rtoy
commented
4 months ago Imported from SourceForge on 2024-07-05 19:34:29 Created by robert_dodier on 2006-07-13 05:59:37 Original: https://sourceforge.net/p/maxima/bugs/447/#ec2e
Logged In: YES user_id=501686
differ package is superseded by solve_rec, which returns valid results (to the best of my knowledge) for the bug examples shown in this report. Also, the solve_rec package is documented. I've moved differ.mac and differ.dem to archive/share/trash/. Closing this report as fixed.
Imported from SourceForge on 2024-07-05 19:34:28 Created by willisbl on 2003-11-18 16:25:24 Original: https://sourceforge.net/p/maxima/bugs/447
differ.mac solves finite difference equations; it has many bugs. And I can't find any user documentation for it either. Specifically
It redefines the functions system and eigenvalues
(C1) load("differ.mac"); Warning - you are redefining the MACSYMA function EIGENVALUES Warning - you are redefining the MACSYMA function SYSTEM (D1)
C:/maxima/Maxima/share/maxima/5.9.0/share/algebra/diff er.mac (C2) display2d : false; (D2) FALSE
It solves this one correctly (C3) difference(x[k+1] = x[k] / 5, x[k]); (D3) x[k] = x[0]/5^k
But make the equation nonhomogeneous and the solution is wrong
(C4) difference(x[k+1] = x[k] / 5 + 1, x[k]); (D4) x[k] = 0 <=== BOGUS
I don't think differ.mac can solve non-constant coefficient equations, but it doesn't check that the coefficients are constant
(C5) difference(x[k+1] = k * x[k], x[k]); (D5) x[k] = x[0]*k^k <=== BOGUS
It can't solve this degenerate equation
(C6) difference(x[k+2] + 2 * x[k+1] + x[k], x[k]); Non-square matrix in inverse #0: SYSTEM(eqnlist=[x[k+1] = -(x[k+2]+x[k])/2,x[k+1] = x[k+1]],varlist=[x[k+1],x[k]])(differ.mac line 91) #1: second_order_difference(eqn=x[k+1] = -(x[k+2]+x [k])/2,var=x[k])(differ.mac line 73) #2: difference(eqn=x[k+2]+2*x[k+1]+x[k],var=x[k]) (differ.mac line 113) -- an error. Quitting. To debug this try DEBUGMODE (TRUE);)
But the non-degenerate equation is okay
(C7) difference(x[k+2] + 8 * x[k+1] + x[k], x[k]); (D7) x[k] = (-SQRT(15)-4)^k*(SQRT(15)-4)*((SQRT(15) + ....
differ.mac doesn't check that the equation is linear and may give an incorrect solution when it is
(C12) difference(x[k+1] - x[k]^2 + x[k] = 0,x[k]); (D12) x[k] = x[0]*(-1)^k-((-1)^k-1)*x[k]^2/2 <== BOGUS
Bugs in differ.mac are far too easy to find. I haven't tried recur.mac; maybe it is somewhat better?
Barton