MAPLE library for the Interval Solver

`cout(eq)`: estimates the cost of the computation of`eq`in terms of number of arithmetic operations. This a rather rough approximation: it just compute the total number of addition, multiplication and function calls without any weight between these operators.`minimal_cout(eq)`: returns an expression equivalent to`eq`but with a minimal cost of computation. Basically it consider the expanded form of the equation and compute its computational cost using the`cout`procedure. Then it consider the Horner forms of the equation using all possible ordering of the unknowns (if you have up to 6 unknowns). The cost of these forms are computed and as soon as a form as a lower cost then it is stored as the potential return for the function. If two forms have equal cost, then the form with the lower number of operations (obtained through the`nops`procedure) is retained.`write_equation`: this procedure takes as argument an equation or a list of equations and a name. The equation will be written in a minimal form in the formula file defined by the name`write_gradient_equation`: this procedures takes as as argument an equation or a list of equations and a name. The gradient of the equations in minimal form will be written in the formula gradient file defined by the name. If no third argument is provided the ordering of the gradient matrix with respect to the unknowns will be the one provided by the MAPLE procedure`indets`. A third argument may be provided and should be a list of unknown names which will be used for the ordering of the gradient matrix (i.e. if the list is`[x1,x2,x3]`for the equation`eq`the first equation will be d`eq`/d`x1`, the second d`eq`/d`x2`..). A fourth argument may be the list of unknowns and is used for parametric system for which the number of undefined variables may be larger than the number of unknowns (otherwise the procedure will return an error message indicating that the equation has more indeterminate than the number of unknowns given in the third argument).`write_hessian_equation`: a similar procedure than for the gradient except it computes the hessian matrix of the equations

readlib(lib_IS): eq1:=y**2*z+2*x*y*t-2*x-z: eq2:=-x**3*z+4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2: eq3:=2*y*z*t+x*t**2-x-2*z: eq4:=-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t-10*t**2+2: write_equation([eq1,eq2,eq3,eq4],"fcap"): write_gradient_equation([eq1,eq2,eq3,eq4],"gcap",[x,y,z,t]): write_hessian_equation([eq1,eq2,eq3,eq4],"hcap",[x,y,z,t]):The formula file for the 4 equations will be written in the file