Review of some Maxima Syntax and Semantics

1. Review of some Maxima Syntax and Semantics

2. Arithmetic and algebra • Exact, unlimited precision • Standard arithmetic operators: + - * / • Use *, not juxtaposition, for multiplication • Use 2 * x, not 2 x • Use ^ for raising to a power • Many algebraic operators: • expand() • factor() • ratsimp • …

3. Execution of statements • Terminate with a semicolon and type <enter> in XMaxima • Terminate with a semicolon and type <shift-enter> in wxMaxima • Use a $ instead of a semicolon to suppress output

4. Variables and constants • Easy to name a variable and assign a value to it • Examples: x:3; abc:4! ; z3: 7 ; • Use % with standard constants • %pi, %e

5. Functions • Built-in functions are always in lower case: • sin, cos, exp, … • sin(%pi/2), log(%e^x) • Use sin(%pi/2) not Sin(%pi/2) • Maxima is case-sensitive

6. Assignments to variables, constants, and functions • x: 3; • z: x + y/2; • f(x,y,z) := x + 2 *y + 3 *z; • g(w) := w/2; • wow(a) := sin(%pi* a);

7. Formal and actual arguments • f(x,y,z) := x + 2 *y + 3 *z^2;

8. Formal and actual arguments • f(x,y,z) := x + 2 *y + 3 *z; Function definition

9. Formal and actual arguments • f(x,y,z) := x + 2 *y + 3 *z; Function definition Formal arguments

10. Formal and actual arguments • f(x,y,z) := x + 2 *y + 3 *z; • f(Fred, Ethel, 7) has the value Fred + 2 * Ethel + 3 *7 Function definition Formal arguments Actual arguments

11. Lists and arrays • Both data structures are needed in Maxima • There are drop-down menus in wxMaxima to help with creation of either lists or arrays.

12. Lists in Maxima

13. Lists in Maxima Remove the %

14. Can also use the command makelist(i, i, 1, 20); to get the output [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] Also, A: makelist(i, i, 1, 20); assigns the result to the list named A

15. Can use lists for the polynomial algebra exercise Plus(p1, p2) := p1 + p2;(I used upper case to denote a user-defined function) Similarly, we need a function for subtracting Minus(p1,p2):= p1 – p2; • Remember, we needed to have the lists be the same length when adding or subtracting • Do this by appending [0] as much as necessary

16. Some useful array functions

17. Arrays in Maxima • Creation, other operations • Max # of dimensions is 5 (system limit) • Arrays and matrices are the same in Maxima • Unlike most programming languages, vectors are not precisely one-dimensional arrays • Vectors are akin to their use in graphics and mechanics for 2- and 3-d drawing

18. Two ways to create matrices in Maxima • Select Enter from the Algebra menu

20. Operations on arrays • They can be created, deleted, and have their entries listed • They can be added, subtracted, and multiplied by numbers and simple variables (scalars). • As with lists, two arrays must have the same size to be operated on together.

21. One way to create them

23. Other ways to create arrays • array(B,20); • C: make_array( any , 20); • Array(D, 20, 10); • E: make_array( any, 20, 10);

24. Other ways to create arrays array(B,20); C: make_array( any , 20); array(D, 20, 10); E: make_array( any, 20, 10);

26. Array entries • Array entries can be accessed by their indicies. • Warning: make sure each index stays within the appropriate range limit. • Often this will require programming.