#4137 simplimplus bugs

[Barton Willis]

The function simplimplus is responsible for determining the limit of a sum of terms. It's easy to find bugs in this function.

Wrong--should be und not 0.

(%i1)   limit(3^x * cos(x) + sin(x),x,inf);
(%o1)   0

Wrong--should be und not inf.

(%i2)   limit(3^x * cos(x) + x,x,inf);
(%o2)   inf

Wrong--should be und not inf.

(%i4)   limit(3^x * cos(x) + 2^x,x,inf);
(%o4)   inf

Wrong---needs to ask about the relative magnitudes of a and b.

(%i7)   limit(a^x * cos(x) + b^x,x,inf);
"Is "abs(b)-1" positive, negative or zero?"p;
"Is "b-1" positive, negative or zero?"p;
"Is "abs(a)-1" positive, negative or zero?"p;
"Is "a-1" positive, negative or zero?"p;
(%o7)   inf

Wrong--shouldn't throw an error

(%i8)   limit(3^x + (9+%i)^x,x,inf);
sign: argument cannot be imaginary; found %i

[Dan Gildea]

Update on these cases.

ok now:

(%i1) limit(3^x * cos(x) + sin(x),x,inf);
(%o1) und

should be und:

(%i2) limit(3^x * cos(x) + x,x,inf);
(%o2)                                 inf

should be und:

(%i3) limit(3^x * cos(x) + 2^x,x,inf);
(%o3)                                 inf

should ask a vs b:

(%i4) limit(a^x * cos(x) + b^x,x,inf);
Is abs(b) - 1 positive, negative or zero?
p;
Is b - 1 positive, negative or zero?
p;
Is abs(a) - 1 positive, negative or zero?
p;
Is a - 1 positive, negative or zero?
p;
(%o4)                                 inf

should be infinity:

(%i5) limit(3^x + (9+%i)^x,x,inf);
(%o5)                                 inf

[Dan Gildea]

should be infinity:

(%i1) limit(2*%i*atan(x) + x, x, inf);
(%o1)                                 inf

[David Scherfgen]

Should now all be fixed by commit [fc6faa].