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Clear

Before we can really begin working with Mathematica we also need to discuss the function Clear , which can be a life-saver.

It just removes any definitions we’ve given to a symbol, which can be a bigger deal than one might think. Consider the following case:

aVariableIUsedBefore=1000;

aVariableIUsedBefore[x_]:=x*10;

Notice we get an error because the way Mathematica reads this, we’re trying to assign a function to the number 1000.

Here, though, all we need to do is use Clear and we’re good to go.

Clear[aVariableIUsedBefore]

Sometimes we’ve made a lot of definitions and we want to Clear them all, just to prevent hard to find errors from cropping up. In this case we can do the following:

Clear["Global`*"]

What this does is removes all the definitions for any symbol that looks like Global`symbolName which is usually every symbol we’ve defined.

Sometimes we want to protect some symbols, like fundamental constants, from being erased. In this case we just need to make a symbol that doesn’t look like Global`symbolName . A useful way to do this is to put the type of thing it is before it:

Constant`PlanckConstant = 6.626*10-34 (*J×s*);

This sort of thing is discussed more at length in the Contexts section, but first let’s just see that this does what we want it to. First let’s define a bunch of things:

a = 100;
b = 2.50;
c[x_] = RandomReal[]*x;
x[x_] := x[x];

a
b
c[10]
x[10]

(*Out:*)

100

(*Out:*)

2.5`

(*Out:*)

9.548010769916973`

(*Out:*)

10[10]

And now we’ll clear them:

Clear["Global`*"]

a
b
c[10]
x[10]

(*Out:*)

a

(*Out:*)

b

(*Out:*)

c[10]

(*Out:*)

x[10]

But our constant is fine:

Constant`PlanckConstant

(*Out:*)

6.6260000000000015`*^-34

And for those who don’t want to type out a long name every time they use this constant in a problem, here’s a trick: use some variable just for the problem to which you assign the value of the constant. e.g:

Constant`SpeedOfLight=3*108(*m/s*);

h = Constant`PlanckConstant;
c = Constant`SpeedOfLight;
λ = 1*10^-3 (*m*);

h*c/λ (*J*)

(*Out:*)

1.9878000000000004`*^-22

Then just clear all of this before starting the next problem:

Clear["Global`*"]

And now none of that can leak into the next problem:

h
c
λ

(*Out:*)

h

(*Out:*)

c

(*Out:*)

λ