Mathematica
Tips on Syntax

1. Commands (function names) are capitalized

e.g.,   Sqrt,   ArcTan,   Pi,   Solve,   ListPlot3D

2. Parameters are put in square brackets, e.g.,

Cos[x],         Plot[ Sin[x^2], {x,0,5} ]

3. Lists (esp. vectors, matrices) appear in curly brackets, e.g.,

{a, b, 17},        { {1,0}, {0,1} }

4. Parentheses are for algebraic grouping; e.g.,

(x+y)^3,        (4Pi-x)/(x y + 1)

5. Double square brackets indicate an index.

For example, if       matrix = {{a, b}, {c, d}}
then

• the first row, {a,b}, is   matrix[[1]]
• the first column, {a,c}, is   Transpose[matrix][[1]]     or     matrix[[All,1]]
• element   b   is       matrix[[1,2]]     or     matrix[[1]][[2]]

6. ``='' indicates value assignment, ``=='' indicates equality, and ``!='' indicates inequality:

equation1 = x + 3y == 8

solution = Solve[ { x+3y==8, 2x-y==7 }, {x,y} ]

If[ v != w, Print["the two values are not equal"]]

7. Multiple commands can be separated by a semicolon, e.g.,

a=3 ; b=4 ; c=a+b

and text output is suppressed if a command is followed by a semicolon, e.g.

x = N[Pi,9999]; (x is defined, but the value is not displayed)

8. Functions which take only one parameter can appear as postfix commands using `//', e.g.,

Sqrt[2] // N      or      {{a,b}, {c,d}} // MatrixForm

9. Multiplication is indicated by `*' or by juxtaposition, but be sure to separate variable names by a space, e.g.,

n * Pi     or     n Pi     but not     nPi     (however, 4Pi is OK)

10. Matrix multiplication is indicated by `.', e.g.,

Mathematica command	notes
matrA . matrB	# of columns in A must equal # of rows in B
matr . vec	# of columns in A must equal # of elements in v
vec . matr	v is automatically transposed: vtA
vecA . vecB	dot product, vectors of equal size

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