Am So., 23. Aug. 2020 um 23:35 Uhr schrieb Linas Vepstas
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> Marc, you asked John Cowan a question about a linear-algebra srfi, but did not cc him in asking it. See below.
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> In related news: ... if you really wanted to one-up python and scipy, you would figure out if something like QR decomposition can be defined for things other than fields, e.g. rings or division algebras or what-nots  Certainly, "modules" capture 98% of the ideas of linear algebra and are defined on rings in general. Maybe the Householder-reflection QR algo has to be restricted to commutative rings; hard to say, at a glance.

The Householder reflection needs a hermitian scalar product (including
a real scalar product as the general case). Thus, if you want to
generalize it over rings other than R, C, or H, you would have to
axiomatize the complex/quaternionic conjugation as well, making the
resulting mathematical structures quite special.

While I generally agree that we should try to enable the use of rings
and modules when no more is needed, in this particular case
restricting to R, C, and H has (besides the above argument) the
advantage that, at least, R and C are already built into Scheme. We
could ask for an extension of the numeric tower to H (which would make
perfect sense), in which we just need the usual generic numerical
operations of section 6.2 of the R7RS.

> That is, much of linear algebra can be defined on rings, and much of the rest on commutative rings, and so for those who just want to run rampant screwing around with arbitrary stuff for no discernible reason, it would be nice to have the ability to plug in any one of these things "under the covers" as needed, and still have a usable linear-algebra library.  The audience is admittedly small, but having an alternative to things like Mathematica, or the patch-work piece-meal libraries out there would be a big win.  If nothing else, forcing working mathematicians to learn scheme/functional-programming would provide good cross-pollination of ideas.

Before can implement a larger part of generic mathematical algorithms,
we need some foundation for generic algorithms, which isn't there yet,
I think.