When you define a complicated function, you will often want to let some of the arguments of the function be "optional". If you do not give those arguments explicitly, you ...

lhs ^= rhs assigns rhs to be the value of lhs, and associates the assignment with symbols that occur at level one in lhs.

Since lists are just a particular kind of expression, it will come as no surprise that you can refer to parts of any expression much as you refer to parts of a list. This ...

Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

PermutationGroup[{perm_1, ..., perm_n}] represents the group generated by multiplication of the permutations perm_1, ..., perm_n.

SetField[obj@field, val] sets a value of an object field.

GroupGenerators[group] returns a list of generators of group.

Union[list_1, list_2, ...] gives a sorted list of all the distinct elements that appear in any of the list_i. Union[list] gives a sorted version of a list, in which all ...

f /: lhs := rhs assigns rhs to be the delayed value of lhs, and associates the assignment with the symbol f.