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FUNCTION: wsolve - prepare the given algebraic system for solving

CALLING SEQUENCE:

wsolve(F)

wsolve(F, X)

wsolve(F, X,nonzero)

e_val(F,X,nonzero)

charset(F,X)

od_wsolve(F,X) (zero decomposition for ordinary differential poly system)

pd_wsolve(F,X) (zero decomposition for partial differential poly system)

PARAMETERS:

F - set or list of polynomials in indeterminates X

X - list of indeterminates (not including parameters)

nonzero - set of polynomials in indeterminates X

SYNOPSIS:

- The command wsolve(F,X,nonzero) computes a collection of ascending sets

corresponding to F.

- First the system corresponding to F is subdivided by factorization.

- Then each subsystem is passed to a variant of Wu's algorithm which

factors all intermediate results.

- The result is a set of subsystems whose roots which are not the zeros of

the initials (leading coefficients to the main variable) are those of the

original system but whose variables have been successively eliminated

- If desired the solveas(asord) function may then be applied to solve

the subsystems

- If desired the simplifyas(as,ord,nonzero) function may then be applied

to simplify the ascending set.

- The set nonzero may be used to prevent certain quantities from being con-

sidered in roots; however this may not stop all such solutions.

EXAMPLES:

> F := [x^2 - 2*x*z + 5, x*y^2 + y*z^3, 3*y^2 - 8*z^3]:

> wsolve(F,[z,y,x]);

{[z, y, x^2 + 5]

[x^2-2*x*z+5, 3*y+8*x, 3*x^6-64*x^5+45*x^4+225*x^2+375]*} *