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Fix discriminant error with polynomials with identically vanishing derivatives (issue #4449) #4472

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Fix discriminant error with polynomials with identically vanishing derivatives (issue #4449) #4472

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ccff7d0
update discriminant method with zero derivative
tbrazel Jul 15, 2026
1977f93
Implement test for zero derivative resultant
tbrazel Jul 15, 2026
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13 changes: 11 additions & 2 deletions M2/Macaulay2/packages/Elimination.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -125,8 +125,10 @@ resultant(RingElement, RingElement, RingElement) := o -> (f,g,x) ->
det sylvesterMatrix(f,g,x)

discriminant = method(Options => { Algorithm => null })
discriminant(RingElement, RingElement) := RingElement => o -> (f,x) -> resultant(f, diff(x,f), x, o)

discriminant(RingElement, RingElement) := RingElement => o -> (f,x) -> (
if diff(f,x) == 0 then return 0;
resultant(f, diff(x,f), x, o)
)
-----------------------------------------------
-- documentation and tests
-----------------------------------------------
Expand Down Expand Up @@ -330,6 +332,13 @@ assert(isHomogeneous J)

assert(eliminate(x,eliminate(y,I)) == eliminate(y,eliminate(x,I)))
///

-- Resultant of a polynomial whose derivative is identically zero should return zero
TEST ///
R=ZZ/2[x]
F=x^24+x^22+x^20+x^14+x^12+x^8+x^4
assert(discriminant(F,x) == 0)
///
end
loadPackage "Elimination"
installPackage Elimination
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