#17088: PeriodicRegion.__div__: use integer arithmetic
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Reporter: jdemeyer | Owner:
Type: defect | Status: needs_review
Priority: critical | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/17088 | 15b7588e82c7d67bbbab14fec4c14c862bcc4c1f
Dependencies: | Stopgaps:
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Comment (by cremona):
Thanks for taking the time to think about this!
The trouble is that before and after the transformation there are exactly
r*c tiles. If the new configuration had (n*r)*(n*c) tiles then everything
would be exact. As it is, there is a loss of resulution: there has to be
because a pattern drawn on r*c tiles is redrawn n*n times, still on the
same number r*c of tiles. Think of this in two steps: first make
(n*r)*(n*c) minitiles which relpicate the original pattern n*n times on
r*c blocks of minitiles, so minitile with coordinates (a*r+i,b*c+j) gets
the value of data[i,j] with a,b in range(n), i in range(r), j in range(c).
Next we rearrange the coordinate blocks: instead of n identical blocks
of r we have r blocks of n (in the x-coordinate and similarly for the y).
These new blocks make up the new tiles, each a union of n*n minitiles with
(in general) different values, and we must give the new tile the value
True if any of those minitiles was True.
Enough for one day.
--
Ticket URL: <http://trac.sagemath.org/ticket/17088#comment:14>
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