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I made a very simple case:

testF[x_, y_, z_] = x^2 + y^2 + z^2
Simplify[testF[x, y, z]]

If {x, y, z} is normalized, the simplified result should just be 1. How could I specify this condition/assumption?

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    $\begingroup$ Simplify[testF[x, y, z], Assumptions -> x^2 + y^2 + z^2 == 1] works on my end. $\endgroup$ – user484 Aug 5 '13 at 0:36
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    $\begingroup$ This question appears to be off-topic because it is too localized; i.e, it applies only to local situation and needs of its poster. $\endgroup$ – m_goldberg Aug 5 '13 at 1:53
  • $\begingroup$ @m_goldberg do you remember why this question was reopened? Because I can't cast a close vote again. $\endgroup$ – Kuba Apr 26 '14 at 8:07
  • $\begingroup$ @Kuba. No, don't remember. I will write up Narain's comment as community wiki answer. You can up-vote it to get the question off unanswered list. $\endgroup$ – m_goldberg Apr 26 '14 at 14:45
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As Rahul Narain wrote in a comment,

testF[x_, y_, z_] = x^2 + y^2 + z^2;
Simplify[testF[x, y, z], Assumptions -> x^2 + y^2 + z^2 == 1]
1

This may seem trivial, but it precisely expresses the condition for normality.

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