I found the following bug in the code of the procedure "int/defDirac":
... if type(f,`*`) then for z in f do if type(z,function) and op(0,z) = Dirac then argument := op(1,z); if nops(z) = 1 and type(argument,linear(x)) then argument := expand(argument); c0 := -coeff(argument,x,0)/coeff(argument,x,1); s1 := signum(c0-a); s2 := signum(b-c0); F := subs(z = 1,f); if b = infinity and a = -infinity or member(s1,{0,1}) and b = infinity or member(s2,{0,1}) and a = -infinity or member(s2,{0,1}) and member(s1,{0,1}) then ans := traperror(eval(subs(x = c0,F))); if lasterror = ans then ans := traperror(limit(F,x = c0)); if lasterror = ans then RETURN('FAIL') else RETURN(ans/abs(coeff(argument,x,1))) fi else RETURN(ans/abs(coeff(argument,x,1))) fi elif s1 = -1 and b = infinity or s2 = -1 and a = -infinity or s2 = -1 or s1 = -1 then RETURN(0) else RETURN('FAIL') fi elif nops(z) = 2 and type(argument,integer) and 1 <= argument and type(op(2,z),linear(x)) then argument := expand(op(2,z)); c0 := -coeff(argument,x,0)/coeff(argument,x,1); s1 := signum(c0-a); s2 := signum(b-c0); # # old code: # F := (-1)^op(1,z)*diff(subs(z = 1,f),x $ op(1,z)); # # new code: # F := (-1/coeff(argument,x,1))^op(1,z)* diff(subs(z = 1,f),x $ op(1,z)); # if b = infinity and a = -infinity or member(s1,{0,1}) and b = infinity or member(s2,{0,1}) and a = -infinity or member(s2,{0,1}) and member(s1,{0,1}) then ans := traperror(eval(subs(x = c0,F))); if lasterror = ans then ans := traperror(limit(F,x = c0)); if lasterror = ans then RETURN('FAIL') else RETURN(ans/abs(coeff(argument,x,1))) fi else RETURN(ans/abs(coeff(argument,x,1))) fi elif s1 = -1 and b = infinity or s2 = -1 and a = -infinity or s2 = -1 or s1 = -1 then RETURN(0) else RETURN('FAIL') fi else RETURN('FAIL') fi fi od ...
This bug causes a lot of strange results when integrating over Dirac functions.
The code hasn’t changed up to Maple 7. For you sent no example of the bug, I can’t decide if the bug is still present. (U. Klein)