!Chapter 1.  Program ITERLIN.TRU
CLEAR                             !Clears the screen
!Iterate the function f(x) = ax + b  n  times
PRINT "Iterate the function  f(x) = ax + b"
INPUT PROMPT "What is a? ": a
INPUT PROMPT "What is b? ": b
INPUT PROMPT "What is the initial value of x? ": x
INPUT PROMPT "How many iterations? ": n
PRINT "The initial value chosen was  x = "; x
FOR I = 1 to n
    LET y = a * x + b
    PRINT  using "i = ###   y = ##.#########":i,y
    LET x = y
NEXT i
END


=======================
!Chapter 2.  Program DIFFER.TRU
! Program: DIFFER.TRU
! Program revision from book's version: 6/23/97
! This program finds differences of distinct non-zero squares
! mod m and counts repetitions

! sqlst(v) counts # times v occurs as square mod m
! difflst(v) counts # times v occurs as diff. of squares 
! sq(i) is the ith distinct non-zero square mod m
DIM sqlst(0 to 1000)
DIM difflst(0 to 1000)
DIM sq(1000)
DO
   CLEAR
   !initialize the counters to 0
   FOR i=0 to 1000
       LET sqlst(i)=0
       LET difflst(i)=0
       IF i>0 then LET sq(i)=0
   NEXT i

   PRINT "What is the modulus m:";
   INPUT m
   FOR i = 1 TO m - 1
       LET value = MOD(i * i,m)
       LET sqlst(value) = sqlst(value) + 1
   NEXT i

   ! Listing and counting distinct non-zero squares mod m
   PRINT "The non-zero squares are"
   ! numsq counts distinct non-zero squares mod m
   LET numsq = 0                  !initialize numsq
   FOR v = 1 TO m - 1
       IF sqlst(v) > 0 THEN
          PRINT v;
          LET numsq = numsq + 1
          LET sq(numsq) = v       !sq(n)=v makes nth square = v
       END IF
   NEXT v
   PRINT
   PRINT "Number of distinct squares is "; numsq

   PRINT "Press a key to continue";
   GET KEY akey
   ! Creating  and counting all possible differences
   FOR i = 1 TO numsq
       FOR j = 1 TO numsq
           LET value = MOD(sq(i) - sq(j) + m ,m)      !Need value >=0
           LET difflst(value) = difflst(value) + 1
       NEXT j
   NEXT i
   ! Listing distinct differences and counting repetitions
   ! numdiff counts distinct non-zero differences of squares mod m
   LET numdiff = 0
   PRINT "Distinct non-zero differences and number of repetitions of each:"

   FOR v = 1 TO m
       IF difflst(v) > 0 THEN
          LET numdiff = numdiff + 1
          PRINT v, difflst(v)
          IF  MOD(numdiff,18)=0 then
             PRINT "Press a key to continue";
             GET KEY:akey         !freeze action at each screenfull
             PRINT
          END IF
       END IF
   NEXT v
   PRINT "Number of distinct differences:", numdiff
   PRINT "Again (y/n): ";
   GET KEY: AGAIN                 ! Define the variable 'again'
   PRINT chr$(again)
LOOP UNTIL (AGAIN <> 121)         ! 121 is ascii for  y 
END


=======================
! Chapter 2.   Program: SQUARES.TRU
! Computes the distinct squares mod m for 1<m<=1000
! sqlst(v) counts  # times v occurs as square mod m
DIM sqlst(0 to 1000)
CLEAR
PRINT "What is the modulus m";
INPUT m
!sqlst(value) automatically initialized at 0
FOR i = 1 TO m - 1
    LET value = MOD(i * i, m)
    LET sqlst(value) = sqlst(value) + 1
NEXT i
PRINT "The non-zero squares are"
FOR v = 1 TO m - 1
    IF sqlst(v) > 0 THEN PRINT v;
NEXT v
END


=======================
!Chapter 3:   Program: Euclid1.tru
CLEAR
INPUT prompt "a = ": a
INPUT prompt "b = ": b
IF a>b then
   LET u=a
   LET v=b
ELSE
   LET u=b
   LET v=a
END IF
PRINT u,v  ! v <= u
LET k=0
LET r=1
DO while(r>0)
   LET q=int(u/v)
   LET r=u-v*q
   LET oldr=v
   LET u=v
   LET v=r
   PRINT oldr, r
   LET k=k+1
LOOP
PRINT
PRINT "GCD(";a;",";b;") = ";oldr
PRINT "Number of steps was ";k
END


=======================
! Chapter 3.   Program: Euclid2.tru
CLEAR
RANDOMIZE
LET N=10000
LET a=int(1+rnd*N)
LET b=int(1+rnd*N)
IF a>b then
   LET u=a
   LET v=b
ELSE
   LET u=b
   LET v=a
END IF
PRINT u,v
LET k=0
LET r=1
DO while(r>0)
   LET q=int(u/v)
   LET r=u-v*q
   LET oldr=v
   LET u=v
   LET v=r
   PRINT oldr, r
   LET k=k+1
LOOP
PRINT
PRINT "GCD(";a;",";b;") = ";oldr
PRINT "Number of steps was ";k
END


=======================
! Chapter 3.   Program: Euclid3.tru
CLEAR
RANDOMIZE
DIM count(20)
LET N=10000
FOR j=1 to 1000
    LET a=int(1+rnd*N)
    LET b=int(1+rnd*N)
    IF a>b then
       LET u=a
       LET v=b
    ELSE
       LET u=b
       LET v=a
    END IF

    LET k=0
    LET r=1
    DO while(r>0)
       LET q=int(u/v)
       LET r=u-v*q
       LET oldr=v
       LET u=v
       LET v=r
       LET k=k+1
    LOOP
    IF(k<21) then LET count(k)=count(k)+1
NEXT j
PRINT "Steps","Occurrences"
FOR j=1 to 20
    PRINT j,count(j)
NEXT j
END


