Random weyl objects — rweyl • weyl

Creates random weyl objects: quick-and-dirty examples of Weyl algebra elements

Usage

rweyl(nterms = 3, vals = seq_len(nterms), dim = 3, powers = 0:2)
rweyll(nterms = 15, vals = seq_len(nterms), dim = 4, powers = 0:5)
rweylll(nterms = 50, vals = seq_len(nterms), dim = 8, powers = 0:7)

Arguments

nterms: Number of terms in output
vals: Values of coefficients
dim: Dimension of weyl object
powers: Set from which to sample the entries of the index matrix

Details

Function rweyl() creates a smallish random Weyl object; rweyll() and rweylll() create successively more complicated objects.

These functions use spray::rspray(), so the note there about repeated rows in the index matrix resulting in fewer than nterms terms applies.

Function rweyl1() returns a one-dimensional Weyl object.

Value

Returns a weyl object

Author

Robin K. S. Hankin

Examples

rweyl()
#> A member of the Weyl algebra:
#> +3*x^2*dy +2*x^2*z^2*dy +x*y^2*dx*dy*dz^2
rweyll()
#> A member of the Weyl algebra:
#> +15*x2^4*x3*x4^4*d2^2 +x1^5*x2^2*x4*d1^4*d2^3*d3^3
#> +3*x1*x2^5*x3^2*x4^2*d1^4*d2^3*d3^2*d4^2 +6*x2^4*x4*d1^3*d4^2
#> +4*x2*x3*x4^3*d1^4*d2^3*d3^3*d4^4
#> +8*x1^5*x2*x3^5*x4^3*d1^5*d2^4*d3^5*d4
#> +14*x2^4*x3^3*x4^5*d1^2*d2^4*d4^2 +5*x1^5*x2*x4*d1^3*d2^5*d4^2
#> +10*x3*d1^3*d2*d3^4*d4^4 +9*x1^5*x2*x3^4*x4^3*d1^4*d2*d3*d4^3
#> +11*x1^2*x2^3*x3^3*x4*d1^5*d2^2*d3^2*d4^4
#> +7*x1^3*x2^4*x3^4*x4^2*d1^3*d2^3*d3^4*d4^5
#> +2*x1^4*x3*x4*d1^5*d2*d3^5*d4 +12*x1^2*x3*x4^3*d1^5*d2^4*d3^4*d4^4
#> +13*x1^2*x2^2*x3^4*x4^4*d1^2*d2*d3*d4^4
rweyl(d=7)
#> A member of the Weyl algebra:
#> +3*x1*x2^2*x7*d2^2*d3^2*d4^2*d5*d6*d7^2
#> +2*x1*x3^2*x5^2*d1*d2^2*d3^2*d4^2*d5^2*d6^2
#> +x1*x2*x3*x4^2*x5^2*x6^2*x7*d1*d2^2*d4*d5^2*d6^2*d7

options(polyform = TRUE)
rweyl1()
#> A member of the Weyl algebra:
#> +5*x^3*d +4*x^3*d^2 +2*x^3*d^3 +6*x^2*d +3*x*d +x^4*d^4
options(polyform = FALSE) # restore default