
DV is a package for solving parametric polynomial systems of equations, inequalities and/or inequations. The current version is a beta version and only few functions are exported. DV stands for Discriminant Variety. Given any constructible set defined by equations and inequations depending on parameters, DV basically computes a so called Discriminant Variety.
A system of polynomial equations and inequations is said parametric when it has a finite number of solutions under a generic choice of the assignation for the parameters.
A Discriminant Variety of a parametric polynomial system S is an algebraic subset of the parameter's space such that over each neightborhood of the parameter's space which do not meet the discriminant variety, the constructible set defined by S is an analytic covering of this neightborhood for the projection on the parameter's space. In particular, for parameters in such a neightborhood, the number of solutions of the system after specializing to these values is constant.
Figure 1.

Figure 2.

DV Maple package is fully written in Maple language but uses Gb,FGb and RS Software.
In the package DV, the varieties are represented by the list of polynomials that defined them. An union of varieties is thus naturally represented by the list of the lists of polynomials defining each variety of the union.
The functions provided by the package DV are:
DV_solve (eqns, ineqns, pars, vars, options): computes a discriminant variety of the constructible set defined by:
f_{1}=0 , ... , f_{s}= 0 , g_{1}≠0, ... , g_{r}≠0
with f1,..,fs in eqns and g1,..,gr in ineqns, pars are the parameters vars are the other variables. The function may also compute a discriminant variety of a constructible set defined by:
U_{j=1, ... ,t} (f_{j,1}= 0 , ... , f_{j,sj}= 0) , g_{1}≠0, ... , g_{r}≠0
Keywords in the options sequence allow some control on the strategy used by the algorithm to find the Discriminant Variety.
The keywords may increase the computation speed for some systems but they also may decrease it for others. They are to be used very carefully!
Here is how we compute the discriminant variety of the variety in Fig. 2, whose equation system is:
T  (x + y)^{2}  =  0 
x  y  (x + y) ((x + y)^{2}  4)  =  0 
with T being a parameter, and x,y being unknowns.
> DV_solve([T(x+y)^2,xy(x+y)*((x+y)^24)],[],[T],[x,y],'factorize'); [[T]], "Minimal"