=======================
! Chapter 3.   Program: Euclid4.tru
CLEAR
RANDOMIZE
DIM count(20)
LET N=10000
FOR j=1 to 1000
    LET a=int(1+rnd*N)
    LET b=int(1+rnd*N)
    IF a>b then
       LET u=a
       LET v=b
    ELSE
       LET u=b
       LET v=a
    END IF

    LET k=0
    LET r=1
    DO while(r>0)
       LET q=int(u/v)
       LET r=u-v*q
       LET oldr=v
       LET u=v
       LET v=r
       LET k=k+1
    LOOP
    IF(oldr<21) then LET count(oldr) = count(oldr)+1
NEXT j
PRINT "GCD","Occurrences"
FOR j=1 to 20
    PRINT j,count(j)
NEXT j
END


=======================
! Chapter 3.   Program: Euclid5.tru
CLEAR
INPUT prompt "a = ": a
INPUT prompt "b = ": b
IF b>a then
   LET c=b
   LET b=a
   LET a=c
END IF
LET a1=a
LET b1=b
LET xold=1
LET yold=0
LET x=0
LET y=1
LET r=1
DO while(r>0)
   LET q=int(a/b)
   LET c=a-q*b
   IF(c=0) then
      PRINT "GCD =";b;" =";a1;"*";x;"+";b1;"*";y
      STOP
   END IF
   LET xnew=xold-q*x
   LET ynew=yold-q*y
   LET xold=x
   LET x=xnew
   LET yold=y
   LET y=ynew
   LET a=b
   LET b=c
LOOP
END


=======================
! Chapter 4.   Program is countmd4.tru   
DEF prime(n)                      ! Returns 1 if n prime, 0 otherwise
    IF n < 2 THEN
       LET p = 0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO UNTIL a > s
          IF n - INT(n/a)*a = 0 then
             LET p=0
             EXIT DO
          END IF
          LET a = a + 1
       LOOP
    END IF
    LET prime = p
END DEF

CLEAR                             ! The program steps begin here
PRINT "Compute pi1(n) and pi3(n).  What is n";
INPUT n

LET pi1 = 0
LET b = 1
DO until 4*b + 1 > n
   IF prime(4*b+1) = 1 then LET pi1 = pi1 + 1
   LET b = b+1
LOOP

LET pi3 = 0
LET c = 0
DO until 4*c + 3 > n
   IF prime(4*c + 3) = 1 then LET pi3 = pi3 + 1
   LET c = c + 1
LOOP

PRINT "pi1 ="; pi1
PRINT "pi3 ="; pi3
END


=======================
! Chapter 4.   Program is countpr1.tru
DEF prime(n)                      ! This function returns 1 if n prime,
    IF n<2 then                   ! and 0 otherwise
       LET p=0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO UNTIL a > s
          IF n - INT(n/a)*a=0 then
             LET p=0
             EXIT DO
          END IF
          LET a = a + 1
       LOOP
       LET prime = p
    END IF
END DEF

CLEAR                             ! The program steps begin here
PRINT "Count primes less than or equal to n.  What is n";
INPUT n
LET m = 2
LET pin =0
DO UNTIL m > n
   IF prime(m) = 1 then LET pin = pin + 1
   LET m = m + 1
LOOP
PRINT "There are";pin;"primes less than or equal to";n
END


=======================
! Chapter 4.   Program is eulerchk.tru
CLEAR
LET q = 41            ! Change this number to change the value of q
PRINT "List numbers from 0 to k for which m^2 + m +";q;"is prime."
INPUT prompt "What is k? ": k
DEF prime(n)                      !returns 1 if n prime, 0 otherwise
    IF n<2 then
       LET p = 0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO UNTIL a > s
          IF MOD(n,a) = 0 then
             LET p=0
             EXIT DO
          END IF
       LET a = a + 1
       LOOP
    END IF
    LET prime = p
END DEF
FOR m = 0 to k
    LET n = m^2 + m + q
    IF prime(n) = 1 then
       PRINT m;
       LET count = count+1
    END IF
NEXT m
PRINT
PRINT "There are ";count; " numbers in this list."
END


=======================
! Chapter 4.   Program is interval.tru
PRINT "Compute pi(k,m) = number of primes in interval [k,m]."
INPUT prompt "What is k? ": k
INPUT prompt "What is m? ": m

DEF prime(n)                      ! Returns 1 if n prime, 0 otherwise
    IF n<2 then
       LET p=0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO UNTIL a > s
          IF n - INT(n/a)*a = 0 THEN
             LET p=0
             EXIT DO
          END IF
          LET a = a + 1
       LOOP
       LET prime = p
    END IF
END DEF

LET b = k
LET count = 0
DO UNTIL b > m
   IF prime(b) = 1 then LET count = count + 1
   LET b = b+1
LOOP
PRINT "There are";count;"primes in the interval"
END


=======================
! Chapter 4.   Program is listprim.tru
CLEAR
PRINT "List primes less than or equal to n.  What is n ";
INPUT n
DEF prime(n)                      ! Returns 1 if n prime, 0 otherwise
    IF n<2 then
       LET p = 0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO until a > s
          IF n-INT(n/a)*a = 0 then
             LET p=0
             EXIT DO
          END IF
          LET a = a + 1
       LOOP
    END IF
    LET prime = p
END DEF
LET m = 1
DO UNTIL m > n
   IF prime(m) = 1 then PRINT m;
   LET m = m + 1
LOOP
END


=======================
! Chapter 4.   Program is mersenne.tru
CLEAR
PRINT "Compute whether 2^p - 1 is prime"
INPUT prompt "What is p? ":p
DEF prime(n)                      ! Returns 1 if n prime, 0 otherwise
    IF n < 2 then
       LET p = 0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO UNTIL a > s
          IF n - INT(n/a)*a = 0 THEN
             LET p=0
             EXIT DO
          END IF
          LET a = a+1
       LOOP
    END IF
    LET prime = p
END DEF
LET n = 2^p -1
IF prime(n) = 1 THEN
   PRINT n;"is a prime."
ELSE
   PRINT n;"is not prime.  "
   PRINT "It is ";a;" times ";n/a
END IF
END


