This algorithm is a strategy for computing the truncated dual space of an ideal I at degree d. A matrix is formed with a column for each monomial in the ring of I of degree at most d, and a row for each monomial multiple of a generator of I which has any terms of degree d or less, storing its coefficients. Any vector in the kernel of this matrix is the coeffeicient vector of an element of the dual space.
See: B.H. Dayton and Z. Zeng. Computing the multiplicity structure in solving polynomial systems. In M. Kauers, editor, Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, pages 116-123. ACM, 2005.