Re: Question about Simplify and related

• To: mathgroup <mathgroup at yoda.ncsa.uiuc.edu>
• Subject: Re: Question about Simplify and related
• From: HAY at leicester.ac.uk
• Date: Tue, 22 JAN 91 22:40:45 GMT

```In response to Paul Schatz's question concerning Simplify and related.

Paul:

AlgebraicRules[ , ] can be very useful in dealing with polynomial
simplification. In the example that you give we have to get inside the lists.
One way  of doing this is as in (1) below - you will see that we do not need to
expand or simplify. If you are doing a lot of this kind of work it might be
worthwhile defining a function that will automatically take the application of
AlgebraicRules inside brackets as in (2).

(1)

In:= u ={ {c1 c2 - c3 s1 s2,c2 s1 + c3 c1 s2,s2 s3},
{-s2 c1 - c3 s1 c2, -s2 s1 + c3 c1 c2, c2 s3},
{s3 s1, -s3 c1, c3}
}

plainuutrans = u.Transpose[u]

eqns = { c1^2 + s1^2 == 1, c2^2 + s2^2 == 1, c3^2 + s3^2 == 1 }

vars = { c1,c2,c3,s1,s2,s3 }

algRls = AlgebraicRules[ eqns, vars ]

plainuutrans/. x_Plus :> (x/.algRls)  (* :> not ->, (...) essential*)

Out = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

(2)

In:= ARL[eqns_, vars_] [expr_List]:= ARL[eqns, vars]/@ expr

ARL[eqns_, vars_] [expr_]:= expr/.AlgebraicRules[eqns, vars]

In:= ARL[eqns,vars][plainuutrans]

Out = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

Allan Hayes
Department of Mathematics
The University
Leicester LE1 7RH
U.K.
hay at le.ac.uk

```

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