=======================
! Chapter 4.   Program is testprim.tru
PRINT "The function prints 1 if n is prime, 0 if not.  What is n";
INPUT n


DEF prime(n)                      ! Returns 1 if n prime, 0 otherwise
    IF n<2 then
       LET p=0
    ELSE
       LET p =1
       LET a = 2
       LET s = INT(SQR(n))
       DO until a > s
          IF n - INT(n/a)*a = 0 THEN
             LET p=0
             EXIT DO
          END IF
          LET a = a + 1
       LOOP
       LET prime = p
    END IF
END DEF

LET answer = prime(n)
PRINT "The function returns";answer
IF answer = 0 then
   PRINT n;"is not a prime.  It is";a;"x";n/a
ELSE
   PRINT n;"is a prime"
END IF
END


=======================
! Chapter 6.   Program is ran1resp.tru
DIM A(3, 3, 3), B(3, 3, 3), ROW$(3)
RANDOMIZE
LET TrueYes = 1
LET TrueNo = 2
LET Real = 1
LET Decoy = 2
LET Yes = 1
LET No = 2
LET Total = 3
LET ROW$(1) = "REAL    "
LET ROW$(2) = "DECOY   "
LET ROW$(3) = "TOTAL   "
LET C1$ = "           T R U E    Y E S         T R U E   N O       W H O L E   G R O U P"
LET C2$ = "          YES |   NO | TOTAL      YES |   NO | TOTAL      YES |   NO | TOTAL"
LET C3$ = "        ------+------+------    ------+------+------    ------+------+------"

!*****GET STARTING INFORMATION*****
CALL get_start_info(GrpSize,YesInGrp,PrRealQ,PrYesDecoy,NRep,PrntFreq)
!
!*****MAIN LOOP.  EACH TIME THROUGH IS ONE REPETITION OF THE SURVEY*****
FOR Survey = 1 TO NRep
    CLEAR
    MAT A = zer(3,3,3)
    !   First survey the True Yes respondents
    FOR Respondent = 1 TO YesInGrp
        !     * Toss the dime to decide which question:
        IF RND < PrRealQ THEN
           !       * Dime lands Heads -- Answer Real question Yes:
           LET A(TrueYes, Real, Yes) = A(TrueYes, Real, Yes) + 1
        ELSE
           !       * Dime lands Tails -- Answer Decoy question by tossing penny
           IF RND < PrYesDecoy THEN
              !         * Penny lands Heads -- Yes to Decoy question:
              LET A(TrueYes, Decoy, Yes) = A(TrueYes, Decoy, Yes) + 1
           ELSE
              !         * Penny lands Tails -- No to Decoy question:
              LET A(TrueYes, Decoy, No) = A(TrueYes, Decoy, No) + 1
           END IF
        END IF
    NEXT Respondent
    !  Now survey the True No respondents
    FOR Respondent = YesInGrp + 1 TO GrpSize
        !     * Toss the dime to decide which question:
        IF RND < PrRealQ THEN
           !       * Dime lands Heads -- Answer Real question No:
           LET A(TrueNo, Real, No) = A(TrueNo, Real, No) + 1
        ELSE
           !       * Dime lands Tails -- Answer Decoy question by tossing penny
           IF RND < PrYesDecoy THEN
              !         * Penny lands Heads -- Yes to Decoy question:
              LET A(TrueNo, Decoy, Yes) = A(TrueNo, Decoy, Yes) + 1
           ELSE
              !         * Penny lands Tails -- No to Decoy question:
              LET A(TrueNo, Decoy, No) = A(TrueNo, Decoy, No) + 1
           END IF
        END IF
    NEXT Respondent
    !  Get marginal totals for component tables
    FOR I = 1 TO 2
        FOR J = 1 TO 2
            LET A(Total, I, J) = A(TrueYes, I, J) + A(TrueNo, I, J)
        NEXT J
    NEXT I
    FOR I = 1 TO 3
        FOR J = 1 TO 2
            LET A(I, J, Total) = A(I, J, 1) + A(I, J, 2)
            LET A(I, Total, J) = A(I, 1, J) + A(I, 2, J)
        NEXT J
        LET A(I, Total, Total) = A(I, Total, 1) + A(I, Total, 2)
    NEXT I
    !  Update cumulative totals
    FOR I = 1 TO 3
        FOR J = 1 TO 3
            FOR K = 1 TO 3
                LET B(I, J, K) = B(I, J, K) + A(I, J, K)
            NEXT K
        NEXT J
    NEXT I
    !*****Check to see whether to print*****
    IF ABS(Survey - PrntFreq * INT(Survey / PrntFreq)) < .1 THEN
       PRINT
       PRINT USING "REPETITION NUMBER #####": Survey;
       PRINT " of ";NRep
       PRINT C1$
       PRINT C2$
       FOR J = 1 TO 3
           PRINT C3$
           PRINT ROW$(J);
           FOR I = 1 TO 3
               FOR K = 1 TO 2
                   PRINT USING " #### |": A(I, J, K);
               NEXT K
               PRINT USING " ####  ": A(I, J, 3);
               PRINT "   ";
           NEXT I
           PRINT
       NEXT J
       PRINT
       PRINT USING "AVERAGES BASED ON ##### REPETITIONS": Survey
       PRINT C1$
       PRINT C2$
       FOR J = 1 TO 3
           PRINT C3$
           PRINT ROW$(J);
           FOR I = 1 TO 3
               FOR K = 1 TO 2
                   PRINT USING "####.#|": B(I, J, K) / Survey;
               NEXT K
               PRINT USING " ####.#": B(I, J, K) / Survey;
               PRINT "   ";
           NEXT I
           PRINT
       NEXT J
       PRINT "Press any key to continue";
       GET KEY :zz
    END IF
NEXT Survey
ASK  CURSOR nr,nc
SET CURSOR nr ,1
PRINT "=================================================================="
PRINT "Initial conditions were:  "
PRINT "Group Size: ";GrpSize; "  Of these, ";YesInGrp;" were YES"
PRINT "Pr(H) for Dime: ";PrRealQ;" and Pr(H) for Penny: ";PrYesDecoy;
PRINT "  Press 'Q' to Quit";
DO until (Ucase$(chr$(dummy)) = "Q")
   GET KEY: dummy
LOOP
END   !End of the program 

