Split each PDF page in two?

Question

I have a large number of PDF files which have two slides to a page (for printing).

The format is A4 pages each with two slides setup like so:

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Answer 1

Thanks to moraes for that answer. In my case, the resulting PDF looked fine in Adobe Reader and Mac preview, but did not appear to have been split into separate pages at all when viewing on iOS. I used Python 2.7.8 and PyPDF 2, and modified the script as follows, which worked fine. (and reordered the pages left/right, rather than right/left).

import copy
import math
from PyPDF2 import PdfFileReader, PdfFileWriter

def split_pages(src, dst):
    src_f = file(src, 'r+b')
    dst_f = file(dst, 'w+b')

    input = PdfFileReader(src_f)
    output = PdfFileWriter()

    for i in range(input.getNumPages()):
        p = input.getPage(i)
        q = copy.copy(p)
        q.mediaBox = copy.copy(p.mediaBox)

        x1, x2 = p.mediaBox.lowerLeft
        x3, x4 = p.mediaBox.upperRight

        x1, x2 = math.floor(x1), math.floor(x2)
        x3, x4 = math.floor(x3), math.floor(x4)
        x5, x6 = math.floor(x3/2), math.floor(x4/2)

        if x3 > x4:
            # horizontal
            p.mediaBox.upperRight = (x5, x4)
            p.mediaBox.lowerLeft = (x1, x2)

            q.mediaBox.upperRight = (x3, x4)
            q.mediaBox.lowerLeft = (x5, x2)
        else:
            # vertical
            p.mediaBox.upperRight = (x3, x4)
            p.mediaBox.lowerLeft = (x1, x6)

            q.mediaBox.upperRight = (x3, x6)
            q.mediaBox.lowerLeft = (x1, x2)


        p.artBox = p.mediaBox
        p.bleedBox = p.mediaBox
        p.cropBox = p.mediaBox

        q.artBox = q.mediaBox
        q.bleedBox = q.mediaBox
        q.cropBox = q.mediaBox

        output.addPage(q)
        output.addPage(p)

    output.write(dst_f)
    src_f.close()
    dst_f.close()