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)