Diophantine linear system solving: Difference between revisions
Diophantine linear system solving (view source)
Revision as of 14:31, 31 December 2021
, 2 years agomoved clarification up, added a paragraph, removed difficulty tag
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{{draft task|matrices}}
;task.
Implement the Havas-Majewski-Matthews
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[[wp:Hermite_normal_form| Hermite normal form]] algorithm for solving
[[wp:Diophantine_equation#Linear_Diophantine_equations| linear Diophantine systems]].
;clarification.▼
The point of this task is not comprehending the
The method is the result of an experimental refinement process over many iterations,
terse to the point of being impenetrable, best copied verbatim from a reliable source, and
hence this task mostly concerns the direct translation of existing (cryptic) code.
You may regard the test set as just random input to validate your solution, no need to delve any deeper.▼
But to make the task a little nicer, and of course to demonstrate the power of the algorithm,▼
the examples aren't really random.<br/>▼
Many are classics, with online resources abound. Others are on Rosetta Code in a different guise;▼
some are copied from the HMM paper. Section headers like 'base cases' or 'polynomial coefficients'▼
should be self-explanatory.<br/>▼
The output is deliberately left somewhat 'raw', so there's plenty of room for implementation▼
dependent refinement. Also, to solve this task you're not obliged to click any wiki-links,▼
but please do if you want some background information.▼
;context.
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To save server space, better not repeat full test results in your post.
Once your solution covers all cases, a selected example will suffice.
▲;clarification.
▲The point of this task is not comprehending the above puzzles, it is implementing the LLLHnf algorithm.
▲You may regard the test set as just random input to validate your solution, no need to delve any deeper.
▲But to make the task a little nicer, and of course to demonstrate the power of the algorithm,
▲the examples aren't really random.<br/>
▲Many are classics, with online resources abound. Others are on Rosetta Code in a different guise;
▲some are copied from the HMM paper. Section headers like 'base cases' or 'polynomial coefficients'
▲should be self-explanatory.<br/>
▲The output is deliberately left somewhat 'raw', so there's plenty of room for implementation
▲dependent refinement. Also, to solve this task you're not obliged to click any wiki-links,
▲but please do if you want some background information.
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