# pretty print from autoindent and ased editor
        # Babylonian Combined Market Rate calculator V3
        # written on Windows 10 on TCL
        # working under TCL version 8.6
        # gold on TCL Club, 15jul2020
        # combined_market_rate proc adapted from TCLLIB
        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 {{} {aa quantity per silver piece MR1:} }
        lappend names {bb quantity per silver piece MR2:}
        lappend names {cc quantity per silver piece MR3: }
        lappend names {dd quantity per silver piece MR4: }
        lappend names {optional usually 1. :}
        lappend names {answers: sum_of_fractions  : }
        lappend names {average market rate: }
        lappend names {combined market rate:}
        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 }
        # adapted from tcl Stats 2011-05-22, arithmetic mean  [RLE]
        # plus other contributors from TCLLIB math library, [AM] Arjen Markus
        # ::math::combined_market_rate --
        #
        # Return the combined_market_rate by  one,two, or more given rates
        # market rate defined as quantity per price
        # or 1 over (price per quantity)
        #
        # Arguments:
        #
        #    args  values are one, two, or more given rates
        #
        # Results: combined_market_rate
        #  works for positive numbers, negative numbers,
        #  and mixed positive & negative numbers.
        #  arg of zero returns zero
        #  arg of null returns zero
        #  filter foreach drops irregular zero elements from argument
        proc ::math::combined_market_rate { args} {
            set sum 0.
            set N [ expr { [ llength $args ] } ]
            if { $N == 0 } { return 0 }
            if { $N == 1 || [ lindex $args 0 ] == 0 } { return 0 }
            set res {};set counter2 0;
            # filter foreach drops irregular zero elements
            foreach item $args {if {$item != 0 } {incr counter2 1; lappend res $item } }
            set counter 0
            foreach val $res {
                set sum [ expr { $sum + 1./$val } ]
                incr counter 1
            }
            #set combined_market_rate1 [ expr { 1./(($sum*1.)/$counter2) } ]
            set combined_market_rate1 [ expr { 1./(($sum*1.)/$counter2) } ]
            return $combined_market_rate1
        }
        # various testcases on combined_market_rate
        # puts  [::math::combined_market_rate  0.5524 0.4807 0.42918 0.47846 ]
        #  answer 0.48131    "
        # puts   [ ::math::combined_market_rate .1 .2 .3 .4 ]
        #  answer 0.192
        # ::math::combined_market_rate -.1 -.2 -.3 -.4
        # answer -0.192, correct
        # operator math formula follows
        # check [/ 1. [/ [+ [/ 1. -.1] [/ 1. -.2] [/ 1. -0.3 ] [/ 1. -0.4] ] 4. ] ]
        # returns  -0.192, correct
        # puts " [ ::math::combined_market_rate .1 ] "
        # :math::combined_market_rate -.1 -.2  .3 .4
        # answer -0.4363636363636364
        # operator math formula follows
        # set check [/ 1. [/ [+ [/ 1. -.1] [/ 1. -.2] [/ 1.  0.3 ] [/ 1. 0.4] ] 4. ] ]
        # check equals    -0.4363636363636364
        # puts " for (::math::combined_market_rates .1)
        # returns .1 "
        # ::math::combined_market_rate  {}
        # null returns zero, correct.
        # ::math::combined_market_rate 0
        # arg 0 returns zero, correct.
        # addition dated 24sep2018
        # added filter foreach to remove zeros
        # and irregular zeros in inputs,
        # test on zero's 0.1 0.0 0.0 0.2 0.3 0.4
        # returns 0.192 , correct
        # test on zero's   0.1 0.0 0.0 0.2 0.3 0.4
        # returns 0.192 , correct
        proc about {} {
            set msg "Calculator for Babylonian Combined Market Rate V3
            from TCL Club,
            written on TCL "
            tk_messageBox -title "About" -message $msg }
        proc self_help {} {
            set msg "Calculator for Babylonian Combined Market Rate V3
            from TCL ,
            # self help listing
            # 4 givens follow.
            1) aa quantity per silver piece MR1
            2) bb quantity per silver piece MR2
            3) cc quantity per silver piece MR3
            4) dd quantity per silver piece MR4
            The answer is combined market rate:
            The solution from the clay tablets
            is genuine antique method from 1600 BCE
            and different looking from modern math methods.
            # The Babylonians did not use modern algebraic notation,
            # so the reader will have to bear some anachronisms in the TCL code.
            # The Bablylonian math problems used base_60,  but
            # the TCL procedures use base_10 in calculator.
            # The moderns normally use  price per quantity, rather
            # than the Babylonian market rate, defined as quantity per price.
            # For comparison, TCL code may include redundant paths & formulas.
            # The TCL calculator normally uses modern
            # units  for convenience to modern users and textbooks.
            # Any convenient and consistent in/output units might be used
            # like inches, feet, nindas, cubits, or dollars to donuts.
            # 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 to conventional texteditor. For testcases
            # testcase number is internal to the calculator and
            # will not be printed until the report button is pushed
            # for the current result numbers.
            # This posting, screenshots, and TCL source code is
            # copyrighted under the TCL/TK 8.6 license terms.
            # Editorial rights retained under the TCL/TK license terms
            # and will be defended as necessary in court.
            Conventional text editor formulas or  grabbed from internet
            screens can be pasted into green console.
            Try copy and paste following into green screen console
            set answer \[* 1. 2. 3. 4. 5. \] 
            returns  120
            Try invoking subroutine inside package
            set answer2 \[ ::math::combined_market_rate 1. 2. 3. 4. 5. \]
            returns 2.189
            # gold on  TCL Club, 10jul2020 "
            tk_messageBox -title "self_help" -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 sum_of_fractions [+ [/ 1. $side1 ] [/ 1. $side2 ] [/ 1. $side3 ] [/ 1. $side4 ] ]
            set average_market_ratex [/ [+  $side1 $side2 $side3 $side4 ] 4. ]
            set combined_market_rate [ ::math::combined_market_rate $side1 $side2 $side3 $side4 ]
            set side6 $sum_of_fractions
            set side7 $average_market_ratex
            set side8 $combined_market_rate
        }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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
            console show;
            console eval {.console config -bg palegreen}
            console eval {.console config -font {fixed 20 bold}}
            console eval {wm geometry . 40x20}
            console eval {wm title . " Babylonian Market Rate Report , screen grab and paste from console 2 to texteditor"}
            console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
            puts "%|table $testcase_number|printed in| tcl Club format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |&"
            puts "&| $side1 :|aa quantity per silver piece MR1: |   |&"
            puts "&| $side2 :|bb quantity per silver piece MR2: | |& "
            puts "&| $side3 :|cc quantity per silver piece MR3: | |& "
            puts "&| $side4 :|dd quantity per silver piece MR4: | |&"
            puts "&| $side5 :|optional:  | |&"
            puts "&| $side6 :|sum_of_fractions |  |&"
            puts "&| $side7 :|average market rate: |  |&"
            puts "&| $side8 :|combined_market_rate |  |&"
        }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1. 2.  3.0 4.  1.0  2.083 2.5 1.92}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 3.0 5.0 7.0 9.0  1.0  .787 6. 5.08 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3.0 4.  5.0 7.0  1.0  0.986 4.75 4.318 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .self_help -text self_help -command {self_help }
        ::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 .self_help .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 Combined Market Rate Calculator V3"