LCALC(1) User Commands LCALC(1)
NAME
lcalc - program for calculating with L-functions
SYNOPSIS
lcalc [OPTIONS]...
DESCRIPTION
lcalc 1.11 Feb 5, 2008
This program computes zeros and values of L-function.
-h, --help
Print help and exit
-V, --version
Print version and exit
-v, --value
compute L-function at x+iy. Should be used in conjuction with x and y options (default=off)
-x, --x=Double
Used with value,value-line-segment, and zeros-interval options (default=`.5')
-y, --y=Double
Used with value,value-line-segment, and zeros-interval options (default=`0')
--value-file=filename
compute L-function at points specified in file
--value-line-segment
compute L-function along a line segment connecting (x,y) to (X,Y) at number-sample points (default=off)
-X, --X=Double
Used with value-line-segment (default=`.5')
-Y, --Y=Double
Used with value-line-segment (default=`100')
-n, --number-samples=INT
Used with value-line-segment, and interpolate options (default=`1000')
-z, --zeros=INT
number of zeros to find
-Z, --zeros-interval
number of zeros to find in an interval (1/2+ix,1/2+iy) using steps of size stepsize. Use with the x,y, and stepsize options
(default=off)
--stepsize=Double
Used with zeros-interval
-d, --derivative=INT
compute derivative. use -d -1 to specify logarithmic derivative.
-e, --elliptic-curve
specify an elliptic curve over Q. Use with the a1 a2 a3 a4 a6 options (default=off)
--a1=rational_number
Used with the elliptic-curve option
--a2=rational_number
Used with the elliptic-curve option
--a3=rational_number
Used with the elliptic-curve option
--a4=rational_number
Used with the elliptic-curve option
--a6=rational_number
Used with the elliptic-curve option
-F, --file-input=filename
input a file with basic L-function data
-u, --url=url
input a web based file with basic L-function data. Specify the url of the file
-i, --interpolate=filename2
interpolate between two L-functions and find their zeros. Should be used in conjunction with file-input
-C, --output-character=STRING if twisting, output the character
(possible values="1", "2" default=`1')
-o, --output-data=number Dirichlet coeffs
output basic data for the underlying L-function
(default=`10')
--verbose=INT
verbosity > 0 outputs extra info (default=`0')
-P, --precision=INT
number digits precision (default=`14')
-S, --sacrifice=INT
number digits to sacrifice (default=`2')
-r, --rank-compute
compute the rank (default=off)
--rank-verify=INT
verify if specified rank is correct
-l, --rank-limit=INT
when doing quadratic twists limit to L-functions with specified rank
-t, --tau
Ramanujan tau L-function (weight 12, full level) (default=off)
-q, --twist-quadratic
twist by fundamental quadratic characters, start <= discriminant <= finish. Use with start and finish options. (default=off)
-s, --start=integer
Used with various twisting options
-f, --finish=integer
Used with various twisting options. Default has finish=start
--twist-quadratic-even
twist by fundamental quadratic characters, even functional eqn, start <= discriminant <= finish (default=off)
-p, --twist-primitive
twist by all primitive Dirichlet characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients,
conjugate characters are considered equaivalent (default=off)
-A, --twist-all
twist by all Dirichlet characters with start <= conductor <= finish. (default=off)
-a, --twist-all-no-conj-pairs twist by all Dirichlet characters with start <=
conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate pairs of characters are considered equivalent
(default=off)
-c, --twist-complex-no-conj-pairs
twist by all complex primitive Dirichlet
characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate pairs of characters
are considered equivalent (default=off)
-g, --twist-generic
twist by a generic complex Dirichlet characters with start <= conductor <= finish. (default=off)
-D, --degree=degree
can only be used in conjuction with twist-primitive (?). Select characters of specified degree. Not yet implemented
SEE ALSO
The full documentation for lcalc is maintained as a Texinfo manual. If the info and lcalc programs are properly installed at your site,
the command
info lcalc
should give you access to the complete manual.
lcalc 1.11 Feb 5, 2008 May 2008 LCALC(1)