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testElement -- find a test element of a ring

Description

Given $R = S/I$, where $S$ is a polynomial ring, the function testElement finds an element of the ambient ring $S$ whose image in $R$ is a test element of $R$. This is done by finding a minor of the jacobian of $I$ that does not lie in any minimal prime of $I$. This function considers random minors until one is found, instead of computing all minors. Thus, repeated calls will not always produce the same answer.

i1 : R = ZZ/11[x,y,z]/(x^3 + y^3 + z^3);
i2 : apply(1..5, i -> testElement(R))

        2    2     2     2    2
o2 = (2y , 2x , -3x , -4x , -y )

o2 : Sequence

If the option AssumeDomain (default value false) is set to true, then testElement does not compute the minimal primes of $I$. This can result in a substantial speedup in some cases.

Ways to use testElement:

  • testElement(Ring)

For the programmer

The object testElement is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/TestIdeals/testIdealsDoc.m2:73:0.