Roots of a function: Difference between revisions

=={{header|Mathematica}}==

There are multiple obvious ways to do this in Mathematica.

===Solve===

This requires a full equation and will perform symbolic operations only:

In[1]:= Solve[x^3-3*x^2+2*x==0,x]

Out[1]= {{x->0},{x->1},{x->2}}

===NSolve===

This requires merely the polynomial and will perform numerical operations if needed:

In[2]:= NSolve[x^3 - 3*x^2 + 2*x , x]

Out[2]= {{x->0.},{x->1.},{x->2.}}

(note that the results here are floats)

===FindRoot===

This will numerically try to find one(!) local root from a given starting point:

In[3]:= FindRoot[x^3 - 3*x^2 + 2*x , {x, 1.5}]

Out[3]= {x->0.}

In[4]:= FindRoot[x^3 - 3*x^2 + 2*x , {x, 1.1}]

Out[4]= {x->1.}

(note that there is no guarantee which one is found).

===FindInstance===

This finds a value (optionally out of a given domain) for the given variable (or a set of values for a set of given variables) that satisfy a given equality or inequality:

In[5]:= FindInstance[x^3 - 3*x^2 + 2*x == 0, x]

Out[5]= {{x->0}}

===Reduce===

This will (symbolically) reduce a given expression to the simplest possible form, solving equations and performing substitutions in the process:

In[6]:= Reduce[x^3 - 3*x^2 + 2*x == 0, x]

Out[6]= x==0||x==1||x==2

(note that this doesn't yield a "solution" but a different expression that expresses the same thing as the original)