magnitude | R Documentation |
Following Perwass, the magnitude of a multivector is defined as
\left|\left|A\right|\right| = \sqrt{A\ast A}
Where A\ast A
denotes the Euclidean scalar product
eucprod()
. Recall that the Euclidean scalar product is never
negative (the function body is sqrt(abs(eucprod(z)))
; the
abs()
is needed to avoid numerical roundoff errors in
eucprod()
giving a negative value).
## S3 method for class 'clifford'
Mod(z)
z |
Clifford objects |
If you want the square,
\left|\left|A\right|\right|^2
and not
\left|\left|A\right|\right|
, it is faster and more accurate
to use eucprod(A)
, because this avoids a needless square root.
There is a nice example of scalar product at rcliff.Rd
.
Robin K. S. Hankin
Ops.clifford
,
Conj
,
rcliff
Mod(rcliff())
# Perwass, p68, asserts that if A is a k-blade, then (in his notation)
# AA == A*A.
# In package idiom, A*A == A %star% A:
A <- rcliff()
Mod(A*A - A %star% A) # meh
A <- rblade()
Mod(A*A - A %star% A) # should be small
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