solving nonlinear algebraic equations as reader of this book you are probably well into mathematics and often "accusedof being particularly good at "solving equations( typical comment at family dinners!howeveris it really true that youwith pen and papercan solve many types of equationsrestricting our attention to algebraic equations in one unknown xyou can certainly do linear equationsax and quadratic onesax bx you may also know that there are formulas for the roots of cubic and quartic equations too maybe you can do the special trigonometric equation sin cos as wellbut there it (probablystops equations that are not reducible to one of the mentioned cannot be solved by general analytical techniqueswhich means that most algebraic equations arising in applications cannot be treated with pen and paperif we exchange the traditional idea of finding exact solutions to equations with the idea of rather finding approximate solutionsa whole new world of possibilities opens up with such an approachwe can in principle solve any algebraic equation let us start by introducing common generic form for any algebraic equationf xd heref xis some prescribed formula involving for examplethe equation sin cos (cthe author( lingeh langtangenprogramming for computations pythontexts in computational science and engineering doi --