1. Enter expressions in Maple: > Enter the Maple input, followed by either a semicolon or a colon. If the input ends with a semicolon, the result is usually displayed. If the input ends with a colon, the result is not displayed. > Press the Enter key. 2. Assigning Expressions to Names You can assign a name to a Maple expression so that you can use the expression again in subsequent calculations by refering to their names.You can also assign names to equations. 3. Execute a line: > Place the cursor in any Maple input in the line. > Press the Enter key. 4. Compute or recompute the entire Maple worksheet when you have changed expressions that affect subsequent Maple commands. >From the Edit menu, select Execute, and then Worksheet OR > Click on !!! from the toolbar menu 5. Find and replace text and input in a active worksheet: > From the Edit menu, select Find. > In the Find box, enter the text or input you want to search for. > In the Replace box, enter the replacement text or input. > Click Change to change the current occurrence. Click Change All to change all occurrences within the current worksheet. 6. The Repetition Statement (for...while...do) The repetition statement provides the ability to execute a statement sequence repeatedly, either for a counted number of times (using the for...to clauses) or until a condition is satisfied (using the while clause). For more information see Maple Help. 7. Explicit return from a procedure: RETURN(expr) will make expr available as input for other computations. 8. Extract operands from an expression: op(i,e) OR op(i..j,e) OR op(e) OR op(list,e) where i, j - integers indicating positions of operands e - expression list - list of integers indicating positions of operands at increasing nesting levels of an expression. 9. Returning the number of operands in an expression: nops(e) where e is an expression. 10. Returning the length of an object: length(expr) where expr is an expression. 11. Converting an expression to a string convert(expr, string) 12. Evaluating expression as a boolean expression: evalb(x) The return values are true, false, and FAIL. 13. The " with " command makes the short form names of the functions of a Maple package available at the interactive level. We will use with(numtheory): 14. Calling a procedure: proc (argseq) where argseq is the formal parameter name. 15. The Selection Statement ( if ... then): if <conditional expression> then , <statement sequence> . . . end if: (or fi:) 16. Concatenating expressions: cat(a,b,c,....) where a,b,c,....are any expressions Note: The cat function is commonly used to concatenate strings and names together. 17. Printing of expressions: print(expr); 18. Printing of strings: printf("str...\n"); where str is a string. 19. Unassigning all the unevaluated names given as input: unassign('name'); 20. Integer factorization ifactor(n); OR ifactors(n);. See Maple Help for more information. 21. Computing a regular or simple continued fraction expansion: cfrac(n); where n can be a rational, float, algebraic, transcendental, real, or complex number 22. Solve equations for integer solutions: isolve(eq); where eq is a set of equations or single equation. 23. Determining the smallest prime that is larger than n: nextprime(n); 24. Determining the largest prime that is less than n: prevprime(n); 25. Computing the Legendre value: legendre(a, p); where a is an integer and p is a prime. 26. Primality test: isprime(n); where n is integer. It returns false if n is shown to be composite, otherwise it returns true. 27. Computing an integer approximation the nearest integer to the square root of x: isqrt(x); where x is an integer. 28. Solving equations in Z (set of integers) mod m msolve(eq, m); where eq is a set of equations or single equation and m is an integer. 29. Computing the totient function of n: phi(n); where n is an integer. 30. Computing a primitive root > primroot(g, n) will compute the first primitive root of n that is greater than g > primroot(n) will return the smallest primitive root of the number n. 31. Finding the greatest integer less than or equal to a number floor(x); where x is a number32. Finding the smallest integer greater than or equal to a number: ceil(x); where x is a number 33. Computing the greatest common divisor of two numbers: gcd(a,b); 34. Computing the set of prime factors of an integer argument n: factorset(n); 35. Chinese Remainder Algorithm: chrem(u, m); where u is a list [u_1,..., u_n] of numbers and m is a list of moduli [m_1,..., m_n]