#### 7.70 bug in inequal in Maple 6 (5.2.01)

In working towards linear programming with my students I found maple 6.01 doing weird
things:

with (plots);
inequal(x+y<2,x=-1..2, y=-1..2);

shows a triangle!!!!

inequal(x+y<2,x=-1..3, y=-1..2);

shows an angle with vertex at (-1,1) !!

inequal(x+y<2,x=-1..3, y=-1..3);

shows the region left and under the 2nd diagonal ???

It is corrected with Maple 7. (U. Klein)

In fact "inequal" always plots a strict inequality `(a*x + b*y < c or a*x + b*y > c)`

as if
`c = 0`

. This aﬀects Maple 6 and 6.01 but not Maple V.

This particular bug can be worked around by using "inequalities" from my Maple Advisor
Database, http://www.math.ubc.ca/~israel/advisor, but it is only a symptom of a more
serious problem.

Consider:

> x - 5 < 0;
x < 5

Maple 5.1 would leave this as-is.

It seems that Maple now automatically simpliﬁes a strict inequality with terms of type
"numeric" on both sides so that the numeric term is only on the right. This means you’ll run
into errors if (as occurs in the code of "inequal") you produce an inequality of the form
`expr < 0`

and then proceed on the assumption that all the terms of expr stay on
the left side. I would not be surprised if this causes bugs in other places besides
"inequal".

I have not seen any mention of this in the ?updates help pages.

It appears that inequal also has problems with `<=`

. In Maple 6.01

>constraints := {5*x[1]+5*x[2]=300,
> .6*x[1]+1.5*x[2]<=63,
> x[1]<=50, x[2]<=35,
> x[1]>=0,x[2]>=0};
>inequal(constraints,x[1]=-5..100,x[2]=-5..100,
> optionsexcluded=(color=white),
> optionsfeasible=(color=grey));

gave me the wrong region.

I tried adding optionsfeasible and optionsexcluded to see if they would help. There must be
a bug in 6.01 when strict inequalities are involved. In R5.1 the following works
ﬁne.

with (plots);
inequal(x+y<2,x=-1..2,y=-1..2,optionsfeasible=(color=yellow),
optionsexcluded=(color=white));

However, in 6.01 there is the error that you described. When the `<`

is changed to `<=`

in 6.01,
the command works as it should.