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## Maple should still try harder

Maple 2022

In an old post, vv reported a bug in simpl/max, which has been "fixed" in Maple 2018. However, it seem that such repairs are not complete enough.
For example, suppose it is required to find the (squared) distance between the origin and a point on x3 - x + y2 = ⅓ which is closest to the origin. In other words, one needs to minimize x²＋y² among the points on this curve, i.e.,

`extrema(x^2 + y^2, {x^3 + y^2 - x = 1/3}, {x, y}, 's'); # in exact form`

Unfortunately, an identical error message appears again:

 > restart;
 >
 (1)
 >
 >
 (2)
 >
 (3)
 >
 (4)

How about changing the values of parameter ?

```for a from -3 by 3/27 to 3 do
try
extrema(x^2 + y^2, {x^3 + y^2 - x = a}, {x, y});
catch:
print(a);
end;
od;
-1
--
3

-2
--
9

-1
--
9

1
-
9

2
-
9

1
-
3
```

By the way, like extrema, Student[MultivariateCalculus]:-LagrangeMultipliers also executes the Lagrange Multiplier method, but strangely,

`Student[MultivariateCalculus][LagrangeMultipliers](y^2 + x^2, [x^3 + y^2 - x - 1/3], [x, y], output = plot):`

does not cause any errors.

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