Description Usage Arguments Value See Also Examples
Macaulay2's implementation of the LLL algorithm. This implementation is still under development and is currently untested.
1 2 3 |
mat |
a matrix (integer entries) |
control |
additional arguments to pass to LLL; see examples |
code |
return only the M2 code? (default: |
an object of class m2_matrix
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | ## Not run: requires Macaulay2
##### basic usage
########################################
# example 1
M <- matrix(c(
1, 1, 1, 1,
2, 0, 3, 4,
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
), nrow = 6, byrow = TRUE)
LLL(M)
# example 2 (wikipedia)
M <- matrix(c(
1, -1, 3,
1, 0, 5,
1, 2, 6
), nrow = 3, byrow = TRUE)
LLL(M)
##### control
########################################
M <- matrix(c(
1, 1, 1, 1,
2, 0, 3, 4,
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
), nrow = 6, byrow = TRUE)
LLL(M, code = TRUE)
LLL(M, control = list(Strategy = "NTL"), code = TRUE)
LLL(M, control = list(Strategy = c("BKZ", "RealFP")), code = TRUE)
LLL(M)
LLL(M, control = list(Strategy = "NTL"))
LLL(M, control = list(Strategy = c("BKZ", "RealFP")))
LLL(M, control = list(Strategy = c("BKZ", "RealQP")))
# method timings with microbenchmark. note they are roughly the same
# for this example matrix
microbenchmark::microbenchmark(
"NTL" = LLL(M, control = list(Strategy = "NTL")),
"BKZ_RealFP" = LLL(M, control = list(Strategy = c("BKZ", "RealFP"))),
"BKZ_RealQP" = LLL(M, control = list(Strategy = c("BKZ", "RealQP"))),
"BKZ_RealRR" = LLL(M, control = list(Strategy = c("BKZ", "RealRR")))
)
##### additional examples
########################################
LLL.(M)
LLL(M, code = TRUE)
## End(Not run)
|
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