Series Deficiency

A concept I came up with that describes the multiplicative error accrued by convolving series representations of integers.

Note that this is intimately connected with GenBase, particularly integral sequences.

Running

If by some miracle you manage to install, the syntax for running the output is:

$ ./deficiency_table list size p

• list is read in as [Integer], but can be preceded with "r" to describe the terms of a recurrence relation (i.e. "r[1,1]" generates the Fibonacci numbers)
• size dictates the width/height of the output image
• p is a number. The numbers in the deficiency table modulo p are those used in writing to the image, in PNG format. If preceded with "-", then a p frame GIF of the deficiency table will be produced, where the frame n is the deficiency table mod n. If preceded with "--", the GIF will use the product table rather than the deficiency table

The output file will have filename that is something like list with only digits.

Examples

# Generates a PNG of the deficiency table mod 2 for the Fibonacci numbers
# output file "1 1 mod 2.png"
$ ./deficiency_table "r[1,1]" 512 2

# Generates a 10 frame GIF of the deficiency table for the Fibonacci numbers
# where the first frame is mod 2, the second is mod 3,...
# output file "1 1.gif"
$ ./deficiency_table "r[1,1]" 512 -10

# Generates a 10 frame GIF of the product table for the Fibonacci numbers
# where the first frame is mod 2, the second is mod 3,...
# output file "1 1.gif"
$ ./deficiency_table "r[1,1]" 512 --10