SKOLEM Tool
Solver for the Skolem Problem on Integer LRS
System Explanation
On the first line write the coefficients of the recurrence relation, separated by spaces.
On the second line write an equal number of space-separated initial values.
The LRS must be non-degenerate, and not the zero LRS. Leapfrogging only supports simple LRS.
Choose the algorithm(s) and option(s) you wish to run on the given LRS.
Input Format
a
1
a
2
... a
k
u
0
u
1
... u
k-1
where:
u
n+k
= a
1
·u
n+k-1
+ a
2
·u
n+k-2
+ ... + a
k
·u
n
Input area
Zero LRS
Degenerate LRS
Non-simple LRS
Trivial
Fibonacci
Tribonacci
Berstel sequence [1]
D-M sequence [3]
Order 5 [4]
Order 6 [4]
Reversible order 8 [4]
Zero with multiplicity 2
LRS input:
Always render full LRS (otherwise restricted to 400 characters)
I solemnly swear the LRS is non-degenerate (skips degeneracy check, it will timeout or break if the LRS is degenerate!)
I solemnly swear the LRS is minimal (skips minimality check)
Use GCD reduction (reduces initial values by GCD)
Debug:print
Choose Algorithm
Use leapfrogging algorithm of
[2]
Factor subcases (merges subcases into single linear set, sometimes requires higher modulo classes)
Find the smallest modulo (often slower)
Use the fast jump algorithm
Use Baker-Davenport algorithm
Bound only (will not search for zeros up to the bound, if timeout try this to see if bound is very big)
List LRS up to bound (up to 400 unless render full LRS also chosen)
Search in both directions
Search for negative indices (note: positive will not be searched)
Use p-adic algorithm of
[5]
Assume all zeros have multiplicity 1 (Hensel-only algorithm)
Lower bound on prime used =
Number of p-adic digits to output =
Go
Clear
Stop
Output area
Baker-Davenport result
p-adic result
Leapfrogging result