FRG begins by creating a target system for which it is intended to find all the roots. The target system is constructed to be numerically general rather than represent a specific synthesis task. The reason for this is that the target system is intended to be solved once where thereafter the target system and its roots can be used to construct parameter homotopies that efficiently solve specific synthesis systems. For the numerical experiment, the target system was constructed by generating 18 random complex numbers within the box defined by corners (−1 − *i*, 1 + *i*), assigning these numbers to *P*_{j} and $P\xafj,\u2009j=0,\u2026,8$,
Display Formula

(21)$P0=0.776874\u22120.642684i,P\xaf0=0.873111+0.292468i,P1=0.549479+0.418241i,P\xaf1=0.689034\u22120.944901i,P2=\u22120.261986\u22120.403618i,P\xaf2=0.854109\u22120.482044i,P3=0.767234\u22120.378801i,P\xaf3=\u22120.268805\u22120.865098i,P4=\u22120.068090+0.919907i,P\xaf4=\u22120.263339\u22120.451987i,P5=0.055654+0.675009i,P\xaf5=\u22120.221326+0.775947i,P6=\u22120.134960\u22120.424099i,P\xaf6=0.165736+0.319065i,P7=\u22120.239858+0.041043i,P\xaf7=0.248468+0.077381i,P8=0.635501\u22120.474101i,P\xaf8=0.342355\u22120.501518i$