maple-1

Basic Maple Commands Command Description 1. General Commands and Conventions P i,exp(1),I the constants π,eandi f(a) evaluating a function fata; e.g. sin(P i) ; command end/result displayed : ” ” /result not displayed % output of previous line cursor on name , click on help help for name settime :=time ();expression ; time ()−settime ;to get elapsed time for computing an expression a:=expression ; assignment a+b, a−b, a∗b, a/b Addition, subtraction, mulitplication, division of a byb aˆn; n-th power of a sqrt(a); the (exact) square root of a evalf (expression, n ); numerical value of expression ton-digit accuracy evalb (a=b); logical comparison (gives true orfalse ) a[n]; n-th element of list a plot(expression, x =a..b); 2-dim plot of expression forxbetween aandb plot3d(expr, x =a..b, y =c..d); 3-dim plot of expr forxbetween aandbandybe- tween candd f:=x−> expr definition of a one-variable function f(x) f:= (x, y, . . . )−> expr definition of multi-variable function f(x, y, . . . ) a:=proc(x, y)local z, w ;...;end; definition of subroutine a 2. Elementary Number Theory iquo(a, b); or floor (a/b); integral part of the quotient a/b irem (a, b); or modp (a, b); remainder of division of abyb frac (x); the fractional part of x igcd(a, b); the gcd of aandb igcdex (a, b,/primex/prime,/primey/prime); the extended gcd x;y; to extract the values of the above extended gcd ithprime (n); then-th prime number isprime (n); test whether or not nis prime (gives true orfalse ) ifactor (n); factor ninto its prime factors a&∧n mod m ; orP ower (a, n)mod m ; compute anmod mefficiently mpl–1 Command Description 3. Sets and Lists: Basic Structure s:={1,2,3,4,5}; defines a set s: an unordered sequence of elements a:= [1 ,2,3,4,5]; defines a list a: an ordered sequence of elements s:={seq(f, i= 1..5)}; create the set sconsisting of the elements f(1),. . . , f(5); here fis an expression (depending on i) a:= [seq(f, i= 1..5)]; create the list aconsisting of the elements f(1), . . . , f(5); here fis an expression (depending on i) nops (a); the number of elements in list a a[i] the ith element of the list a a[i..j] or [ op(i..j, a )] the list consisting of elements ithrough j(inclusive) a[select (k−> k < m or k > n , 1..nops (a))];listawith elements mthrough ndropped member (e, a); test whether eoccurs in list a(true orfalse ) member (e, a,/primep/prime);p; the position(s) at which eoccurs in a type(s, set ); check whether sis a set (has type “set”); gives true orfalse type(a, list ); check whether sis a list (has type “list”); gives true orfalse 4. Operations on Sets and Lists s:=convert (a, set ); convert a list to a set a:=convert (s, list ); convert a set to a list s union t ; or ` union `(s, t, . . . ) combine sets s,t, . . . , removing repeated elements s intersect t ; intersection of sets sandt s minus t the set of elements which are in sbut not in t [op(a), op(b), . . .] concatenate (join) the lists a, b, . . . a:= [e, op(a)]; add element eat the beginning of list a a:= [op(a), e]; add element eat the end of list a a:=subsop (i=e, a); replace the ith element of the list abye a:=subsop (i=NULL, a ); delete ith element from list a [op(a[1..n−1]), e, op (a[n..nops (a)])]; insert eat position nin list a sort(a); sort the elements of list a(into a standard order) [select (bool, a )]; list consisting of the elements of afor which the boolean-valued function bool is true map(f, a); apply the function fto each element of the list a mpl–2 Command Description 5. Character Strings str:= ”T his is a string ”; defining a character string length (str); the number of characters in a string substring (str, m..n ); extract a substring from string strstarting with the mth and ending with the nth character [seq(substring (str, k..k ), k= 1.. length (str)]give the list of characters in a string searchtext (st, str ) find the place where stoccurs in string str cat(s1, s2, . . .) join the strings s1,s2, . . . together convert (expr, string ); convert an expression to a string (textual form) type(str, string ) check whether stris a string ( true orfalse ) 6. Boolean expressions b:=true;b:=false ; assigning true/false to the variable b =, <>, <, < =, >, > = relation operators (equal, not equal, less than, etc.); can be used to form boolean expressions and, or, not logical operators ( →boolean expressions) evalb (bool) evaluate the boolean expression bool (gives true or false ) type(b, boolean ) check whether bis a boolean expression ( true or false ) 7. Looping control for i to m do ;expr ;od; evaluate expr repeatedly with ivarying from 1 to m in steps of 1 for i from n to m by s do ;expr ;od;evaluate expr repeatedly with ivarying from ntom in steps of s while test do ;expr ;od; evaluate expr until test becomes false for i from n to m by s while test do;expr ;od;evaluate expr repeatedly with ivarying from n to m in steps of sas long as test is true RET URN (expr ) or return (expr ) (explicit) return from a subroutine, assigning the value expr to the subroutine 8. Conditionals if test then statmt fi ; execute the statement (sequence) statmt only if test is true if test then statmt 1else statmt 2fi;execute the statement (sequence) statmt 1iftest is true, otherwise execute statmt 2 mpl–3 Command Description 9. Complex Numbers z:=x+y∗I; defining a complex number abs(expr ); the absolute value of expr argument (expr ) the argument of expr Re(expr );Im(expr ); the real and imaginary part of expr conjugate (expr ); the complex conjugate of expr evalc (expr ) evaluating an expression (as a complex number) convert (expr, polar ) convert expr to its polar form type(expr, complex ) check that expr has type “complex” 10. Polynomials f:=x∧n+a1∗x∧(n−1) + . . .; defining a polynomial f=f(x) (assuming that xhas no value) type(f, polynom (integer, x )) check that fis an integer polynomial in x degree (f, x) degree of finx coeff (f, x, n ) extract the coefficient of xninf coeffs (f, x) list of coefficients of f(x) lcoeff (f, x) the leading (highest) coefficient of f(x) tcoeff (f, x) the constant (trailing) coefficient of f(x) collect (f, x) collect all coefficients of fwhich have the same pow- ers in x expand (expr ) distribute products over sums sort(f) sort into decreasing order subs(x=a, f) evaluate f(x) atx=a Eval (f, x=a)mod p ; evaluate f(x) (mod p) atx=a f mod n ; reduce the coefficients of fmodulo n quo(f, g, x );rem(f, g, x ); the quotient and remainder of division of fbyg (viewed as polynomials in x) gcd(f, g, x ) the greatest common divisor of f(x) and g(x) gcd(f, g, x,/primes/prime,/primet/prime) the extended Euclidean algorithm of f(x) and g(x); i.e.s,tsatisfy f∗s+g∗t=g:=gcd(f, g) factor (f) factor finto its irreducible factors F actor (f)mod p factor fmodulo p roots (f) find the rational roots of f interp (x, y, t ) The Lagrange Interpolation polynomial mpl–4