NID Bugfixing

[PBrdng]

NID still has bugs. This PR attempts to fix them. In particular, the following example still gives errors:

using HomotopyContinuation

@var xx_Di, xx_Da, xx_Ya, xx_Yi, xx_CXY, xx_CXYp, xx_G, xx_CNA, xx_X, xx_A, xx_N, xx_CXA, xx_T, xx_CXT, xx_Xp


F = [-(5/3)*xx_Di+(2/3)*xx_Da, 
              (5/3)*xx_Di-(2/3)*xx_Da, 
              -(1/3)*xx_Ya*xx_X-(2/3)*xx_Ya+(5/6)*xx_Yi+(6/5)*xx_CXY+4*xx_CXYp, 
              -8*xx_Da*xx_Yi+(5/7)*xx_G*xx_CNA+(2/3)*xx_Ya-(49/30)*xx_Yi, 8*xx_Da*xx_Yi-(5/7)*xx_G*xx_CNA+(4/5)*xx_Yi, 
              8*xx_Da*xx_Yi-(5/7)*xx_G*xx_CNA+(2/3)*xx_A*xx_N+(4/5)*xx_Yi-(8/3)*xx_CNA, 
              -(2/3)*xx_A*xx_N-(7/8)*xx_A*xx_X+(8/3)*xx_CNA+(5/7)*xx_CXA, 
              -(2/3)*xx_A*xx_N+(8/3)*xx_CNA-(5/2)*xx_N+1, 
              -(1/3)*xx_Ya*xx_X-(7/8)*xx_A*xx_X-xx_X*xx_T-(4/3)*xx_X+(6/5)*xx_CXY+3*xx_CXT+(5/7)*xx_CXA+1, 
              (1/3)*xx_Ya*xx_X-(26/5)*xx_CXY, 
              4*xx_CXY-4*xx_CXYp, 
              4*xx_CXYp-5*xx_Xp, 
              -xx_X*xx_T+3*xx_CXT, 
              xx_X*xx_T-3*xx_CXT, 
              (7/8)*xx_A*xx_X-(5/7)*xx_CXA]

f = System(F)
s = 0x8800baf3
R = regeneration(f, seed = s)
N = decompose(R)