test_multiply = ->
  if DEBUG then console.log "test_multiply ----------------------------"
  run_test [

      "0*a",
      "0",

      "a*0",
      "0",

      "1*a",
      "a",

      "a*1",
      "a",

      "0.0*a",
      "0.0",

      "a*0.0",
      "0.0",

      "1.0*a",
      "1.0*a",

      "a*1.0",
      "1.0*a",

      "a*a",
      "a^2",

      "a^2*a",
      "a^3",

      "a*a^2",
      "a^3",

      "a^2*a^2",
      "a^4",

      "2^a*2^(3-a)",    # symbolic exponents cancel
      "8",

      "sqrt(2)/2",
      # leave the roots nice and
      # clean in numerator, avoid these
      # forms
      #"2^(-1/2)",
      "1/2*2^(1/2)",

      "2/sqrt(2)",
      "2^(1/2)",

      "-sqrt(2)/2",
      # avoid having roots in denominator
      #"-1/(2^(1/2))",
      "-1/2*2^(1/2)",

      "2^(1/2-a)*2^a/10",
      # avoid roots in denominator
      #"1/(5*2^(1/2))",
      "1/10*2^(1/2)",

      "i/4",
      "1/4*i",

      "1/(4 i)",
      "-1/4*i",

      # ensure 1.0 is not discarded

      "1.0 pi 1/2",
      "1.570796...",

      "1.0 1/2 pi",
      "1.570796...",

      # https://github.com/davidedc/Algebrite/issues/121

      "1 - 1/2*0^2",
      "1",

      "1 - 3/2*0^2",
      "1",

      "1 - 1/2*0^1",
      "1",


      "1 - 1/2*(-0^2)",
      "1",
 
      "1 - 1/2*5^2",
      "-23/2",

      "1 + 1/2*0^2",
      "1",

      "1 + (-1/2*0^2)",
      "1",

      "-1/2*0^2",
      "0",

      "1 - 1/2*0*0",
      "1",

      "1 - 1/x*0^2",
      "1",

      "1 - 10/2*0^2",
      "1",

      "1 - 2*0^2",
      "1",

      "1 - 0^2",
      "1",

      "1 - 0^2*(1/2)",
      "1",


    ]