Functions defined in the edit field: Functions of one or up to 10 variables may be defined by the user by entering a definition of the form <function_name>(X1,X2,...):=function_of_X1,X2... in the current edit field. Examples: sinh(X):=(exp(X)-exp(-X))/2 norm(X,Y):=sqrt(X*X+Y*Y) Fisher(r):=0.5*log((1+r)/(1-r)) Roots of equation X^2+P*X+Q=0: Root1(P,Q):=-P/2+S(P,Q) S(P,Q):=sqrt(P*P/4-Q) Root2(P,Q):=-P/2-S(P,Q) The Least Common Denominator: lcd(u,v):=u*v/gcd(u,v) Any function defined in such a way may be used as any standard function. Examples: sinh(1)=1.1752011936 norm(12,norm(3,4))=13 Root1(1,-6)=2 Root2(1,-6)=-3 lcd(144,240)=720 Recursive functions: By means of the if()then()else() structure recursive definitions for functions may given as follows: factorial(N):=if(N=1)then(1)else(N*factorial(N-1)) Serial expansion of the exponential function: expn(X,N):=if(N=0)then(1)else(expn(X,N-1)+term(X,N)) term(X,N):=if(N=1)then(X)else(term(X,N-1)*X/N) Examples: factorial(7)=5040 expn(1,20)=2.7182818285 ........................................................................ Since recursive computations take much space and time, it is more efficient to use the 'for' statement for definitions above: factorial(N):=for(I=1)to(N)product(I) expn(X,N):=for(I=0)to(N)sum(X^I/factorial(I)) Another way to speed up recursive computation is to employ a `remember' option (see next page). ................................................................................ A recursive function can also be defined as follows: factorial(N)|=if(N=1)then(1)else(N*factorial(N-1)) See a '|' instead ':' in the definition! Then each numerical value once obtained in recursion process is saved temporarily in a table and instead of a recursion step a table-lookup is used in subsequent evaluations. Computation of function values is then much faster. Recursive computing requires much stack memory and may lead to a stack overflow. The stack size given for the Survo Editor is currently 10'000'000 bytes. The system parameter check_stack (in SURVO.APU) determines the maximum size allowed in editorial arithmetics. The default setting is check_stack=5000000 and it can be changed temporarily by the SYSTEM command. E = More information on editorial computing

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