How can I force the assumption that a symbol is a vector of n zeros

Using

$Assumptions = Element[n, Integers] && Element[a, Vectors[n, Reals]] I can assume that a is a n-dimensional vector of Reals. How can I assume that a is a n-dimensional vector of zeros? I tried adding this to the assumptions Norm[a] == 0 such that the assumptions now look like this$Assumptions = Element[n, Integers] && Element[a, Vectors[n, Reals]] && Norm[a] == 0

Since a is a vector and only the 0 vector has a Norm of zero, mathematica should now know that a is a vector of n zeros. However,

Refine[3*a]

returns 3 a instead of 0.

• Why not simply define your vector to be what you seek? a = Table[0,{n}] – David G. Stork May 8 '15 at 22:51
• I suspect that the question is about cases where n is a parameter/variable? I for one am curious about how Vectors[n, Reals] even works: does Mathematica ever respect the use of a symbol for the dimensionality or is Vectors[] meant for vectors whose size you know beforehand only? – nben May 8 '15 at 23:58
• "Since a is a vector and only the 0 vector has a Norm of zero, mathematica should now know that a is a vector of n zeros" is a very dubious assertion. – m_goldberg May 9 '15 at 4:53
• @m_goldberg I think that assumption is strictly true. The norm is zero iff the vector is zero. But Refine simply doesn't use the norm. – Jens May 9 '15 at 5:29
• @Jens. The dubious part of the quote is "mathematica should now know". – m_goldberg May 9 '15 at 13:23