#input.maple interface(quiet=true): # Maple script to create Singular input file for verifying that # the system for the example in "Some remarks on real and complex # output feedback" is indeed nondegenerate. This example gives a # a real linear system (m=2, p=4) that cannot be controlled with # real output feedback. # with(linalg): F := x-> transpose(matrix([ [ x^4 -16*x^3 + 3*x^2 +11*x , 6*x^3 - 4*x^2 - 9*x - 5], [ -26*x^3 +10*x^2 + 7*x +16, x^4 +3*x^3 - x^2 -16*x -13], [ 9*x^3 -12*x^2 +13*x -17, 8*x^3 - 6*x^2 + 5*x +15], [ -31*x^3 -16*x^2 +43*x -23, 26*x^3 -14*x^2 -11*x +12], [ x^3 -36*x^2 + 8*x -13, 11*x^3 + 5*x^2 +11*x +33], [ 23*x^3 - x^2 + 2*x -21, -7*x^2 +11*x + 5]])): Poles := vector([-8,-6,-4,-2,1, 2, 3, 4]): Coords := matrix([ [X11,X12], [X21,X22], [X31,X32], [X41,X42]]): equations := {}: for ii from 1 to 8 do equations := equations union {det(stack(F(Poles[ii]), concat(Coords,band([1],4))))}: od: lprint(`ring R = 0,(X11,X12,X21,X22,X31,X32,X41,X42), (dp(7),dp(1));`); lprint(`ideal I =`); for ee in equations do lprint(ee,`,`);od; lprint(`0;`); lprint(`ideal G = std(I);`); lprint(`dim(G);`); lprint(`mult(G);`); lprint(`print(" ");`); lprint(`quit;`); quit