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6.1.2 Package bbsmingensys
The following are commands and functions within the package bbf:
BBSGen.BBFinder Let LF be a list of indeterminates from the ring K[t[k,l,i,j] that is the subset of the ring XX:=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]] . This function finds the defining equations of border basis scheme and their degrees that correspond to the elements of the list LF.
BBSGen.JacobiFull Let R:=K[x_1,...,x_N]. This function computes the entries of the Jacobi identity matrix J^klm [ A_m[A_k,A_l]]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ], where m,k,l is from {1...N}.
BBSGen.JacobiLin This function computes the K[c]-linear polynomial entries of the Jacobi identity matrix [ A_m[A_k,A_l ] ]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ] where m,k,l is from {1,...,N}.
BBSGen.JacobiStep Let R:=K[x_1,...,x_N] and let OO be an order ideal. This function computes the entry in the position (I,J) of the Jacobi identity matrix J^klm [ A_m[A_k,A_l ] ]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ] where m,k,l is from {1,...,N} and I,J in {1,...,Len(OO)}.
BBSGen.LinIndepGen Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list.
BBSGen.NonStand This function computes the non-standard indeterminates from K[c] with respect to the arrow grading.
BBSGen.NonStandPoly This function computes the non-standard polynomial generators of the vanishing ideal of border basis scheme with respect to the arrow grading.
BBSGen.NonTriv This function computes the non-trivial polynomials of the generating set of the vanishing ideal of a border basis scheme.
BBSGen.PolDeg This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see BBSGen.WMat).
BBSGen.PurPow This function finds the pure power indeterminates in the ring K[c].
BBSGen.TraceSyzFull This function computes the trace polynomials.
BBSGen.TraceSyzLin : This function computes the K[c]-linear summand of trace polynomials.(see BBSGen.TraceSyzFull)
BBSGen.TraceSyzLinStep This function computes the K[c]-linear summand of the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull)
BBSGen.TraceSyzStep This function computes the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull)
BBSGen.WMat This function computes the Weight Matrix with respect to the arrow grading.




For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").