AlgebraicRules

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• Subject: [mg127477] AlgebraicRules
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 28 Jul 2012 02:38:59 -0400 (EDT)
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```In a very recent post by Fred Simons, he cited his paper "Computer
algebra in service courses", available as:

http://alexandria.tue.nl/openaccess/Metis217845.pdf

In it, he proves a certain trig identity. He begins by using TrigExpand
to obtain a certain polynoial, call it "expanded", in Sin[x] and Cos[x].
Then he uses the function AlgebraicRules:

expanded/.AlgebraicRules[{
Sin[x]^2 + Cos[x]^2 == 1, TrigExpand[Sin[3x]] == 1/2}]

I only vaguely recall having seen AlgebraicRules back in Version 2.2 but
have not come across it since.

Although AlgebraicRules persists in the current version of Mathematica,
the docs say that since Version 3.0, Algebraic Rules has been superseded
by PolynomialReduce.

Can PolynomialReduce in fact be used _directly_ on an expression that is
not a polynomial in, say, a single variable x but rather in the pair of
functions Sin[x] and Cos[x]?

Or must one revert to the artifice of replacing Sin[x] and Cos[x] by new
variable names, use PolynomialReduce, and finally reverse the
replacement to get back to the original variable x?

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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