fbackelj

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14 years, 18 days

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These are questions asked by fbackelj

Hello all,

I have a question regarding printing to PDF. I am using Maple 2016.1 on Mac OS Sierra. When I choose print and use "Open PDF in Preview", I get to see something like this:

As you can see, the fonts are ugly and not anti-aliased at all (and it makes no difference whether I select that option explicitly in Maple preferences or not).
I've also tried Maple 2015, and it gives the same ugly result.

As a comparison, here is an example of a similar print of the same document that I've made in 2015:

Here, the font looks much better, properly aliased this time.
I also get this result when using Maple 18 on Sierra.

I am wondering: do other people also get this ugly result? In that case, it could indicate an issue with Maple 201X and Mac OS Sierra. Unfortunately, I no longer have Mac OS X El Capitan to compare...

P.s.: If someone wishes to try: just create some text input, choose Print, Open PDF in Preview, and then zoom in on the document.

Many thanks for your reply.

Regards,

Franky

 

How does one explain this? 

restart;

A := Matrix( 3, 3, [ 1, 1, 1, 1, 0, 0, 1, -1, 1 ] );
LinearAlgebra[ConditionNumber]( A );
linalg[cond]( A );

A := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 1, (1, 3) = 1, (2, 1) = 1, (2, 2) = 0, (2, 3) = 0, (3, 1) = 1, (3, 2) = -1, (3, 3) = 1})

 

6

 

6

 

B := evalf( A );
LinearAlgebra[ConditionNumber]( B );
linalg[cond]( B );

B := Matrix(3, 3, {(1, 1) = 1., (1, 2) = 1., (1, 3) = 1., (2, 1) = 1., (2, 2) = 0., (2, 3) = 0., (3, 1) = 1., (3, 2) = -1., (3, 3) = 1.})

 

3.000000000

 

6.000000000

 


Is this not a valid way for creating a floating-point matrix?
Otherwise, how do I explain the wrong result here?

-- Regards,

Franky

 

Hello,

While doing some tests, we encountered an issue with LinearAlgebra[ConditionNumber], possibly caused by another routine in the LinearAlgebra package (MatrixInverse?). I include an example worksheet bug-maple.mw for easy testing.

To reproduce, you should start by creating this matrix:

restart;
with( LinearAlgebra ):
Digits := 50:
n := 4;
M := [ seq( cos( Pi*j/n ), j=0..n ) ];
V := VandermondeMatrix( M );

Now compute the condition number (infinity-norm) of V:

c1 := ConditionNumber(V);
c1 := simplify(%);
evalf(c1); # this gives exactly 40

We can still compute this exactly and get 40.

This is the same result as with linalg[cond]:

c2 := linalg[cond](V);
c2 := simplify(%);
evalf(c2);

Now increase the value of n to 5 and redo the test.
The exact result should be 120, but LinearAlgebra[ConditionNumber] gives the wrong result!
On the other hand, linalg[cond] gives the correct, exact result (after simplification).

n := 5; # this gives a wrong result :-(

We could use Norm(V) * Norm(Inv(v)) since this should be equal to the condition number.
But then it seems there's something bad inside the MatrixInverse routine.
Again, linalg[inverse] gives the correct, exact result.
So compare the two results:

n := 4;
simplify(MatrixInverse(V));
linalg[inverse](V);

Finally, to make matters even worse, ConditionNumber gives completely wrong results when using a float-matrix, while linalg[cond] does not:

n := 3;
V := VandermondeMatrix( evalf(M) );
c1 := ConditionNumber( V );
c2 := linalg[cond]( V );

For n=3, we get c1=10.6 and c2=16.
For n=4, we get c2=5 and c2=40.
For n=5, we get c1=68.07 and c2=119.999.

Is this what it looks like? With it being a really, really ugly bug?

-- Many thanks for your reply,

Franky

Hello all,

Yesterday, I upgraded to Mac OS X El Capitan.

Now, when working with Maple 2015, I feel the gui is very slow and sometimes irresponsive, when trying to scroll through my worksheets as well as through help pages (e.g., "help plot3d"). When I do the same within Maple 18, it works without any problems.

Does anybody else have the same issue?

Cheers,

Franky

Hello,

Just a small question: what's the difference between writing

product( (2*i-1) mod 3 + 1, i=1..10 )

which incorrectly gives 105411381075, and writing

mul( (2*i-1) mod 3 + 1, i=1..10 )

which correctly gives 432...

And what's the reasoning behind this?

-- Regards,

Franky

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