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hadamardPower(Ideal,ZZ) -- computes the $r$-th Hadmard powers of varieties

Description

Give a homogeneous ideal $I$, the $r$-th Hadamard power of $I$ is $r$-times Hadamard product of I to itself; $( I x\cdots x I)_{r-times}$

i1 : S=QQ[x,y,z,w]

o1 = S

o1 : PolynomialRing
i2 : I=ideal(random(1,S),random(1,S),random(1,S))

            9    9    3    7   7     7     7    7        3    6
o2 = ideal (-x + -y + -z + -w, -x + --y + --z + -w, 7x + -y + -z + 6w)
            2    4    4    4   9    10    10    3        7    7

o2 : Ideal of S
i3 : hadamardPower(I,3)

o3 = ideal (714516984z + 60190200559w, 714516984y - 2454911549w, 26463592x +
     ------------------------------------------------------------------------
     1860867w)

o3 : Ideal of S

Ways to use this method:


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Hadamard.m2:376:0.