SUB get_start_info(GrpSize,YesInGrp,PrRealQ,PrYesDecoy,NRep,PrntFreq)
    !*****GET STARTING INFORMATION*****
    CLEAR
    PRINT
    PRINT
    PRINT "RANDOMIZED RESPONSE SIMULATION"
    PRINT
    PRINT "First set up the group you will survey:"
    INPUT prompt "  What is the size of the group? ": GrpSize
    INPUT prompt "  How many of these are (true) Yes? ": YesInGrp
    PRINT
    PRINT "Now set up the survey:"
    INPUT prompt "  What is Pr(Real Question), i.e. Pr(H) for the dime? ": PrRealQ
    INPUT prompt "  What is Pr(Yes|Decoy), i.e., Pr(H) for the penny? ": PrYesDecoy
    PRINT
    PRINT "Now set up your simulation:"
    INPUT prompt "  How many times do you want to repeat the survey? ": NRep
    PRINT "  How often do you want to see the results"
    INPUT prompt "   (1=every time, 2=every other time, etc.)? ": PrntFreq
END SUB


=======================
! Chapter 6.   Program is ran2resp.tru
! User-defined functions
DEF Estimate (NYes, GrpSize, PrRealQ, PrYesDecoy)
    LET Estimate = NYes / GrpSize
END DEF

DEF OpChar (Estimate, True)
    LET OpChar = Estimate
END DEF

DEF Toss (PrHead)
    IF (rnd <PrHead) then
       LET Toss = 1
    ELSE
       LET Toss = 0
    END IF
END DEF

RANDOMIZE

!*****GET STARTING INFORMATION*****
CALL get_start_info(GrpSize,YesInGrp,PrRealQ,PrYesDecoy,NRep,PrntFreq)

!*****MAIN LOOP.  EACH TIME THROUGH IS ONE REPETITION OF THE SURVEY*****
LET Sum = 0
FOR Survey = 1 TO NRep
    LET NYes = 0                  !Initialize the number of Yes answers
    !  First survey the True Yes respondents
    FOR Respondent = 1 TO YesInGrp
        LET Dime = Toss(PrRealQ)
        LET Penny = Toss(PrYesDecoy)
        LET NYes = NYes + Dime + (1 - Dime) * Penny
    NEXT Respondent
    !  Now survey the True No respondents
    FOR Respondent = YesInGrp + 1 TO GrpSize
        LET Dime = Toss(PrRealQ)
        LET Penny = Toss(PrYesDecoy)
        LET NYes = NYes + (1 - Dime) * Penny
    NEXT Respondent
    !  Update the sum and print
    LET Sum = Sum + OpChar(Estimate(NYes, GrpSize, PrRealQ, PrYesDecoy), YesInGrp / GrpSize)
    !*****Check to see whether to print*****
    IF ABS(Survey - PrntFreq * INT(Survey / PrntFreq)) < .1 THEN
       PRINT Survey;" of ";NRep; " trials. ";
       PRINT "Result: ";Sum / Survey, " Press a key to continue"
       GET KEY dummy              ! stops here -- waits until a key is pressed
    END IF
NEXT Survey
PRINT "=================================================================="
PRINT "Initial conditions were:  "
PRINT "Group Size: ";GrpSize; "  Of these, ";YesInGrp;" were YES"
PRINT "Pr(H) for Dime: ";PrRealQ;" and Pr(H) for Penny: ";PrYesDecoy
PRINT "              Press 'Q' to Quit";
DO until (Ucase$(chr$(dummy)) = "Q")
   GET KEY: dummy
LOOP
END


SUB get_start_info(GrpSize,YesInGrp,PrRealQ,PrYesDecoy,NRep,PrntFreq)
    !*****GET STARTING INFORMATION*****
    CLEAR
    PRINT
    PRINT
    PRINT "RANDOMIZED RESPONSE SIMULATION"
    PRINT
    PRINT "First set up the group you will survey:"
    INPUT prompt "  What is the size of the group? ": GrpSize
    INPUT prompt "  How many of these are (true) Yes? ": YesInGrp
    PRINT
    PRINT "Now set up the survey:"
    INPUT prompt "  What is Pr(Real Question), i.e. Pr(H) for the dime? ": PrRealQ
    INPUT prompt "  What is Pr(Yes|Decoy), i.e., Pr(H) for the penny? ": PrYesDecoy
    PRINT
    PRINT "Now set up your simulation:"
    INPUT prompt "  How many times do you want to repeat the survey? ": NRep
    PRINT "  How often do you want to see the results"
    INPUT prompt "   (1=every time, 2=every other time, etc.)? ": PrntFreq
END SUB


