## 729 Reputation

8 years, 183 days

## evala(e) still does not equal e...

I'm perplexed by the fact that this bug is not fixed in Maple 2018:

```seq(alias(a[i] = RootOf(_Z1^6-3*_Z1^2-2*_Z1+11, index = i)), i = 1 .. 6);
ee := a[1]*a[5]+a[2]*a[6]+a[3]*a[4];
evala(ee); # wrong
-320/449*a[1]-(16/449*(a[2]^2))*a[1]^4*a[3]-(16/449*(a[2]^3))*a[3]*a[1]^2-
(56/449*(a[2]^2))*a[1]^3*a[3]-(16/449*(a[2]^2))*a[1]^5*a[3]+(32/449*a[2])*
a[3]*a[1]^5-(60/449*(a[2]^2))*a[1]^2*a[3]-(256/449*a[2])*a[1]*a[3]+(64/449*
a[2])*a[3]*a[1]^2+(128/449*(a[2]^2))*a[3]*a[1]-(32/449*(a[2]^3))*a[3]*a[1]^3-
(16/449*(a[2]^3))*a[3]*a[1]^4-(24/449*a[2])*a[3]*a[1]^4+(256/449*a[1])*a[2]+
(88/449*(a[1]^4))*a[2]-220/449*a[3]-680/449*a[2]-128/449*(a[1]^4)-(48/449*
(a[2]^2))*a[1]^4-(32/449*(a[1]^5))*a[2]-(48/449*(a[2]^2))*a[1]^3+(128/449*
a[2])*a[1]^3-(48/449*(a[2]^3))*a[1]^3+(256/449*(a[2]^3))*a[1]-(32/449*
(a[2]^3))*a[1]^5-(88/449*(a[2]^3))*a[1]^2-(232/449*a[3])*a[2]+(66/449*
(a[2]^2))*a[3]+(130/449*(a[1]^2))*a[3]+(24/449*(a[1]^5))*a[3]+(64/449*
(a[1]^4))*a[3]+(228/449*(a[2]^3))*a[3]+(164/449*a[3])*a[1]^3-(192/449*
a[3])*a[1]-(256/449*(a[2]^2))*a[1]-196/449*(a[1]^3)+40/449*(a[1]^5)+110/449*
(a[2]^2)-324/449*(a[2]^3)-18/449*(a[1]^2)+1780/449+(40/449*(a[2]^2))*a[1]^2+
(32/449*(a[2]^2))*a[1]^5```

(along with quite a few bugs that are less critical but seem trivial to fix, like INTERVAL(1..2, 3..4) being displayed as INTERVAL(1..2)).

Are the issues reported on MaplePrimes not being looked into by anyone?

EDIT: And now the original post (the first link above) is gone, for which I don't have any reasonable explanation. Here is the post: i.imgur.com/9kIhPz5.jpg. Here is what I'm seeing now: i.imgur.com/yC4cqE3.jpg.

## list[list, ...]...

Is the first output correct?

```m := [[1, 2], [3, 4]];

m[[1, 2], 2];
[3, 4]
Matrix(m)[[1, 2], 2];
Vector[column](2, [2, 4])

m[1 .. 2, 2];
[2, 4]
Matrix(m)[1 .. 2, 2];
Vector[column](2, [2, 4])```

The other three map the index 2 over the indices [1,2], giving the second column. The first one does m[[1,2]][2] instead.

I couldn't find a definite statement in the documentation about how this should work for lists (not rtables).

Also, ?selection says:

"To select trailing elements, use A[..n]."

"Use A[...,a[i]] to select the ith column."

I think it should have been

"To select trailing elements, use A[n..]."

"Use A[...,i] to select the ith column."

## series and csgn...

Maple

1. The general case (the first output) is fine, but the second output is wrong. Surprisingly, replacing series(ee, ...) with series(sqrt(1/x)*erf(sqrt(x)), ...) does something different:

```ee := sqrt(1/x)*erf(sqrt(x));

series(ee, x = 0, 2);
% assuming x < 0;
-2/sqrt(Pi)+2*x/(3*sqrt(Pi))+O(x^2)

series(ee, x = 0, 2) assuming x < 0; # wrong
2/sqrt(Pi)-2*x/(3*sqrt(Pi))+O(x^2)

series(sqrt(1/x)*erf(sqrt(x)), x = 0, 2) assuming x < 0;
Error, (in assuming) when calling '`series/signum`'. Received: 'no series at 0'```

2. Should Maple be able to handle nested discontinuities? The constant term here is incorrect, so the remainder is not O(z^2).

```series(ln(I*ln(-1+z)), z = 0, 2);
ln(Pi)-(1/2*I)*csgn(ln(-1+z))*(csgn(I*(-1+z))+1)*Pi-I*csgn(I*(-1+z))*z/Pi+O(z^2)```

3. This is wrong (it would mean that I^z is unbounded for large positive z):

```series(a^z, z = infinity, 2);
exp((1/2*I)*z*(1-signum(a))*Pi)*abs(a)^z```

## simplify/assuming...

1. Why doesn't simplify(subs(...)) as a single expression work?

```simplify(subs(z = -z, erf(z)));
subs(z = -z, erf(z));
simplify(%);
erf(-z)
erf(-z)
-erf(z)```

2. This just hangs. Would be nice if simplify could deal with this, but in any case I don't think it should take so long:

```timelimit(60, simplify(n <= p*n+sqrt(n)*p*(1-p))) assuming n > p*(n+(1-p)*sqrt(n));
Error, (in assuming) when calling '`property/ObjProperty`'. Received: 'time expired'```

3. It seems that assuming doesn't like f(constant) objects. Doesn't seem right, because x(a) would work fine:

```simplify(abs(x(0))) assuming x(0) > 0;
abs(x(0))

simplify(abs(y)) assuming x(0) > 0, y > 0;
Error, (in assuming) when calling 'assume'. Received: 'cannot assume on a constant object'```

4. Can simplify be made to work on things like this (since it can handle the coefficient at (t+1))?

```simplify((sqrt(1-I)*sqrt(1+I)-sqrt(2))*(t+1));
-(-sqrt(1-I)*sqrt(1+I)+sqrt(2))*(t+1)```

## center(conic(...)) is wrong...

```with(geometry):

eq := subs([x, y] =~ convert(Student:-LinearAlgebra:-RotationMatrix(Pi/3).<x, y>, list),
2*(x-1)^2+sqrt(2)*y^2-1);

conic(c, eq, [x, y]);
(evala@coordinates@center)(c);
[160/119-(72/119)*sqrt(2), -(8/119)*sqrt(3)-(44/119)*sqrt(2)*sqrt(3)]```

Which should have been [cos(-Pi/3), sin(-Pi/3)].

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