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Coamoeba


The coamoeba of an algebraic variety V subset (C^*)^n is its image under the coordinatewise argument map

 Arg(z_1,...,z_n)=(arg(z_1),...,arg(z_n)) in (R/2piZ)^n.

It is therefore a subset of the real n-torus (R/2piZ)^n. Whereas the amoeba of V records the logarithms of the complex moduli of its coordinates and discards the complex arguments, the coamoeba does the reverse.


See also

Algebraic Variety, Amoeba, Complex Argument, Complex Modulus, Torus

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References

Nisse, M. and Sottile, F. "The Phase Limit Set of a Variety." Algebra Number Theory 7, 339-352, 2013. https://doi.org/10.2140/ant.2013.7.339.

Cite this as:

Weisstein, Eric W. "Coamoeba." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Coamoeba.html

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