=======================
! Chapter 9.   Program: param1.tru
! Parametric function plotter with moving cursor 
DEF x(t) = cos(t)                 ! Change as desired
DEF y(t) = sin(t)                 ! Change as desired
! Setting up window boundaries
LET left = -3                     ! Change as desired
LET right = 3                     ! Change as desired
LET bottom = -2.25                ! Change as desired
LET top = 2.25                    ! Change as desired
SET WINDOW left,right,bottom,top
ASK MAX CURSOR mr,mc
LET boxwidth = (right-left)/80    !setting up square moving cursor
LET boxheight = (top-bottom)/60
BOX LINES -boxwidth,boxwidth,-boxheight,boxheight
BOX KEEP -boxwidth,boxwidth,-boxheight,boxheight in box$
SET COLOR "white"
DO
   CLEAR
   PLOT LINES : left,0;right,0
   PLOT LINES : 0,bottom;0,top
   PRINT "x = x(t) as entered"
   PRINT "y = y(t) as entered"
   !********* ADD SPECIAL DATA HERE **********
   !Enter desired speed of plotting
   SET CURSOR 1,30
   INPUT prompt "Enter speed (f/s): ":sp$
   LET spd = 200
   IF sp$ = "s" then LET spd=5
   LET a = 0                      ! Change as desired
   LET b = 2*pi                   ! Change as desired
   LET n = 1000                   ! Change as desired
   LET t = a
   LET h = (b - a) / n
   SET COLOR "yellow"
   FOR k = 1 to n
       LET x1 = x(t)
       LET y1 = y(t)
       ! Draw first box or erase a previous box
       BOX SHOW box$ at x1-boxwidth,y1-boxheight using "XOR"
       LET x2 = x(t+h)
       LET y2 = y(t+h)
       ! Draw next box
       BOX SHOW box$ at x2-boxwidth,y2-boxheight using "XOR" 
       IF mod(k,spd) = 0 then
          PAUSE .0001
       END IF
       PLOT LINES :x1,y1 ; x2, y2
       LET t = t+h
   NEXT k
   ! Draw final box
   BOX SHOW box$ at  x2-boxwidth,y2-boxheight using "OR"
   SET CURSOR mr,1
   SET COLOR "white"
   PRINT "Again (y/n):";
   DO                             ! gets response to the question
      GET KEY :again
   LOOP until ((again=121) or (again=110))  ! until "y" or "n"
LOOP until (again<>121)           ! end when you don't press "y"
END


=======================
!Chapter 10.    Program: ball.tru
RANDOMIZE
PRINT "n is the dimension"
INPUT prompt "What is n? ":n
PRINT "m is the number of points to be chosen in the unit cube"
INPUT prompt "What is m? ":m
LET s = 0
FOR i = 1 TO m
     Let sum = 0
     FOR j = 1 TO n
          LET x = rnd
          LET sum = sum + (x - 1/2) * (x - 1/2)
     NEXT j
     IF sum <= 1/4 then LET s = s+1
NEXT i
PRINT "The volume of the ball is approximately "; s/m
END


=======================
!Chapter 10     ! Program: Integral.tru
DIM Fval(0 to 2000)
! Enter any function  and any interval [a,b] here
DEF f(x) = cos(x)
LET a = 0
LET b = 1.570796                  !approx pi/2
CLEAR
PRINT
INPUT prompt "What is m (a positive integer)? ":m
LET n = 2 * m
LET h = (b - a)/n
! Computing the function at endpoints of subintervals (array)
LET x = a
FOR i = 0 TO n
    LET Fval(i) = f(x)
    LET x = x + h
NEXT i

! Computing the master sum for left, right, and trap sums
LET Sum = 0
FOR i = 0 to m
    LET Sum = Sum + Fval(2 * i)
NEXT i

LET Leftsum = [Sum - Fval(n)] * (2 * h)
LET Rightsum = [Sum - Fval(0)] * (2 * h)
LET Trapsum = [Leftsum + Rightsum]/2

! Computing the midpoint approximation
LET x = a
LET MidTotal = 0
FOR i = 1 to m
    LET MidTotal = MidTotal + Fval(2*i-1)
NEXT i
LET Midsum = MidTotal * (2 * h)

! Computing the Simpson's rule approximation
LET E = 0
IF (m > 1) THEN
   FOR i = 1 to (m - 1)
       LET E = E + Fval(2 * i)
   NEXT i
END IF
LET U = 0
FOR i = 1 to m
    LET U = U + Fval(2 * i - 1)
NEXT i
LET Simpsum = ( Fval(0) + 4 * U + 2 * E + Fval(n) ) * h/3
! Display values
PRINT
PRINT "The left endpoint sum gives:   "; Leftsum
PRINT "The right endpoint sum gives:  "; Rightsum
PRINT "The midpoint sum gives:        "; Midsum
PRINT "The trapezoidal rule gives:    "; Trapsum
PRINT "Simpson's rule gives:          "; Simpsum
END


=======================
! Chapter 10.   Program: Integr-2.tru
DIM Fval(0 to 2000)
! Enter any function  and any interval [a,b] here
DEF f(x) = cos(x)
LET a = 0
LET b = 1.570796  !approx pi/2
! Enter actual value of the integral here
LET Actual = 1

! Lines copied from integral.tru
CLEAR
PRINT
INPUT prompt "What is m (a positive integer)? ":m
LET n = 2 * m
LET h = (b - a)/n
! Computing the function at endpoints of subintervals (array)
LET x = a
FOR i = 0 TO n
    LET Fval(i) = f(x)
    LET x = x + h
NEXT i

! Computing the master sum for left, right, and trap sums
LET Sum = 0
FOR i = 0 to m
    LET Sum = Sum + Fval(2 * i)
NEXT i

LET Leftsum = [Sum - Fval(n)] * (2 * h)
LET Rightsum = [Sum - Fval(0)] * (2 * h)
LET Trapsum = [Leftsum + Rightsum]/2

! Computing the midpoint approximation
LET x = a
LET MidTotal = 0
FOR i = 1 to m
    LET MidTotal = MidTotal + Fval(2*i-1)
NEXT i
LET Midsum = MidTotal * (2 * h)

