Babylonian False Position Algorithm and eTCL demo example calculator, numerical analysis

Babylonian False Position Algorithm and eTCL demo example calculator, numerical analysis

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gold Here is some eTCL starter code for Babylonian false position algorithm.

The Babylonian false position algorithm was loaded into an eTCL calculator. The Babylonians did not use algebra notation, so the reader will have to bear some anachronisms in the eTCL pseudocode. The field is assumed to be a square or right rectangle. The area of the field and the short side constraint ratio are given values. The tablet has a set of line by line calculations which effectively guess the two sides of a field and compute a scale factor from the sqrt ratio of true area to the product of the guessed or false position sides. The short and long false position sides are constrained, multiplied, and rescaled to calculate the short and long sides of the field. The answer was checked to see if product of the corrected short and long sides equal the given initial area. For restating the problem in a computer algorithm, the sides and field area will be in meters and square meters, respectively.


Pseudocode Section

    # using  pseudocode for Babylonian false position algorithm
    # possible problem instances include separate tables for  cubes n*n*n and quasi_cubes
     true_area = supplied value
     false_long_side = initial guess
     false_short_side  =  2/3 length, supplied ratio
     set false_area [expr  $false_long_side*$false_short_side   ]
     initialise correction = 0.25
     correction  = sqrt (true_area / false_area)
     long_side = false_long_side * correction
     short_side  =  false_short_side  * correction
     check_answer   long_side * short_side  =? true_area    (yes/no)
     set answers and printout with resulting values

Testcases Section

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines).

Testcase 1

table 1printed in tcl wiki format
quantity value comment, if any
1:testcase_number
1000.0 :true area meters squared
0.6660 :short side is x of long (ratio)
100.0 :initial guess of long side meters
66.600 :answers: false short side meters
6660.000 :false area meters squared
0.387 :correction factor (ratio)
25.806 :short side meters
38.7492 :long side meters

Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
1200.0 :true area meters squared
0.666 :short side is x of long (ratio)
120.0 :initial guess of long side meters
79.920 :answers: false short side meters
9590.399 :false area meters squared
0.353 :correction factor (ratio)
28.270 :short side meters
42.447 :long side meters

Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
60.0 :true area meters squared
0.666 :short side is x of long (ratio)
10.0 :initial guess of long side meters
6.660 :answers: false short side meters
66.599 :false area meters squared
0.949 :correction factor (ratio)
6.321 :short side meters
9.491 :long side meters

Screenshots Section

figure 1.

Babylonian False Position Algorithm screenshot


References:


Appendix Code

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Babylonian False Position Algorithm calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 15jan2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { true area meters squared :} }
        lappend names { short side is x of long (ratio) :}
        lappend names { initial guess of long side meters : }
        lappend names { answers: false short side meters : }
        lappend names { false area meters squared :}
        lappend names { correction factor (ratio) : }
        lappend names { short side meters : }
        lappend names { long side meters :} 
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Babylonian False Position Algorithm 
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number 
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            set true_area $side1
            set false_long $side3
            set false_short [* $false_long $side2 ]
            set false_area [* $false_long  $false_short  ]
            set correction_ratio .25
            set correction_ratio [/  $true_area $false_area]
            set correction_ratio [sqrt $correction_ratio ]
            set side4 $false_short
            set side5 $false_area
            set side6 $correction_ratio
            set side7 [* $false_short $correction_ratio ]
            set side8 [* $side3 $correction_ratio ]  
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number reference_factor flag
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |& "
            puts "&| $side1 :|true area meters squared |   |&"
            puts "&| $side2 :|short side is x of long (ratio)| |& "  
            puts "&| $side3 :|initial guess of long side meters| |& "
            puts "&| $side4 :|answers: false short side meters| |&"
            puts "&| $side5 :|false area meters squared  | |&"
            puts "&| $side6 :|correction factor (ratio) |  |&"
            puts "&| $side7 :|short side meters  |  |&"
            puts "&| $side8 :|long side meters |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1000.0 .666  100.0 66.0  6660.0  0.38 26. 38.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1200. .666 120. 79.  9590.0  0.35 28. 42. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 60.0  .666  10.0 6.66  66.0  0.5  3.33 5.0 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
               . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Babylonian False Position Algorithm Calculator"   

Pushbutton Operation

For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console.

For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. The command { calculate; reportx } or { calculate ; reportx; clearx } can be added or changed to report automatically. Another wrinkle would be to print out the current text, delimiters, and numbers in a TCL wiki style table as

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  

gold12Dec2018. This page is copyrighted under the TCL/TK license terms, this license .


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Please place any comments here with your wiki MONIKER and date, Thanks.gold12Dec2018