Opened 2 years ago

Last modified 2 years ago

#22699 new enhancement

simplify arccos+arcsin

Reported by: kcrisman Owned by:
Priority: minor Milestone: sage-wishlist
Component: symbolics Keywords:
Cc: rws Merged in:
Authors: Reviewers:
Report Upstream: Reported upstream. No feedback yet. Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

assume(x>-1)
assume(x<1)
arcsin(x)+arccos(x)

should, in principle, over the reals, simplify to pi/2 on the interval -1 to 1. I'm sure numerous problems would result with branches and step functions and whatnot if one actually attempted to implement this ... but in a wishlist world, one can dream!

Upstream at https://sourceforge.net/p/maxima/bugs/3298/

Change History (4)

comment:1 Changed 2 years ago by mforets

not sure if this makes dreams come true, but just in case:

sage: giac('assume(x>-1 and x<1)')
x
sage: giac('simplify(acos(x)+asin(x))')
1/2*pi

comment:2 Changed 2 years ago by kcrisman

Ha, nice! This can definitely be part of the solution given that giac is apparently now going to be standard?

comment:3 Changed 2 years ago by mforets

.. if it makes sense to add interfaces to the simplify function, then i'd be willing to collaborate

comment:4 Changed 2 years ago by kcrisman

  • Cc rws added

It may, but that would definitely be a different ticket! We have had .simplify() be just sending to Maxima and back for so long it would make quite the changes in our documentation. .simplify_full() all the more so. But maybe it is time for that discussion. rws is currently taking the lead on a lot of this, as you know, so copying him (however, not to suggest this tiny ticket is worth adding giac in that way all by itself).

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