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Default simplifications in Calc (adding simplifications)

From: Jay Belanger
Subject: Default simplifications in Calc (adding simplifications)
Date: Sat, 16 Jun 2012 22:17:29 -0500
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/24.1.50 (gnu/linux)

I'm wondering if anyone has any opinions on moving some algebraic
simplifications to Calc's default simplifications.

Calc does not do some "natural" simplifications by default, but
these simplifications can be done using the "a s" command or by using
Calc's Algebraic Simplification mode.  For example,  by default:
* Calc will simplify `x+x+y' to `2x+y' but will not simplify `x+y+x',
* Calc will not simplify 'x*y + y*x', 
* Calc will not reduce i^2 to -1,
* Calc will not cancel common factors in the top and bottom of a fraction
* Calc will not simplify cos(x)tan(x) to sin(x).
There are others, see (info "(Calc) Algebraic Simplifications")

I think the simplifications done by Algebraic Simplification mode (or
at least some of them) should be done by default; they are not done by
default (according to the manual) "because they may be too slow to
apply all the time, or may not be desirable all of the time."  
I don't think speed is an issue any longer (computers are a bit faster
than they were when Calc was originally written), but since this would
be a change to default behavior I thought I should see if anyone has any
thoughts on the matter. 


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