# # $Id: bivariat.dem%v 3.38.2.56 1993/01/22 02:44:12 woo Exp woo $ # # This demo is very slow and requires unusually large stack size. # Do not attempt to run this demo under MSDOS. # # the function integral_f(x) approximates the integral of f(x) from 0 to x. # integral2_f(x,y) approximates the integral from x to y. # define f(x) to be any single variable function # # the integral is calculated as the sum of f(x_n)*delta # do this x/delta times (from x down to 0) # f(x) = exp(-x**2) delta = 0.2 # delta can be set to 0.025 for non-MSDOS machines # # integral_f(x) takes one variable, the upper limit. 0 is the lower limit. # calculate the integral of function f(t) from 0 to x integral_f(x) = (x>0)?integral1a(x):-integral1b(x) integral1a(x) = (x<=0)?0:(integral1a(x-delta)+delta*f(x)) integral1b(x) = (x>=0)?0:(integral1b(x+delta)+delta*f(x)) # # integral2_f(x,y) takes two variables; x is the lower limit, and y the upper. # claculate the integral of function f(t) from x to y integral2_f(x,y) = (xwill result in (gif mode)y)?0:(integral2(x+delta,y)+delta*f(x)) set autoscale set title "approximate the integral of functions" set samples 50 plot [-5:5] f(x) title "f(x)=exp(-x**2)", 2/sqrt(pi)*integral_f(x) title "erf(x)=2/sqrt(pi)*integral_f(x)"

f(x)=sin(x) plot [-5:5] f(x) title "f(x)=sin(x)", integral_f(x)will result in (gif mode)

set title "approximate the integral of functions (upper and lower limits)" f(x)=(x-2)**2-20 plot [-10:10] f(x) title "f(x)=(x-2)**2-20", integral2_f(-5,x)will result in (gif mode)

f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5 plot [-10:10] f(x) title "f(x)=sin(x-1)-0.75*sin(2*x-1)+(x**2)/8-5", integral2_f(x,1)will result in (gif mode)

# # This definition computes the ackermann. Do not attempt to compute its # values for non integral values. In addition, do not attempt to compute # its beyond m = 3, unless you want to wait really long time. ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1)) set xrange [0:3] set yrange [0:3] set isosamples 4 set samples 4 set title "Plot of the ackermann function" splot ack(x, y)will result in (gif mode)

set xrange [-5:5] set yrange [-10:10] set isosamples 10 set samples 100 set key 4,-3 set title "Min(x,y) and Max(x,y)" # min(x,y) = (x < y) ? x : y max(x,y) = (x > y) ? x : y plot sin(x), x**2, x**3, max(sin(x), min(x**2, x**3))+0.5will result in (gif mode)

# # gcd(x,y) finds the greatest common divisor of x and y, # using Euclid's algorithm # as this is defined only for integers, first round to the nearest integer gcd(x,y) = gcd1(rnd(max(x,y)),rnd(min(x,y))) gcd1(x,y) = (y == 0) ? x : gcd1(y, x - x/y * y) rnd(x) = int(x+0.5) set samples 59 set xrange [1:59] set auto set key set title "Greatest Common Divisor (for integers only)" plot gcd(x, 60)will result in (gif mode)

set xrange [-10:10] set yrange [-10:10] set auto set isosamples 10 set samples 100 set title ""

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