Numeric errors???

[Christophe TROESTLER]

Hi,

I am a beginner using Octave.  The two sets of functions below (H1,
H2, H3 and H11, H22, H33) should give the same result.  However, the
final results are dramatically different.  Anyone can help me with
this?  (Probably a stupid misunderstanding of mine.)

Thanks,
ChriS

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#!/usr/bin/octave -qf

global Id = eye(3,3)
global Y = zeros(3,3)
global X = [3, 0, 0;     0, 2, -1;     0, -2, 1]
global Z = [1, 1, 1;     1, 1, 1;     1, 1, 1]  # rank 1


function y = H1(a)
  global Id; global X; global Y; global Z;
  y = det( (a*Id - Y) + X * (a * Id - Z));
endfunction

function y = H2(a,b)
  global Id; global X; global Y; global Z;
  y = (a-b) * det( (a*Id-Y) * (b*Id-Y) + X * (a*Id-Z) * (b*Id-Z) );
endfunction

function y = H3(a,b,c)
  y = H1(a) * H2(b,c) - H1(b) * H2(a,c) + H1(c) * H2(a,b);
endfunction

#rank(X * Z - Y * X) # = 1
H3(2,30,400) # = 120

function y = H11(a)
  y = -12 * a^2 + 16 * a^3;
endfunction
function y = H22(a,b)
  y = (a-b) * (36 * a^2 * b^2 - 12 * a^3 * b^2 - 12*a^2*b^3 + 16*a^3*b^3);
endfunction
function y = H33(a,b,c)
  y = H11(a) * H22(b,c) - H11(b) * H22(a,c) + H11(c) * H22(a,b);
endfunction

H33(2,30,400) # = 0

printf("H2(30,400) - H22(30,400) = %.20fŠÜn", H2(30,400) - H22(30,400));
printf("H1(2)H2(30,400) - H11(2)H22(30,400)= %fŠÜn", 
       H1(2) * H2(30,400) - H11(2) * H22(30,400) );

printf("H1(400) -  H11(400) = %.20fŠÜn",   H1(400) - H11(400));
printf("H1(400)H2(2,30) - H11(400)H22(2,30)= %fŠÜn", 
       H1(400) * H2(2,30) - H11(400) * H22(2,30) );



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