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ReesAlgebra :: isReduction

isReduction -- Determine whether an ideal is a reduction

Synopsis

Description

For an ideal I, a subideal J of I is said to be a reduction of I if there exists a nonnegative integer n such that JIn=In+1.

This function returns true if J is a reduction of I and returns false if J is not a subideal of I or J is a subideal but not a reduction of I.

i1 : S = ZZ/5[x,y]

o1 = S

o1 : PolynomialRing
i2 : I = ideal(x^3,x*y,y^4)

             3        4
o2 = ideal (x , x*y, y )

o2 : Ideal of S
i3 : J = ideal(x*y, x^3+y^4)

                  4    3
o3 = ideal (x*y, y  + x )

o3 : Ideal of S
i4 : isReduction(I,J)

o4 = true
i5 : isReduction(J,I)

o5 = false
i6 : isReduction(I,I)

o6 = true
i7 : g = I_0

      3
o7 = x

o7 : S
i8 : isReduction(I,J,g)

o8 = true
i9 : isReduction(J,I,g)

o9 = false
i10 : isReduction(I,I,g)

o10 = true

See also

Ways to use isReduction :