Implement algorithm=pari for characteristic polynomial of a matrix

[Krishnadubey1008]

This PR fixes #39815

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

[user202729]

The problem is sage method should probably not return pari Gen object. It is especially confusing when it prints out identical to a sage polynomial.

( conversion from pari polynomial to sage polynomial doesn't work yet → #39814 )

[Krishnadubey1008]

@user202729 I have added following lines to handle the conversion of the PARI Gen object to a SageMath polynomial

pari_poly = pari(x).charpoly(var)
return pari_poly.sage()

[user202729]

Need documentation and doctest. Also avoid importing from .all, all other occurrences of importing pari in the code base doesn't.

[Krishnadubey1008]

@user202729 I have provided a doctest example showing how to use the algorithm="pari" and changed the import statement to import pari from sage.libs.pari.gen instead of from .all.

[user202729]

Need documentation of the possible values of the algorithm input to the function. Also test for polynomials over RR, ZZ, QQ[i], other fields that pari supports

[Krishnadubey1008]

@user202729 I have improved documentation and doctests as suggested

[user202729]

this should go to charpoly method instead of here? Also the format of the documentation is incorrect, search for INPUT in documentation of other functions