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Bug #1104

Eigenvectors: inconsistent return type

Added by John Abbott over 6 years ago. Updated about 2 years ago.

Status:
In Progress
Priority:
Normal
Assignee:
John Abbott
Category:
enhancing/improving
Target version:
CoCoA-5.4.2
Start date:
22 Sep 2017
Due date:
% Done:

10%

Estimated time:
Spent time:
0.75 h

Description

From the manual for eigenvectors:

------<  example  >------
/**/  Use R ::= QQ[x];
/**/  M := mat([[1,2,3],[4,5,6],[7,8,9]]);
/**/  eigenvectors(M, x);
[record[MinPoly := x, eigenspace := matrix(QQ,
 [[-1],
  [2],
  [-1]])],
record[MinPoly := x^2 -15*x -18,
eigenspace := [[1, (1/8)*x +1/4, (1/4)*x -1/2]]]
]

In one case the eigenspace is a matrix, in the other it is a list.
This is inconsistent!

Related issues

Related to CoCoALib - Feature #442: EigenvectorsNew2014-02-19

History

#1 Updated by John Abbott over 6 years ago

#2 Updated by John Abbott over 4 years ago

  • Target version changed from CoCoA-5.?.? to CoCoA-5.4.0

Even the example in the manual exhibits this... that's embarrassing. We should decide what to do, and then take action.

#3 Updated by John Abbott over 2 years ago

  • Status changed from New to In Progress
  • Assignee set to John Abbott

Get started!

#4 Updated by John Abbott over 2 years ago

  • % Done changed from 0 to 10

Which type of answer do we prefer? LIST or MAT?

If we prefer MAT, are the eigenvectors the rows or the columns? [currently columns, it seems]

Advantage of MAT is that there is a guarantee all vectors are the same length (and over same ring);
but even if the fn returns a LIST it should implicitly guarantee these properties.

#5 Updated by John Abbott over 2 years ago

Here is an observation about the given example:
  • in the case that the eigenvalue is rational (i.e. in the field), the eigenvector was a column matrix over the field
  • in the case that the eigenvalue is not rational (i.e. algebraic), the eigenvectors involves entries in the ring of x (supplied as argument)

So if we want to return eigenvectors as columns in a matrix, then we mist also consider the ring in which the matrix entries lie.
We could choose entries the coeff field when the eigenvalue is rational; and use the ring of x for irrational eigenvalues.
This could be a "nice" solution, but must be well documented!

#6 Updated by John Abbott about 2 years ago

  • Target version changed from CoCoA-5.4.0 to CoCoA-5.4.2

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