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# isPrimeSimple(ChordalNet) -- simple primality test of a chordal network

## Synopsis

• Function: isPrimeSimple
• Usage:
isPrimeSimple N
• Inputs:
• Outputs:
• , if the test is positive then each chain of N is prime; otherwise, they may or may not be prime

## Description

Performs a simple test to determine whether each of the chains of the network defines a prime ideal.

 i1 : I = adjacentMinorsIdeal(QQ,2,5) o1 = ideal (a*d - b*c, c*f - d*e, e*h - f*g, g*j - h*i) o1 : Ideal of QQ[a..j] i2 : N = chordalNet I; i3 : chordalTria N; i4 : topComponents N; i5 : N o5 = ChordalNet{ a => { , a*d - b*c} } b => { , } c => {c, , c*f - d*e} d => {d, , } e => { , e*h - f*g, e, , e*h - f*g} f => { , , f, , } g => {g, g*j - h*i, g*j - h*i} h => {h, , } i => { , } j => { , } o5 : ChordalNet i6 : isPrimeSimple N o6 = true i7 : C = nextChain N o7 = ChordalNetChain{a => a*d - b*c} b => c => c*f - d*e d => e => f => g => g h => h i => j => o7 : ChordalNetChain i8 : isPrimeSimple triaSystem(N,C) o8 = true