+526.8118304*x3*x10*x14-316.9718956*x3*x10*x13-3330.079159*x3*x7*x10-883.2079174*x3*x8*x10-296.2039174*x3*x9*x13+358.0457201*x3*x7*x9+162.9671336*x3*x8*x9+286.2861049*x3*x4*x10-286.2861049*x3*x5*x9+718.5997844*x3*x9*x12-718.5997844*x3*x10*x11+256.1362527);

D5 = 1e-3*(197.6100570*x8*x10+39.35299557*x8*x12+489.2848620*x5*x9*x13-104.8065467*x5*x9*x14+6.331791900*x7*x9*x14-6.331791900*x8*x9*x13-754.9187565*x7*x9-571.3037701*x7*x11-571.3037701*x6*x9*x13+127.7685753*x6*x9*x14+286.0265836*x6*x9+571.3037701*x4*x13-127.7685753*x4*x14-58.23568570*x7*x14-331.6569173*x3*x8*x9*x13+331.6569173*x3*x7*x9*x14+151.6330108*x3*x5*x9*x14+403.8059119*x3*x5*x9*x13+279.5673724*x1*x7*x10*x14+151.6330108*x1*x6*x10*x14+403.8059119*x1*x6*x10*x13+172.0029869*x8*x9+127.7685753*x8*x11+279.5673724*x2*x8*x9*x13-279.5673724*x2*x7*x9*x14-151.6330108*x2*x6*x9*x14-403.8059119*x2*x6*x9*x13-151.6330108*x3*x4*x10*x14-403.8059119*x3*x4*x10*x13-33.03817710*x3*x8*x10*x13+33.03817710*x3*x7*x10*x14+151.6330108*x3*x8*x10*x11-151.6330108*x3*x8*x9*x12+403.8059119*x3*x7*x10*x11-403.8059119*x3*x7*x9*x12-545.0688225*x7*x10-480.0405624*x3*x7*x10+194.3299844*x3*x9*x12-194.3299844*x3*x10*x11-245.8508900*x3*x9*x13-251.9279470*x3*x9*x14-41.35852830*x3*x10*x14-67.79862700*x3*x10*x13-242.6483771*x3*x4*x10+242.6483771*x3*x5*x9+403.8059119*x2*x4*x13+151.6330108*x2*x4*x14-242.6483771*x2*x6*x9+13.99361510*x7*x12-416.7626529*x5*x11-489.2848620*x7*x9*x12+489.2848620*x7*x10*x11-39.35299557*x5*x14-416.7626529*x6*x9*x12+416.7626529*x4*x12-194.3299844*x1*x12+245.8508900*x1*x13+251.9279470*x1*x14-403.8059119*x1*x5*x13-441.1771806*x3*x9+190.2771760*x3*x10-82.57195330*x2*x9+194.3299844*x2*x11+67.79862700*x2*x13+41.35852830*x2*x14-487.0345986*x6*x10-13.99361510*x5*x13-779.0525492*x9*x12+441.1771806*x1-190.2771760*x2+104.8065467*x8*x9*x12-104.8065467*x8*x10*x11+779.0525492*x10*x11-286.0265836*x4+487.0345986*x5+658.0295872*x7-176.3203089*x8-151.6330108*x1*x5*x14+242.6483771*x1*x6*x10+416.7626529*x6*x10*x11+1544.004183*x9-789.6760912*x10+528.6770600*x11+63.23967900*x12+104.4411480*x13+30.53292320*x14+13.99361510*x6*x10*x13+39.35299557*x6*x10*x14+49.72002000*x7*x10*x14+58.23568570*x8*x13-49.72002000*x8*x10*x13-1688.609415*x9*x13+371.7877560*x9*x14-661.2210737-242.6483771*x1*x5-609.7599107*x1*x7-29.67692632*x1*x8+242.6483771*x2*x4+480.0405624*x2*x7+200.1126120*x2*x8-1055.807755*x2*x7*x9-403.8059119*x2*x7*x11-33.03817710*x2*x7*x14-228.4729783*x2*x8*x9-151.6330108*x2*x8*x11+33.03817710*x2*x8*x13-982.9785410*x2*x9*x13-234.5772308*x2*x9*x14+89.46575030*x10*x14-48.08601700*x10*x13+795.6720137*x4*x10+1055.807755*x1*x7*x10+403.8059119*x1*x7*x12-331.6569173*x1*x7*x14+228.4729783*x1*x8*x10+151.6330108*x1*x8*x12+331.6569173*x1*x8*x13+982.9785410*x1*x10*x13+234.5772308*x1*x10*x14-200.1126120*x3*x8*x10+609.7599107*x3*x7*x9+29.67692632*x3*x8*x9-279.5673724*x1*x8*x10*x13+82.57195330*x1*x10-489.2848620*x4*x10*x13+104.8065467*x4*x10*x14-795.6720137*x5*x9);

END;

[linux]:~$ time

real 318m32.524s
user 1095m53.433s
sys 3m54.091s

3.6 GHz processors used. Total processing power:

2.749480917 GHz-days