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Noether's Fundamental Theorem


If two curves phi and psi of multiplicities r_i!=0 and s_i!=0 have only ordinary points or ordinary singular points and cusps in common, then every curve which has at least multiplicity

 r_i+s_i-1

at every point (distinct or infinitely near) can be written

 f=phipsi^'+psiphi^'=0,

where the curves phi^' and psi^' have multiplicities at least r_i-1 and s_i-1.


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References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 29-30, 1959.

Referenced on Wolfram|Alpha

Noether's Fundamental Theorem

Cite this as:

Weisstein, Eric W. "Noether's Fundamental Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NoethersFundamentalTheorem.html

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