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# evaluate -- evaluate a polynomial system or matrix at a point

## Synopsis

• Usage:
y = evaluate(f,x)
• Inputs:
• f, or
• x, or
• Outputs:
• y, the value f(x)

## Description

Evaluates a PolySystem or a matrix with polynomial entries at a point.

 i1 : R = CC[x,y]; S = polySystem {x^2+y^2-6, 2*x^2-y}; i3 : p = point {{1.0+3*ii,2.3+ii}}; i4 : evaluate(S,p) o4 = | -9.71+10.6ii | | -18.3+11ii | 2 1 o4 : Matrix CC <-- CC 53 53 i5 : evaluate(jacobian S, p) o5 = | 2+6ii 4.6+2ii | | 4+12ii -1 | 2 2 o5 : Matrix CC <-- CC 53 53

## Ways to use evaluate :

• evaluate(Matrix,AbstractPoint)
• evaluate(Matrix,Matrix)
• evaluate(PolySystem,Matrix)
• evaluate(System,AbstractPoint) -- see System -- a system of functions
• evaluate(System,AbstractPoint,AbstractPoint) -- see System -- a system of functions
• evaluate(System,Matrix) -- see System -- a system of functions
• evaluate(System,Matrix,Matrix) -- see System -- a system of functions

## For the programmer

The object evaluate is .