Mathematica.ries

# Mathematica format for RIES        a.k.a. "Stump Wolfram Alpha" mode
#
# Use these settings to get RIES output in a format that can be cut and
# pasted directly into Wolfram Alpha.
#
# To use this file:
#
#   Put it in your current directory and give it a name, like "Mma.ries"
#   To use it, use the option "-pMma", for example:
#
#   ries 2.50618 -pMma
#
#   Your target value: T = 2.50618                         www.mrob.com/ries
#
#                   x^x == 1+9                    for x = T + 4.14559e-06 {59}
#              Log[x]^5 == Sqrt[3/7]              for x = T + 2.08332e-06 {93}
#                 E^x-E == Pi*E+1                 for x = T + 9.45041e-08 {92}
#             [x+x^2]/E == E*Sqrt[Sqrt[2]]        for x = T - 1.76964e-08 {105}
#     x-Sqrt[Sqrt[x+1]] == 1/Sqrt[Sqrt[Pi]-1]     for x = T + 1.44938e-08 {111}
#
# Try it with your favorite irrational number, then take a few of the
# equations RIES gives you and see if Wolfram Alpha can get your number back.
# (You may need to select a button that says "Approximate form" or "More
# digits").
#   For Mathematica, add "Solve[ ... ,x]" or "FindRoot[ ... , {x, K}]"
# around the RIES equation, where K is a starting value.
#
# 20130206: First version. We format everything we can, and exclude the
#   operators we can't handle.
# 20130207: Use '=='; add example and FindRoot[] syntax.

--no-solve-for-x    # It's fun to copy the whole equation into WolframAlpha and
                    # see if they can solve it (-:

--symbol-weights    # Make multiple 'x's more likely so the resulting
  10:x              # equations are more of a challenge to Mathematica.
  #
  15:S 15:C 15:T    # I don't care much for trig functions (-:

--max-match-distance 0.0001 # Ask RIES for closer matches, just to make
                            # it interesting.

-NLv # RIES can't (yet) do the necessary fixity for these two operators

-F2  # Infix format

--explicit-multiply  # Make sure multiply is always shown as '*'

--trig-argument-scale 1.0  # There's no way to get RIES to outout
                           # "Cos[Pi*...]", so we'll remove the Pi

# Now redefine the symbol names for all the functions and constants
--symbol-names
  :=:==
  :q:Sqrt
  :v:_Root_  # Needs to be a two-argument function rather than an infix symbol
  :p:Pi
  :f:GoldenRatio
  :e:E
  :L:Log_    # Needs to be the two-argument function Log[a,b]
  :l:Log
  :S:Sin
  :C:Cos
  :T:Tan
  # We can also tell RIES to use brackets instead of parentheses
  # %%% this does not work, I need to distinguish function-argument brackets
  # from precedence-level-grouping brackets. MMA needs parentheses for the
  # latter.
  :(:[
  :):]