Low-level helper functions for clifford objects

Helper functions for clifford objects, written in C using the STL map class.

Usage

c_identity(L, p, m)
c_grade(L, c, m, n)
c_add(L1, c1, L2, c2, m)
c_multiply(L1, c1, L2, c2, m, sig)
c_power(L, c, m, p, sig)
c_equal(L1, c1, L2, c2, m)
c_overwrite(L1, c1, L2, c2, m)
c_cartan(L, c, m, n)
c_cartan_inverse(L, c, m, n)

Arguments

L,L1,L2

Lists of terms

c1,c2,c

Numeric vectors of coefficients

m

Maximum entry of terms

n

Grade to extract

p

Integer power

sig

Two positive integers, \(p\) and \(q\), representing the number of \(+1\) and \(-1\) terms on the main diagonal of quadratic form

Details

The functions documented here are low-level helper functions that wrap the C code. They are called by functions like clifford_plus_clifford(), which are themselves called by the binary operators documented at Ops.clifford.Rd. The functions documented here are not really intended for day-to-day use.

Function c_identity() checks that the list of terms L is the same length as the vector coefficients p; if not, an error is given. Note that R function clifford() will recycle the coefficient vector if of length 1, so that clifford(list(1,1:2),7) works as expected (but c_identity(list(1,1:2),7,2) will throw an error).

Function clifford_inverse() is problematic as nonnull blades always have an inverse; but function is.blade() is not yet implemented. Blades (including null blades) have a pseudoinverse, but this is not implemented yet either.

Value

The high-level functions documented here return an object of class clifford. But don't use the low-level functions.

Author

Robin K. S. Hankin

See also

Ops.clifford