The work with not quadrat matrix.
How better solve?
See please the attached sm-file.
1-Asteroid-5-Points.sm (25,84 KiB) scaricato 1470 volta(e).

Wrote

The work with not quadrat matrix.
How better solve?

As it looks, the blue planet and green voyager are tangent.
Take care Valery ... Jean.

1-Asteroid-5-Points.sm (34,41 KiB) scaricato 1429 volta(e).

Hi Valery. You can use dn_LinAlgLLS_SVD or dn_LinAlgLLS_COF or dn_LinAlgLLS_QRorLQ for non-square matrices, instead dn_LinAlgSolve.

1-Asteroid-5-Points.sm (27,71 KiB) scaricato 1484 volta(e).

Best regards.
Alvaro.

Thanks Alvaro.
10-2-Asteroid-7-points.sm (21,89 KiB) scaricato 1446 volta(e).

A little more compact.



Best regards.
Alvaro.

Thanks Alvaro.
New problem with Ranks
10-2-Asteroid-7-points-Rank.sm (16,06 KiB) scaricato 1477 volta(e).

Wrote

... New problem with Ranks

Hi Valery. SMath really needs to improve on linear algebra. As a workaround, you can redefine rank with a plugin



Also, the problem with rank is not that it can't deal with complicated arrays, it can't handle simple ones either



10-2-Asteroid-7-points-Rank.sm (19,23 KiB) scaricato 1439 volta(e).

Best regards-
Alvaro.

Why?
10-2-Asteroid-7-points-Rank.sm (28,74 KiB) scaricato 1498 volta(e).

Wrote

Why?

Hi. Due to numerical errors. These ranks are evaluated with numerical procedures. That means that for some cases they must necessarily fail. You can introduce some kind of tolerance in the function. Maple also fails in this example.



This shows that the rank function that is executed is that of maple.



However, I don't know how to call Maxima's rank function, it is not in the Takeover options.

Here some notes about how to handle a little better the issue.

10-2-Asteroid-7-points-Rank.sm (35,26 KiB) scaricato 1482 volta(e).

Best regards.
Alvaro.

Maxima gives the correct answer. Yet I think that maple is not to blame, because maple(rank(M)) sends 4 to maple. At least this happens with Maxima(rank(M)).

In Maxima I have a workaround for such cases. First I convey the definition of M to Maxima and then call rank(M). The format "$...§" conveys everything inside the markup as verbatim expression to Maxima. without giving SMath the chance to interfere.

Should not be too complicated to add rank() to the takeover candidates.


10-2-Asteroid-7-points-Rank _Kr.sm (40,03 KiB) scaricato 1467 volta(e).

Hi Martin.

Wrote

Maxima gives the correct answer ...

Nope. The issue is about a matrix C=augment( A,b ), where b is a column vector so, it must to have the same rank as A.

Wrote

... Yet I think that maple is not to blame, because maple(rank(M)) sends 4 to maple. At least this happens with Maxima(rank(M)).

Either. In some way maple holds the rank function and evaluates it on its own kernel. Actually, the example with the matrix M is for show that.

Best regards.
Alvaro.