set i 1
   set a [expr {$b($i-1)+$b($i)]

 % set b(0) 1
 1
 % set b(1) 2
 2
 % set i 1        
 1
 % set a [expr {$b($i-1)+$b($i)}]
 can't read "b(1-1)": no such element in array
 % 

# mathlang.tcl --
#    Provide commands that allow a more usual mathematical syntax:
#
#    mathfunc {x} {
#       sinc = sin(x)/x if x != 0
#       sinc = 0        otherwise
#    }
#    math {
#       a = x*x + y*y
#    }
#
#    Still to do: mathfunc
#
# (7 july 2004) Small improvement:
#               recognise array elements
#

namespace eval ::mathsyntax {
    namespace export math
    variable cached_calcs {}
    variable func_names \
       {abs acos asin atan atan2 ceil cos cosh double
        exp floor fmod hypot int log log10 pow rand round
        sin sinh sqrt srand tan tanh wide}
}

 # ToExpr --
 #    Transform an expression to the form expr wants
 # Arguments:
 #    expression     A right-hand side of an assignment
 # Result:
 #    Valid Tcl expression
 #
 proc ::mathsyntax::ToExpr { expression } {
    variable func_names

    set rhs [string map {" " ""} $expression]
    set indices [regexp -inline -all -indices {[a-zA-Z][a-zA-Z0-9_]*} $rhs]
    set offset 0
    foreach idx $indices {
       foreach {start stop} $idx {break}
       set start [expr {$start+$offset}]
       set stop  [expr {$stop+$offset}]
       set next  [expr {$stop+1}]

       if { [string index $rhs $next] != "(" } {
          set char [string index $rhs $start]
          set rhs  [string replace $rhs $start $start "\$$char" ]
          incr offset
       } else {
          set char [string index $rhs $start]
          set name [string range $rhs $start $stop]
          if { [lsearch $func_names $name] < 0 } {
             set rhs  [string replace $rhs $start $start "\$$char" ]
          }
       }
    }
    return $rhs
 }

 # Transform --
 #    Transform a series of mathematical expressions into Tcl code
 # Arguments:
 #    id         ID to use
 #    calc       One or more mathematical assignments
 # Result:
 #    None
 # Side effects:
 #    A private procedure is created
 # Note:
 #    No conditions yet
 #
 proc ::mathsyntax::Transform { id calc } {
    set calc [split $calc "\n"]
    set body {"uplevel 2 \{"}

    foreach assign $calc {
       set assign [string trim $assign]
       if { $assign != "" } {
          regexp {([a-zA-Z][a-zA-Z0-9_()]*) *= *(.*)} $assign ==> lhs rhsfull

          #
          # Is there a condition?
          #
          set cond1 [string first " if"        $rhsfull]

          # PM: set cond2 [string first " otherwise" $rhsfull]

          set cond  ""
          if { $cond1 > 0 } {
             set rhs  [string range $rhsfull 0 [expr {$cond1-1}]]
             set cond [string range $rhsfull [expr {$cond1+3}] end]
             lappend body "if { [ToExpr $cond] } \{"
          } else {
             set rhs $rhsfull
          }

          # If the left-hand side refers to an array element,
          # we need to add a dollar-sign
          #
          set lhs [string map {"(" "($"} $lhs]

          #
          # Prepare the assignment
          #
          set rhs [ToExpr $rhs]

          lappend body "set $lhs \[expr {$rhs}\]"

          if { $cond != "" } {
             lappend body "\}"
          }
       }
    }

    lappend body "\}"

    proc Cached$id {} [join $body "\n"]
 }

 # math --
 #    Allow mathematical expressions inside Tcl code
 # Arguments:
 #    calc       One or more mathematical assignments
 # Result:
 #    None
 # Side effects:
 #    As the code is executed in the caller's scope, variables
 #    in the calling procedure are set
 #    The code is transformed into a procedure that is cached
 #
 proc ::mathsyntax::math { calc } {
    variable cached_calcs

    set id [lsearch $cached_calcs $calc]
    if { $id < 0 } {
       lappend cached_calcs $calc
       set id [expr {[llength $cached_calcs]-1}]
       Transform $id $calc
    }

    ::mathsyntax::Cached$id
 }

 #
 # Simple test
 #
 namespace import ::mathsyntax::math

 set a 1
 set b 1
 set c ""
 set d ""
 set sinc ""
 math {
    c = a + b
    d = a + cos(b+c)
 }
 puts "$c $d"

 for {set i 0} {$i < 20} {incr i} {
    math {
       x = 0.1*i
       sinc = 1 if x == 0
       sinc = sin(x)/x if x != 0
       y(i) = sinc*sinc
    }
    puts "$i $x $sinc $y($i)"
 }
 #
 # Just to check
 #
 parray y

variable Res [list]

set calc [split $calc "\n\;"] 

lappend body "lappend ::mathsyntax::Res \[set $lhs \[expr {$rhs}\]\]"

lindex $::mathsyntax::Res

 ## to test :
pack [canvas .c]
.c create line {*}[set L [list]; for {set i -200} {$i < 200} {incr i} {
    math {
       x = 0.1*i
       sinc = 1 if x == 0
       sinc = sin(x)/x if x != 0
    }
    lappend L {*}[math {X=200+10*x;Y=200-100*sinc}]
 }; set L]