I have a list of relations of the form
x[1] x[2] + y[1] y[2] - z[1] z[2] == 0
and I want Mathematica to simplify certain expressions using these relations.
I have been using FullSimplify
with assumptions, and I have found that it doesn't work occasionally. For example:
FullSimplify[(a b - e f)/c, Assumptions -> {a b + c d - e f == 0}]
works just fine, and gives the correct answer -d
, but for some reason
FullSimplify[(c d - e f)/a, Assumptions -> {a b + c d - e f == 0}]
returns (c d - e f)/a
.
Any idea why this happens and how to make sure that Mathematica recognizes the second example as -b
?
Reduce
is more appropriate for this sort of thing. For example:Reduce[(c d - e f)/a == y && a b + c d - e f == 0]
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