Magnitude of a clifford object

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).

Usage

# S3 method for class 'clifford'
Mod(z)

Arguments

z

Clifford objects

Author

Robin K. S. Hankin

Note

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.

See also

Ops.clifford, Conj, rcliff

Examples

Mod(rcliff())
#> [1] 12.24745


# 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
#> [1] 82.19489

A <- rblade()
Mod(A*A - A %star% A)  # should be small
#> [1] 0