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Parsed input into list of Term object (coefficient and mapping from var name to its power value), recursively parsing inside parentheses. Combined likes by mapping from strings representing terms without coefficients (x2y3z) to List<Term>. Sorted by term's highest power value.

// ZoomBA
def term_parse( s ){
  term = [ 0.0 , '' ]
  p = tokens('^[\+\-]?(\d+(\.\d+)?)?')
  m = p.matcher( s ) ; m.find() // true always 
  opts = { '' : 1.0 , '+' : 1.0 , '-' : -1.0 }
  if ( m.group @ opts ) {
    term[0] = opts[ m.group ] 
  } else {
    term[0] = float( m.group ) 
  }
  inx = index ( s.value ) :: { str($.item) =~ '[a-zA-Z]' }
  term[1] = s[ (inx < 0 ? 0 : inx) : -1 ] 
  if ( inx < 0 ){ term[1] = '' }
  term 
}
def gen_expr( s ){
  l = tokens(s, '[\+\-]?[^\+\-]+') -> { term_parse( $.item ) }
  d = mset ( l ) -> {  $.item.1 }
}
def normalize( s ){
  s = s.replace(' ','')
  #(l,r) = s.split('=')
  ld = gen_expr ( l )
  rd = gen_expr ( r )
  // merge 
  u = ld.keys | rd.keys // union 
  poly = list ( u ) -> { 
     k = $.item ; coeff = 0.0 
     if ( k @ ld ){ coeff += sum ( ld[k] )->{  $.item[0] }  }
     if ( k @ rd ){ coeff -= sum ( rd[k] )->{  $.item[0] }  }
     [ k , coeff ]
  }
  sortd ( poly ) :: { #(l,r) = $.item ; l.0 < r.0 }
  str( poly , '' ) -> { #(k,c) = $.item  ; str( '%+f%s' , c , k ) } 
}
x = normalize ( 'x^2 + 3.5xy + y = y^2 - xy + y + 10' )
println ( x )

what language is it? php or python or ruby?