id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
30091 Linear functionals on vector spaces and modules Matthias Köppe "We propose to add a method `dual` to modules `M` as an abbreviation for `Hom(M, M.base_ring())`.
For vector spaces, we create a specialized class so that it prints in a more concise way than this:
{{{
sage: Hom(QQ^2, QQ)
Set of Morphisms (Linear Transformations) from Vector space of dimension 2 over Rational Field to Rational Field
}}}
and has more functionality to make linear algebra less awkward.
{{{
sage: _.an_element()
NotImplementedError: please implement _an_element_ for Set of Morphisms (Linear Transformations) from Vector space of dimension 2 over Rational Field to Rational Field
}}}
`FiniteRankFreeModule` already has this functionality. The new interface should be compatible with it.
{{{
sage: Q3 = FiniteRankFreeModule(QQ, 3)
sage: Q3.dual()
Dual of the 3-dimensional vector space over the Rational Field
sage: l = Q3.linear_form(); l
Linear form on the 3-dimensional vector space over the Rational Field
}}}
Related (more general):
- #13372: add functionality for duals of algebras, coalgebras, hopf algebras, etc.
" enhancement new major sage-9.8 categories Travis Scrimshaw Simon Brandhorst Eric Gourgoulhon N/A