By A Seidenberg

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**Additional resources for An Elimination Theory for Differential Algebra**

**Example text**

For j=O,l, ... l = 0 and where the order of J the Pj is determined by the order of the uj . Identify the optimal value of j as the value j = T for which Fj . l < IhFn _I and Fj > VzFn _I . The optimal slope is then given by y * = lIu r , the corresponding intercept by z* = D+a*-y*P, and the ith correction by Vi' = z* + y'Pi-ai' ° Laplace's (1793, § 11) analytical formulation of Boscovich's procedure is now obtained as the variant of this translation which sets a * = in step 1 (so that d i = a i and D = A), negates P - Pi in step 2 and D - di in step 3, evaluates Wi = (a i - A)/(Pi - P) in step 4, and arranges the Wi in decreasing order in step 5.

However, none of these contributions would seem to have been sufficient to stimulate the development of linear programming as a discipline in its own right; see Grattan-Guinness (1994) and Brentjes (1994) for detailed accounts of the history of this subject. Following the text of a memoir written by Fourier (1829) in the last years of his life, Grattan-Guinness (1970, p. 361) has suggested that Fourier attributed his interest in the calculus of inequalities to his encounter with an important practical problem when a senior member of the scientific staff accompanying Napoleon Buonaparte's military expedition to Egypt in 1798-1801.

112): "It thus appears that Boscovich discussed the whole subject with completeness, penetration, and ... accuracy. Had his remarks been published in a work better known and more accessible to naturalists, a detailed refutation of Reaumur and Krenig [by Glaisher] a hundred and thirteen years later would have been rendered superfluous. " Even if we allow that Boscovich could write in Latin with considerable facility, it seems inconceivable to a modern reader that he should have chosen to devote so much of his time to writing a detailed commentary on a poem in Latin hexameters by a kinsman and colleague.