**Division into Parts by Multiple Ratios and eTCL demo example calculator, numerical analysis** This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,[gold] ---- <> **Introduction** [gold] Here is some eTCL starter code for Division into Parts by Multiple Ratios in calculator shell. Additional console programs below are used to check or improve subroutines in calculator shell. ---- **Pseudocode Section** ====== # using pseudocode proc test1 { # possible problem instances, low vs high middle vs low high vs middle} proc test2 { initialize algorithm_result = 1. initialize terms of tianji combined probability proc test6 { check algorithm f(solution) =? initial product check_sum = a+b+c+d+e set answers and printout with resulting values pseudocode: need test cases > small,medium, giant pseudocode: need testcases within range of expected operation. pseudocode: are there any cases too small or large to be solved? pseudocode: limit to size of eTCL list, ref versions. } #end of file ====== ***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 1|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 1:|testcase_number | |& &| 84.0 :|quantity | |& &| 1.0 :|ratio 1 | |& &| 2.0 :|ratio 2 | |& &| 4.0 :|ratio 3 | |& &| 0.0 :|optional: | |& &| 84.0 :|answers: quantity | |& &| 7.0 :|sum of ratios | |& &| 12.0 24.0 48.0 :|list| |& **** Testcase 2 **** %|table 2|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 2:|testcase_number | |& &| 120.0 :|quantity | |& &| 1.0 :|ratio 1 | |& &| 2.0 :|ratio 2 | |& &| 3.0 :|ratio 3 | |& &| 0.0 :|optional: | |& &| 120.0 :|answers: quantity | |& &| 6.0 :|sum of ratios | |& &| 20.0 40.0 60.0 :|list| |& **** Testcase 3 **** %|table 3|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 3:|testcase_number | |& &| 360.0 :|quantity | |& &| 1.0 :|ratio 1 | |& &| 2.0 :|ratio 2 | |& &| 3.0 :|ratio 3 | |& &| 0.0 :|optional: | |& &| 360.0 :|answers: quantity | |& &| 6.0 :|sum of ratios | |& &| 60.0 120.0 180.0 :|list| |& ---- ***Screenshots Section*** ****figure 1.**** [General Tianji' Horse Race Strategy from China and eTCL demo example screenshot] ---- ***References:*** * Plugging a Math Gap with Harvard mathematician Shing-Tung Yau, Forbes Magazine 2007, * Institute of Mathematical Sciences * in Hong Kong studies betting on horse races and predicting the weather * [Sumerian Construction Rates and eTCL Slot Calculator Demo Example] * [Oneliner's Pie in the Sky] * [One Liners] * [Category Algorithm] * [Babylonian Number Series and eTCL demo example calculator] * [Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator] * [Gauss Approximate Number of Primes and eTCL demo example calculator] * Taking a Weighted Average, Dr Math, mathforum.org/dr.math, dated 03/20/2003 * google , mathforum.org/dr.math * Using Weighted Criteria to Make Decisions, Dr Math>, mathforum.org/dr.math, dated 07/18/2008 * google * harmonic mean discussed in [Additional math functions] * harmonic mean discussed in [Tcl Normalized Extended Benchmarks] * see arithmetic mean on tcl-wiki [Stats] 2011-05-22, [RLE] * see similar 1/(1/nth) terms method used in * [Babylonian Combined Market Rates and eTCL demo example calculator, numerical analysis ] **Appendix Code** ***appendix TCL programs and scripts *** ====== # pretty print from autoindent and ased editor # Division into parts by ratios calculator # written on Windows XP on eTCL # working under TCL version 8.5.6 and eTCL 1.0.1 # gold on TCL WIKI, 2mar2017 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 {{} {quantity :} } lappend names {ratio 1:} lappend names {ratio 2: } lappend names {ratio 3: } lappend names {optional:} lappend names {answers: quantity : } lappend names {sum of ratios : } lappend names {list :} 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 Division into Parts by Ratios from TCL WIKI, written on eTCL " tk_messageBox -title "About" -message $msg } # adapted from tcl-wiki Stats 2011-05-22, arithmetic mean [RLE] # # ::math::quantity_into_ratios -- # # Return the division of quantity by two or more given ratios # # Arguments: # val first value is quantity # args other values are two or more given ratios # # Results: parts of quantity divided by ratios # proc ::math::quantity_into_ratios {quantity args} { set sum 0. set N [ expr { [ llength $args ] + 1 } ] if { $N == 1 } { return 0 } foreach val $args { set sum [ expr { $sum + $val } ] } foreach val $args { lappend answer [ expr { $quantity * ($val/$sum) } ] } set answer } #puts " ::math::quantity_into_ratios ( 84 2 2 2 ) answer 12.0 24.0 48.0 " #puts " [ ::math::quantity_into_ratios 84 1 2 4 ] " #puts " [ ::math::quantity_into_ratios 84 ] for (::math::quantity_into_ratios 84) returns zero " 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 answer2 [ ::math::quantity_into_ratios $side1 $side2 $side3 $side4 ] set sum_of_ratios [+ $side2 $side3 $side4 ] set side6 $side1 set side7 $sum_of_ratios set side8 $answer2 } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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; puts "%|table $testcase_number|printed in| tcl wiki format|% " puts "&| quantity| value| comment, if any|& " puts "&| $testcase_number:|testcase_number | |&" puts "&| $side1 :|quantity | |&" puts "&| $side2 :|ratio 1 | |& " puts "&| $side3 :|ratio 2 | |& " puts "&| $side4 :|ratio 3 | |&" puts "&| $side5 :|optional: | |&" puts "&| $side6 :|answers: quantity | |&" puts "&| $side7 :|sum of ratios | |&" puts "&| $side8 :|list| |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { set side8 0 ; calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 84.0 1. 2.0 4.0 0.0 84. 7.0 12.0} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 120.0 1.0 2.0 3.0 0.0 120.0 6.0 20.0} ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 360.0 1.0 2.0 3.0 0.0 360.0 12.0 30.0} ::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 . "Division into Parts by Ratios Calculator" # end of deck ====== ---- *** 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 |&" ====== ---- ** Console program for ** ====== #end of deck ====== ---- ** Console program for ** ====== #end of deck ====== [gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. **Comments Section** <> Please place any comments here, Thanks. <> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI ---- <> Development | Concept| Algorithm | Statistics |