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- - **generate all possible math expr of one term**
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generate all possible math expr of one termHere's a example of Expressiveness of a Language.
The following is Mathematica code that generates all possible equations of one term involving trig function. (tweak the funList and nesting level to define what “all possible” means. if nesting level is 2, it takes about 20 minutes and returns a list of 2876 terms on a 2004 personal computer. << DiscreteMath`Combinatorica` funList = {Sin, Tan, Power[#, -1] &}; Nest[Module[{li = #}, (Union[#, SameTest -> (Module[{arg1 = #1, arg2 = #2}, If[(*both expression contains both x and y*) And @@ (((((StringMatchQ[#, "*x*"] && StringMatchQ[#, "*y*"]) &)@ ToString@#) &) /@ {arg1, arg2}) , SameQ[arg1, arg2 /. {x -> y, y -> x}], SameQ[arg1, arg2]] ] &)] &)@ Union@Flatten@(Table[(Times @@ # &) /@ KSubsets[#, i], {i, 1, 2}] &)@Flatten@{li, Outer[#1@#2 &, funList, li]} ] &, {x, y}, 1]; Select[%, (StringMatchQ[ToString@#, "*x*"] && StringMatchQ[ToString@#, "*y*"]) &] The problem is this: generate a list of all possible math expressions using the following combination and rules: • the math expression involves both x and y. (must have both present) • you can use any of the 6 trig functions (you must, since the goal is to create all possibilities) • The binary operations you can use are multiply, divide. (no addition or substraction, since that can make the result 2 terms) • a sub-expression (such as x or y) can be replaced by a more complicated one. (i.e. you can nest) For example, these are first few items from the above code: {1/(x^2*y^2), 1/(x*y^2), x/y^2, 1/(x*y), x/y, x^2/y, x*y, x^2*y, x^2*y^2, Cos[x]/y^2, Cos[x]/y, Cos[x]/(x*y), (x*Cos[x])/y, y*Cos[x], (y*Cos[x])/x, x*y*Cos[x], y^2*Cos[x], Cos[x]*Cos[y], Cot[x]/y^2, Cot[x]/(x*y^2)} For a gallery of selection plots of these equations, see http://xahlee.org/MathGraphicsGaller...se/dense1.html The above i wrote in 2002. If there are requests, i'll translate the above code into emacs lisp. The result lisp expression should match Mathematica's, token for token. (the code make a lot use of nested lambda and or apply and or map) If you are interested, you could translate the above into lisp too, it's not difficult (though the number of lines will increase maybe 10 fold. And if Common Lisp doesn't have combinatorics library providing KSubsets, and also since CL doesn't have Outer, so the above in CL might be few hundred lines). (see here for a example of how to: http://xahlee.org/UnixResource_dir/writ/notations.html ) PS as a after-thought, i decided to post this to perl, python, and java too. This will take about the same number of lines in perl as in Common Lisp. Probably llightly more in Python due to syntax. In Java, it will be one million lines. Gratuitous poem of the day: in the climb to geekdom, you have few rungs to catch, before you see my ass. —Xah Lee, 2005 Xah xah@xahlee.org ∑ http://xahlee.org/ ☄ |

Re: generate all possible math expr of one termOn Thu, 15 May 2008, Lew wrote:
> xahlee@gmail.com wrote: >> Xah Lee, 2005 > > Blah, blah, blah. Plonk. One of the most amazing things i found on returning to this group after an N-year absence was that Xah is still going. But then, so are Roedy and Patricia, so we need someone to balance them out ... tom -- .... but when you spin it it looks like a dancing foetus! |

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