Sage cannot simplify arccos, but can simplify arcsin?

asked 2013-04-20 18:07:12 +0100

sgia
91 ●2 ●4 ●10

I am using Sage 5.7. It can simplify expressions involving arcsin, but not arccos, why?

Thanks

assume(x > 0)
assume(x < pi/2)
acos(cos(x)).simplify_full()

output: arccos(cos(x))

asin(sin(x)).simplify_full()

output: x

answered 2013-04-20 23:01:20 +0100

kcrisman
12242 ●42 ●136 ●255

This is in fact just about Maxima's simplification.

sage: F = asin(sin(x))
sage: F.simplify() # sends to Maxima, nothing else
x
sage: G = acos(cos(x))
sage: G.simplify()
arccos(cos(x))

This Maxima help thread suggests that, as of a couple years ago, this was known but not resolved. I've opened Maxima bug 2570 for this, though I wouldn't expect immediate response as it may be something somewhat deep in the code that isn't easy to unravel - simplification routines can be notorious for this, I guess.

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This has now been fixed upstream, and I've opened [Trac 14637](http://trac.sagemath.org/sage_trac/ticket/14637) to add a confirming doctest.

kcrisman ( 2013-05-24 09:22:04 +0100 )edit

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