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If e is a
bivector, then we have
or equivalently
. In
quaternions much the same formula is true. We have
, but
holds only if x is purely quaternionic:
for real j and k.
Now let x, p, d and μ be real numbers and e a bivector on a
compact 2-
manifold R. Then we can calculate the integral
and it is a real number. On the other hand it is much easier to simply calculate
, because it is infinity. Unfortunately
Greek letters are autoitalicized.
This stuff is all pretty simple. Let's get into some deeper waters.
Let
. Then
so we have
. On the other hand
.
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Articles significantly edited
Mathematics,
manifold,
topological manifold,
differentiable manifold,
Laplace operator,
scalar,
scalar field,
bijection, injection and surjection
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Illegal numbers
I am in support of fully stating
illegal primes,
AACS encryption keys and other numbers and facts while they pose no legal risk to Wikipedia and while no official decision from the operators of Wikipedia has been made to censor such numbers.
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