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LatticeReduce[{v1,v2,…}]
gives a reduced basis for the set of vectors vi.
Details Examplesopen allclose all Basic Examples (1)Find the reduced norm basis for a lattice:
Applications (3)Starting with trivial integer linear relationships, LatticeReduce can produce more interesting ones:
Find integer linear relationships for and of the form :
LatticeReduce preserves linear relationships, and the third row provides , , and :
Find polynomial relationships for :
The trivial initial relationships:
Find linear relationships x0+x1 ArcTan[1]+x2 ArcTan[1/5]+x3 ArcTan[1/239]==0:
Initial trivial relationships:
Properties & Relations (2)LatticeReduce produces a new reduced basis for the same lattice:
The product of the norms will decrease:
The determinant or volume of the generator cell is preserved:
The lattice is generated by {v1,v2}, but also by {w1,w2} produced by LatticeReduce:
The original cell is pink, and the one produced by LatticeReduce is cyan:
Possible Issues (1)The set of vectors must have rational or Gaussian rational coefficients:
HistoryIntroduced in 1988 (1.0)
Wolfram Research (1988), LatticeReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/LatticeReduce.html. TextWolfram Research (1988), LatticeReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/LatticeReduce.html.
CMSWolfram Language. 1988. "LatticeReduce." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LatticeReduce.html.
APAWolfram Language. (1988). LatticeReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LatticeReduce.html
BibTeX@misc{reference.wolfram_2025_latticereduce, author="Wolfram Research", title="{LatticeReduce}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/LatticeReduce.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_latticereduce, organization={Wolfram Research}, title={LatticeReduce}, year={1988}, url={https://reference.wolfram.com/language/ref/LatticeReduce.html}, note=[Accessed: 12-July-2025 ]}
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