! Computing the Simpson's rule approximation
LET E = 0
IF (m > 1) THEN
   FOR i = 1 to (m - 1)
       LET E = E + Fval(2 * i)
   NEXT i
END IF
LET U = 0
FOR i = 1 to m
    LET U = U + Fval(2 * i - 1)
NEXT i
LET Simpsum = ( Fval(0) + 4 * U + 2 * E + Fval(n) ) * h/3
! Display values
PRINT
PRINT "The left endpoint sum gives:   "; Leftsum
PRINT "The right endpoint sum gives:  "; Rightsum
PRINT "The midpoint sum gives:        "; Midsum
PRINT "The trapezoidal rule gives:    "; Trapsum
PRINT "Simpson's rule gives:          "; Simpsum

! Display values
PRINT
PRINT "The error in the left endpoint sum is:   "; Leftsum - Actual
PRINT "The error in the right endpoint sum is:  "; Rightsum - Actual
PRINT "The error in the midpoint sum is:        "; Midsum - Actual
PRINT "The error in the trapezoidal rule is:    "; Trapsum - Actual
PRINT "The error in Simpson's rule is :         "; Simpsum - Actual
END


=======================
! Chapter 10.   Program: Monte-1.tru
! Enter a function with 0 <= f(x) <= H on  the interval [a,b]
DEF f(x) = cos(x)
LET a = 0
LET b = 1.570796  ! approx pi/2
LET H = 1
RANDOMIZE    ! User resets the seed
CLEAR
INPUT prompt "What is m? ":m
LET s = 0
FOR i = 1 TO m
    LET x = a + (b - a) * rnd  ! Choose x randomly in [a,b]
    LET y = H * rnd            ! Choose y randomly in [0,H]
    IF (f(x) - y) >= 0 THEN    
       LET s = s + 1
    END IF
NEXT i
LET estimate = H * (b - a) * s / m
PRINT
PRINT "estimate = ";
PRINT estimate
END


=======================
! Chapter 10.   Program Monte-2.tru
! Enter any function  and an interval [a,b]
DEF f(x) = cos(x)
LET a = 0
LET b = 1.570796   !approx pi/2
RANDOMIZE   !lets the user reset the seed
CLEAR
INPUT prompt "What is m? ":m
! Loop here to sum values of f(x)
LET sum = 0
FOR i = 1 TO m
    LET x = a + (b - a) * rnd  !choose x randomly in [a,b]
    LET sum = sum + f(x)
NEXT i
LET estimate =  (b - a) * sum / m
PRINT
PRINT "estimate = "; estimate
END


=======================
! Chapter 11.   Program: Euler.tru 
!Variable L holds the natural logarithm
!Initialize: n to 0, SUM to 0, L to 0, DIFF to 0
LET n=0
LET SUM = 0
LET L = 0
LET DIFF = 0
CLEAR                             !Clears the screen
PRINT "A reasonable answer here is 20."
INPUT prompt "How many rows do you want to see at a time? ": ROWS
IF ROWS < 1 then STOP             !Assures value is at least 1
CALL heading
PRINT
DO
   LET n = n+1
   PRINT using "#####":n;
   LET SUM = SUM + 1/n            ! the SUM is accumulating, 
   ! adding 1/n in the loop
   PRINT using "  ##.############":SUM;
   PRINT " ";
   LET L=log(n+1)
   PRINT using "  ##.############":L;
   PRINT " ";
   LET DIFF=SUM-L
   PRINT using "  ##.############":DIFF
   IF mod(n, ROWS) = 0 then
      IF ROWS > 22 then CALL heading
      PRINT "Press 'q' to exit the program, ENTER to continue";
      GET KEY:quitter             !to pause for an input 
      IF quitter = 113 then       !checks for "q" pressed
         STOP                     !gets you out of the loop
      ELSE
         CLEAR                    ! Clears the screen
         IF ROWS <= 22 then CALL heading
      END IF                      ! This ends the IF A$ = "q" then...
   END IF                         ! This ends the IF MOD(N,ROWS) = 0 then
LOOP                              ! This ends the "do" loop

SUB heading
    PRINT "==================================";
    PRINT "=================================="
    PRINT "    n      SUM(n)            ";
    PRINT "LN(n+1)          DIFF=SUM-LN"
    PRINT "==================================";
    PRINT "=================================="
END SUB
END


=======================
! Chapter 13.   Program: Solver.tru
CLEAR 
! Iterate the function f(x) = cos(x)  n  times 
DEF f(x) = cos(x)
INPUT PROMPT "What is the initial value of x? ": x 
INPUT PROMPT "How many iterations? ": n 
PRINT "The initial value chosen was  x = "; x 
FOR I = 1 to n
     LET y = f(x) 
     Print i, y
     LET x = y 
NEXT i 
END


=======================
!Chapter 14.     Program: diagram.tru
!The Feigenbaum Diagram for f(x) = Ax(1 - x)
!The vertical axis shows the values of the iterates
!The horizontal axis shows values of A between 0 and 4
SET WINDOW -.2, 4.5, -.2, 1.2
DEF fnf(x) = A*x*(1 - x)

!This part draws axes 
PLOT LINES: 0, -.1; 0, 1.2   ! y-axis
PLOT LINES: -.1,0; 4.5,0     ! x-axis

!The outside loop (indexed by i) varies A
!The inside loop (indexed by j) computes 100 iterates of f(x) = Ax(1-x)

FOR i = 1 to 100
    LET A = 4*i/100
    LET x = .1
    FOR j = 1 TO 100
        LET x = fnf(x)
        !Only the last 50 iterates are plotted
        !The plot is a tiny line, not a dot, to be more visible
        IF j > 49 THEN plot lines: A, x; A + .001, x
    NEXT j
NEXT i
END


=======================
!Chapter 14.     Program: itergraf.tru
!Slightly changed from the textbook version

