This is the documentation of NumGfun v. 0.1; it is NOT up-to-date.

# Procedures marked (*) are highly experimental, inefficient, or lack some cases.
#
#
# ANALYTIC CONTINUATION
#
#   ac_eval(deq, y(z), path, precision)
#       Numerical analytic continuation along path of the solution of deq (in 0).
#       deq - differential equation with initial values
#       y(z) - variables
#       path - list of elements of Q[i] starting in 0 (e.g. [0,1,1+I])
#       precision - (absolute) number of digits needed
#       
#   transition_matrix(deq, y(z), path, precision)
#       Same as ac_eval, but compute the whole transition matrix.
#       deq - differential equation (initial values are ignored)
#       y(z), path, precision - as above
#       
#   diffeqtoproc
#
#   local_monodromy(deq, y(z), sing, start, precision)  (*)
#       Trivial wrapper around transition_matrix. 
#       start - basepoint
#       sing - singularity
#       deq, y(z), precision - as above
#   
# NTH TERM FOR RECURRENT SEQUENCES
#
#   nth_term(rec, u(n), N [, ringname])
#       Nth term of the sequence defined by rec.
#       deq - recurrence equation (with initial values)
#       u(n) - variables
#       N - positive integer
#       ringname - if set to ndmatrix, compute Sum(u(j),j=0..n-1) instead
#
#   fnth_term
#       Same as nth_term, with floating-point instead of rational result
#       
#   rectoproc_binsplit(rec, u(n))
#       Returns a procedure computing u as defined by rec.
#       rec, u(n) - as above
#
# BOUNDS
#   
#   bound_diffeq(deq,y(z))
#       Compute a majorant series valid for all fundamental solutions of deq.
#       deq - differential equation (initial values are ignored)
#       y(z) - variables
#       
#   bound_rec(rec, u(n))
#       Compute a simple bound for the solution of rec.
#       rec - recurrence equation (with initial values)
#       u(n) - variables
#       
#   bound_ratpoly(rat,z)
#       Computes a sharp (exact up to logarithmic factors) majorant series for rat.
#       rat - rational polynomial
#       z - variable
#
# MISC
#       
#   waksman_product(r)
#       Returns a procedure to multiply r*r matrices using Waksman's algorithm.


