Updated 2017-01-14 15:29:45 by gold

## Aryabhat Sum of Squares and Cubes and eTCL demo example calculator, numerical analysis  edit

gold Here is some eTCL starter code for Aryabhat Sum of Squares and Cubes.

### 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
10.0 :number n
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
385.0 :sum of squares series
3025.0 :sum of cubes series

#### Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
3.0 :number n
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
14.0 :sum of squares series
36.0 :sum of cubes series

#### Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
5.0 :number n
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
1.0 :optional
55.0 :sum of squares series
225.0 :sum of cubes series
```                      #  series of squares =  1.0 4.0 9.0 16.0 25.0 36.0 49.0 64.0 81.0 100.0
proc add {args} {return [ ::tcl::mathop::+ 0. {*}\$args]}
add 1.0 4.0 9.0 16.0 25.0 36.0 49.0 64.0 81.0 100.0
#   sum for  series of squares to n(10) is  385.0
#   sum for  series of squares to n(3) is  14.0
#   sum for  series of squares to n(3) is  30.0```

## Appendix Code edit

### appendix TCL programs and scripts

```        # pretty print from autoindent and ased editor
# Aryabhat Sum of Squares and Cubes Series
# 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 {{} {number \$n :} }
lappend names {optional :}
lappend names {optional: }
lappend names {optional: }
lappend names {optional:}
lappend names {optional: }
lappend names {sum of squares : }
lappend names {sum of cubes :}
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
set msg "Calculator for Aryabhat Sum of Squares and Cubes Series
from TCL WIKI,
written on eTCL "
tk_messageBox -title "About" -message \$msg }
proc calculate {     } {
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 n \$side1
set sum_squares [* [* [/ 1. 6. ] \$n ] [+ \$n 1. ] [+ [* 2. \$n ] 1. ]]
#set sum_s [/ [* \$n [+ \$n 1.] ] 2. ]
set sum_cubes  [+ [/ [** \$n 4. ] 4.] [/ [** \$n 3. ] 2.] [/ [** \$n 2. ] 4.]]
set side7 \$sum_squares
set side8 \$sum_cubes
}
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 :|number n|   |&"
puts "&| \$side2 :|optional  | |& "
puts "&| \$side3 :|optional | |& "
puts "&| \$side4 :|optional | |&"
puts "&| \$side5 :|optional  | |&"
puts "&| \$side6 :|optional |  |&"
puts "&| \$side7 :|sum of squares series |  |&"
puts "&| \$side8 :|sum of cubes series |  |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate   }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 10.0 1.  1.0 1.0  1.0  1. 385. 3025.}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 3.0 1.0 1.0 1.0  1.0  1. 14. 36. }
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 5.0 1.  1.0 1.0  1.0  1. 55. 225. }
::ttk::button .clearallx -text clear -command {clearx }
::ttk::button .cons -text report -command { reportx }
::ttk::button .exit -text exit -command {exit}
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 . "Aryabhat Sum of Squares and Cubes Series 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   |&"  ```