//   input.singular
//
//	Singular input file created by input.maple.  Computes an
//eliminant and verifies that there are only 14 feedback laws in this
//example, as claimed in "Some remarks on real and complex output feedback"
//
ring R = 0,(X11,X12,X21,X22,X31,X32,X41,X42), (dp(8));
ideal I =
27278-124844*X11+70630*X12+79255*X22-238625*X21-40549*X41+91844*X32-208288*X31+
48843*X42-236426*X31*X42+236426*X32*X41-309460*X21*X42+309460*X22*X41-198270*
X21*X32+198270*X22*X31-118549*X11*X42+118549*X12*X41+118968*X11*X32-118968*X12*
X31+255135*X11*X22-255135*X12*X21   ,
-807205*X11+421777*X12+368419*X22-1313375*X21-420285*X41+444489*X32-1082045*X31
+360009*X42-1211364*X31*X42+1211364*X32*X41-1900011*X21*X42+1900011*X22*X41-
1106207*X21*X32+1106207*X22*X31-677190*X11*X42+677190*X12*X41+583102*X11*X32-
583102*X12*X31+1532993*X11*X22-1532993*X12*X21+167360   ,
-48320893*X11+73751677*X12+127603795*X22-234080387*X21+23623575*X41+75941937*
X32-67112081*X31+45311049*X42-62207676*X31*X42+62207676*X32*X41-175250127*X21*
X42+175250127*X22*X41-118533971*X21*X32+118533971*X22*X31-50586978*X11*X42+
50586978*X12*X41+16469434*X11*X32-16469434*X12*X31+142788581*X11*X22-142788581*
X12*X21+77722544   ,
-9938705*X11+12828607*X12+20843299*X22-40008005*X21+1638365*X41+12873869*X32-
12169315*X31+8506989*X42-10735124*X31*X42+10735124*X32*X41-32261161*X21*X42+
32261161*X22*X41-22519197*X21*X32+22519197*X22*X31-9094060*X11*X42+9094060*X12*
X41+2426352*X11*X32-2426352*X12*X31+26368383*X11*X22-26368383*X12*X21+11608280
   ,
-1027893*X11+1136121*X12+1713027*X22-3471351*X21-123429*X41+1100985*X32-1082805
*X31+826473*X42-859860*X31*X42+859860*X32*X41-3010627*X21*X42+3010627*X22*X41-
2228375*X21*X32+2228375*X22*X31-803534*X11*X42+803534*X12*X41+111590*X11*X32-
111590*X12*X31+2473113*X11*X22-2473113*X12*X21+882720   ,
13688-19609*X11+19435*X12+26995*X22-58025*X21-9759*X41+16869*X32-12983*X31+
16893*X42-3996*X31*X42+3996*X32*X41-52365*X21*X42+52365*X22*X41-45905*X21*X32+
45905*X22*X31-10344*X11*X42+10344*X12*X41-5732*X11*X32+5732*X12*X31+43715*X11*
X22-43715*X12*X21   ,
-28*X11+106*X12+337*X22-611*X21+141*X41+540*X32-620*X31-27*X42-540*X31*X42+540*
X32*X41-282*X21*X42+282*X22*X41-1100*X21*X32+1100*X22*X31-129*X11*X42+129*X12*
X41+460*X11*X32-460*X12*X31+503*X11*X22-503*X12*X21+110   ,
-8673*X11+5367*X12+8835*X22-21837*X21+1605*X41+11517*X32-23691*X31+1389*X42-
26436*X31*X42+26436*X32*X41-22897*X21*X42+22897*X22*X41-21701*X21*X32+21701*X22
*X31-10628*X11*X42+10628*X12*X41+14024*X11*X32-14024*X12*X31+20871*X11*X22-
20871*X12*X21+1944   ,
0;
ideal G = std(I);
dim(G);
mult(G);
print(" ");
//poly J= G[1];
//type(J);
quit;