The second issue is generally solved by outputting regular chains of a special form, sometimes called " shape lemma ", for which all but the first one are equal to.
32.
The " rational univariate representation ", described below, allows to compute such a special regular chain, satisfying Dahan Schost bound, by starting from either a regular chain or a Gr�bner basis.
33.
The " rational univariate representation ", described below, allows to compute such a special regular chain, satisfying Dahan Schost bound, by starting from either a regular chain or a Gr�bner basis.
34.
One of the main purposes of this subpackage is to offer efficient basic routines in order to suppor the implementation of modular algorithms for computing with regular chains and algebraic numbers.
35.
In the early 90's, the notion of a regular chain, introduced independently by Michael Kalkbrener in 1991 in his PhD Thesis and, by Lu Yang and Jingzhong Zhang led to important algorithmic discoveries.
36.
The "'SemiAlgebraicSetTools "'subpackage contains a collection of commands for isolating and counting real roots of zero-dimensional semi-algebraic systems or regular chains ( that is regular chains with a finite number of complex solutions ).
37.
The "'SemiAlgebraicSetTools "'subpackage contains a collection of commands for isolating and counting real roots of zero-dimensional semi-algebraic systems or regular chains ( that is regular chains with a finite number of complex solutions ).
38.
The definition of regular chains implies that the univariate equation obtained from has degree and thus that the system has solutions, provided that there is no multiple root in this resolution process ( fundamental theorem of algebra ).
39.
Mason said the key to Laxalt's role is that he will be " knowledgeable about the campaign but will sit outside the regular chain of command, so he can say " hey, you're missing a big issue . ""
40.
Major General John Numbi, former Air Force chief, now inspector general of police, ran a parallel chain of command in the east to direct the 2009 Eastern Congo offensive, Operation Umoja Wetu; the regular chain of command was by-passed.