!Graphical iteration of f(x) = Ax(1 - x)
SET WINDOW -.1, 1.1, -.1, 1.1
PRINT "Choose the parameter A, 0 <= A <= 4.  What is A ";
INPUT A
DEF fnf(x) = A*x*(1 - x)
PRINT "Choose the initial value 0 <= x0 <= 1.  What is x0";
INPUT x0
PRINT "Choose the number of iterations: ";
INPUT n

!This part draws axes and the line y = x.
PLOT LINES: -.1,-.1; 1,1          ! y = x
PLOT LINES: -.1,0; 1,0            ! x-axis 
PLOT LINES: 0,-.1; 0,1            ! y-axis

!This part draws the graph of y = f(x).
LET old_x = -.1
LET delta = .01
LET x = old_x + delta
FOR j = 1 TO 110
    PLOT LINES: old_x, FNF(old_x) ; x, FNF(x)
    LET old_x = x
    LET x = x + delta
NEXT j

!this part draws the cobwebs
LET x = x0
FOR i = 1 TO n
    LET y = FNF(x)
    PLOT LINES: x,x ; x,y
    PLOT LINES: x,y ; y,y
    LET x = y
NEXT i
END


=======================
!Chapter 14.     Program name: iterquad.tru
!Program iterates f(x) = Ax(1-x)
CLEAR
PRINT "Choose A such that 0 <= A <= 4.  What is A";
INPUT A
DEF FNF (x) = A*x*(1-x)
PRINT "Choose the initial value.  What is x0";
INPUT x0
PRINT "Choose the number of iterations.  What is n";
INPUT n

!This part iterates the function
PRINT "The iterates are:"
LET x = x0
FOR i = 1 TO n
    LET y = FNF(x)
    PRINT i,x
    LET x = y
    IF (mod(i,20)=0) then
       PRINT "Press a key to continue"
       GET KEY:z         ! Pauses every 20 lines
    END IF
NEXT i
END


=======================
!Chapter 14.     Program: iterqua2.tru
!Look at dependence on initial conditions of f(x) = 4x(1 - x)
CLEAR
PRINT "Choose initial value of x1, 0 <= x1 <= 1"
INPUT x1
PRINT "Choose initial value of x2, 0 <= x2 <= 1"
INPUT x2
PRINT "Choose the number of iterations"
INPUT n
PRINT "The iterates are"
FOR i = 1 TO n
    PRINT i, x1, x2
    LET y1 = 4*x1*(1 - x1)
    LET y2 = 4*x2*(1 - x2)
    LET x1 = y1
    LET x2 = y2
NEXT i
END


=======================
!Chapter 14.     Program: music.tru
!The sound of iterating f(x) = 4x(1 - x)
PRINT "How many notes would you like?"
INPUT n
LET x = .1
FOR i = 1 TO n
    SOUND 40 + 500*x, 3  !frequency (pitch) 40 + 500x for 3 seconds
    SOUND 32767, 1       !silence for 1 second
    LET y = 4*x*(1-x)
    LET x = y
NEXT i
END


=======================
!Chapter 14.     Program: random.tru
!This program looks at randomness of f(x)=4x(1 - x)
PRINT "Choose initial value of x, 0 <= x0 <= 1"
INPUT x0
PRINT "Choose the number of iterations"
INPUT n
LET n1 = 0
LET n2 = 0
LET x = x0
LET i = 0
FOR i = 1 to n
    IF x < (1/2) THEN
       LET n1 = n1 + 1
    ELSE
       LET n2 = n2 + 1
    END IF
    LET y = 4*x*(1 - x)
    LET x = y
NEXT i
PRINT "The number of values between 0 and 1/2 is "; n1
PRINT "The number of values between 1/2 and 1 is "; n2
END


=======================
! Chapter 14.     Program: transit2.tru
! This is a REPLACEMENT PROGRAM for that on p. 240 of the text.

! This program looks at transitivity of f(x)=4x(1-x).
! It iterates the function f(x) until the iteration value falls
! in the chosen interval, or until it has done MAX_IT iterations.
LET MAX_IT = 1000
CLEAR

PRINT "Choose target interval [k/m , (k+1)/m]."
PRINT
PRINT "First choose m > 0.        What is m";
INPUT m
PRINT
DO
   PRINT "Now choose 0 <= k < ";m;".  What is k";
   INPUT k
LOOP WHILE ((k<0) or (k>=m))
DO
   PRINT
   PRINT "The target interval is";
   PRINT
   PRINT " = [";k;"/";m;",";k+1;"/";m;"] = [";k/m;",";(k+1)/m;"]"
   PRINT
   PRINT "Choose an initial value of x, 0 <= x <= 1,"
   PRINT "  NOT in the target interval.  What is x";
   INPUT x
LOOP WHILE ((x<0) or (x>1))
LET i = 0
DO WHILE ((abs(x-(2*k+1)/(2*m)) > 1/(2*m)) and (i < MAX_IT))
   LET y = 4*x*(1 - x)
   LET x = y
   LET i = i + 1
LOOP
IF ((k/m<=x) and (x<=(k+1)/m)) then
   PRINT
   PRINT "After i =";i;" iterations, the value x =";x;" is in the chosen"
   PRINT "  target interval: ";
ELSE
   PRINT
   PRINT "x(";MAX_IT;") = ";x
   PRINT "After ";MAX_IT;" iterations, x has not appeared ";
   PRINT "in the chosen target interval:"
END IF
PRINT "  [";k;"/";m;",";k+1;"/";m;"] = [";k/m;",";(k+1)/m;"]."

