int Global_Positive_Bound_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound); int Global_Negative_Bound_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound);with:

`Degree`: degree of the polynomial`Coeff`: the`Degree+1`coefficients of the polynomial in increasing degree`Bound`: the bound on the positive or negative roots

- if a bound have been previously determined, then the step
size is fixed to except if the global variable
`Step_Laguerre_Interval`has been defined to be a double not equal to 0, in which case this variable is used as the step size. - if a bound as not been determined the step size is fixed to 1
except if the global variable
`Step_Laguerre_Interval`has been defined to be a double not equal to 0, in which case this variable is used as the step size. - if the step if lower than the global variable
`Min_Step_Laguerre_Interval`(which is 0.1 by default) the step is substituted by`Min_Step_Laguerre_Interval`

int Global_Positive_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff, INTERVAL &Lower,INTERVAL &Upper); int Global_Negative_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff, INTERVAL &Lower,INTERVAL &Upper);where

Both procedures for real roots have been regrouped in

void ALIAS_Find_Bound_Polynom(int Degree, INTERVAL_VECTOR (* TheCoeff)(INTERVAL_VECTOR &), INTERVAL_VECTOR &PALL,INTERVAL &Space, INTERVAL &Bound)where

`PALL`: the first component is the bound for the real roots the polynomial while the following are the value of the parameters for which the bounds will be obtained`Space`: a default bound for the real roots; may be used to indicate that we are looking only for bounds on the positive or negative real roots by specifying a positive or a negative lower bound`Bound`: bounds for the real roots