alg_deg: Algebraic degree of semidefinite programming
In damelunx/symconivol: A package for curvature measures of symmetric cones

Description Usage Arguments Details Value See also Examples

alg_deg produces a table for the algebraic degree of semidefinite programmin (see the accompanying vignette for reference to literature).

1	alg_deg(n)

`n`	size of matrix

Only some precomputed values of n are available. See the literature referenced in the accompanying vignette for general (combinatorial) formulas for the algebraic degree.

The output of alg_deg is a table of the algebraic degrees for the given value of n. To avoid loss of precision, the algebraic degrees are given as strings. See the below example for a simple conversion to numeric, including the problems associated with that step.

curv_meas_exact

Package: symconivol

AD_str <- alg_deg(6)

# convert to integer matrix
AD <- matrix( as.numeric(AD_str), dim(AD_str) )
colnames(AD) <- colnames(AD_str)
rownames(AD) <- rownames(AD_str)

# compare both matrices
print(AD_str)
print(AD)

# doing the same for larger n
AD_str <- alg_deg(14)
AD <- matrix( as.numeric(AD_str), dim(AD_str) )

# the conversion introduces rounding errors
i <- which.max(AD_str)
print(AD_str[i])
print(AD[i],digits=20)