END


=======================
! Chapter 15.   Program: Planar1.tru
DIM A(2,2)
SET WINDOW -10, 10, -10, 10
INPUT x0
INPUT y0

!plot it
PLOT xold,yold

LET A(1,1) = 1/5
LET A(1,2) = 99/100
LET A(2,1) = 1
LET A(2,2) = 0
LET xold = x0
LET yold = y0

FOR iteration = 1 to 25
    ! Map vector and plot
    LET xnew = A(1,1) * xold + A(1,2) * yold
    LET ynew = A(2,1) * xold + A(2,2) * yold
    PRINT xnew/xold, ynew/yold, ynew/xnew
    PLOT xnew, ynew
    ! Keep the new vectors for the next iteration
    LET xold = xnew
    LET yold = ynew
NEXT iteration
END


=======================
! Chapter 15.   Program: Planar2.tru
DIM x0(17), y0(17), xold(17), yold(17), xnew(17), ynew(17), A(2,2)
SET WINDOW -10, 10, -10, 10
!17 initial random vectors in plane
FOR j = 1 to 17
    LET X0(j) = 2 * rnd - 1       ! 0 <= rnd <= 1
    LET y0(j) = 2 * rnd - 1       ! -1 <= x0, y0 <= 1
    LET xold(j) = x0(j)
    LET yold(j) = y0(j)
NEXT j

! Plot them
FOR j = 1 to 17
    PLOT x0(j), y0(j)
NEXT j

LET A(1,1) = 1/5
LET A(1,2) = 99/100
LET A(2,1) = 1
LET A(2,2) = 0

FOR iteration = 1 to 25
    !map vectors and plot them
    FOR j = 1 to 17
        LET xnew(j) = A(1,1) * xold(j) + A(1,2) * yold(j)
        LET ynew(j) = A(2,1) * xold(j) + A(2,2) * yold(j)
        PLOT xnew(j), ynew(j)
        !keep the new vectors for the next iteration
        LET xold(j) = xnew(j)
        LET yold(j) = ynew(j)
    NEXT j
NEXT iteration
END


=======================
!Chapter 16.    Program: euclid-c.tru
PRINT "Enter a = a1 + a2 i"
INPUT prompt "a1 = ":a1
INPUT prompt "a2 = ":a2
PRINT "Enter b = b1 + b2 i"
INPUT prompt "b1 = ":b1
INPUT prompt "b2 = ":b2
LET k=0
LET v1 = a1                       ! v = a
LET v2 = a2
DO WHILE (b1 <> 0) OR (b2 <> 0)   ! While b <> 0
   LET u1 = a1                    ! u = a
   LET u2 = a2
   LET v1 = b1                    ! v = b
   LET v2 = b2
   LET a1 = b1                    ! a = b
   LET a2 = b2
   ! c = u/v = c1 + c2 i  is in Q(i)
   LET c1 = (u1 * v1 + u2 * v2) / (v1 ^ 2 + v2 ^ 2)
   LET c2 = (u2 * v1 - u1 * v2) / (v1 ^ 2 + v2 ^ 2)
   ! Replace  c  by "nearby" complex integer q
   IF c1 - INT(c1) <= .5 THEN
      LET c1 = INT(c1)
   ELSE
      LET c1 = INT(c1) + 1
   END IF
   IF c2 - INT(c2) <= .5 THEN
      LET c2 = INT(c2)
   ELSE
      LET c2 = INT(c2) + 1
   END IF
   LET b1 = u1 - (v1 * c1 - v2 * c2)   ! r = b1 + b2 i = u - vq 
   LET b2 = u2 - (v1 * c2 + v2 * c1)   ! r is a complex integer
   PRINT "q="; c1; "+"; c2; "i"; "     r="; b1; "+"; b2; "i"
   LET k = k + 1
LOOP
PRINT "GCD is"; v1; "+"; v2; "i"
PRINT "Number of steps was"; k
END


=======================
!Chapter 16.    Program: proportn.tru
RANDOMIZE
! m = number of pairs a, b selected randomly
! N = bound on coeffs of  a  and  b
PRINT "Integer m is the number of pairs a, b selected randomly."
INPUT prompt "What is m? ": m
PRINT "N is the bound on the coefficients of a and b."
INPUT prompt "What is N? ": N

LET s = 0                         ! Counts relatively prime pairs 
FOR j = 1 TO m
    LET a1=INT(1+N*RND)           ! Randomly choose complex integer a
    LET a2=INT(1+N*RND)
    LET b1=INT(1+N*RND)           ! Randomly choose complex integer b
    LET b2=INT(1+N*RND)
    LET v1 = a1                   ! v = a
    LET v2 = a2
    DO WHILE (b1 <> 0) OR (b2 <> 0)    ! While b <> 0 
       LET u1 = a1                ! u = a 
       LET u2 = a2
       LET v1 = b1                ! v = b
       LET v2 = b2
       LET a1 = b1                ! a = b
       LET a2 = b2
       ! c = u/v = c1 + c2 i  is in Q(i)
       LET c1 = (u1 * v1 + u2 * v2) / (v1 ^ 2 + v2 ^ 2)
       LET c2 = (u2 * v1 - u1 * v2) / (v1 ^ 2 + v2 ^ 2)
       ! Replace  c  by  "nearby" complex integer q
       IF c1 - INT(c1) <= .5 THEN
          LET c1 = INT(c1)
       ELSE
          LET c1 = INT(c1) + 1
       END IF
       IF c2 - INT(c2) <= .5 THEN
          LET c2 = INT(c2)
       ELSE
          LET c2 = INT(c2) + 1
       END IF
       LET b1 = u1 - (v1 * c1 - v2 * c2)    ! r = b1 + b2 i = u - vq 
       LET b2 = u2 - (v1 * c2 + v2 * c1)    ! r is a complex integer
    LOOP
    ! If last nonzero remainder v is 1, -1, i, or -i, 
    ! then  a and b are relatively prime
    IF (v1=1) AND (v2=0) THEN LET s = s + 1
    IF (v1=-1) AND (v2=0) THEN LET s = s + 1
    IF (v1=0) AND (v2=1) THEN LET s = s + 1
    IF (v1=0) AND (v2=-1) THEN LET s = s + 1
NEXT j
PRINT "Proportion of relatively prime pairs is"; s/m
END