# Simplify function with normalized vector

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?

• Simplify[testF[x, y, z], Assumptions -> x^2 + y^2 + z^2 == 1] works on my end. – user484 Aug 5 '13 at 0:36
• 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. – m_goldberg Aug 5 '13 at 1:53
• @m_goldberg do you remember why this question was reopened? Because I can't cast a close vote again. – Kuba Apr 26 '14 at 8:07
• @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. – m_goldberg Apr 26 '14 at 14:45

## 1 Answer

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.