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Re: Help Mathematica - Generating Patterns

  • To: mathgroup at
  • Subject: [mg54887] Re: [mg54852] Help Mathematica - Generating Patterns
  • From: "David Park" <djmp at>
  • Date: Sat, 5 Mar 2005 01:34:31 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Here are a couple of routines that I have in one of my packages.

SymbolsToPatterns::usage =
    "SymbolsToPatterns[symbollist][expr] will convert symbols in expression,
which are on symbollist, to named patterns.";
SymbolsToPatterns[symbols : {_Symbol ..}][expr_] :=
  expr /. Thread[symbols -> (Pattern[#, Blank[]] & /@ symbols)]

LHSSymbolsToPatterns::usage =
    "LHSSymbolsToPatterns[symbollist][expr] will apply SymbolsToPatterns to
the first part of expr.";
LHSSymbolsToPatterns[symbollist_][expr_] :=
  MapAt[SymbolsToPatterns[symbollist], expr, 1]

{x1, x2, x3}
% // SymbolsToPatterns[{x1, x2, x3}]
{x1_, x2_, x3_}

Often we may have derived an equation and then wish to use the equation as a
substitution rule in subsequent derivations. That means we want to change
the equation into a rule and specified symbols on the left hand side into
patterns. Here is a trivial made-up example.

(x + y)^2 == Expand[(x + y)^2] // Reverse
rule = Rule @@ % // LHSSymbolsToPatterns[{x, y}]
x^2 + 2*x*y + y^2 == (x + y)^2
(x_)^2 + 2*(x_)*(y_) + (y_)^2 -> (x + y)^2

David Park
djmp at

From: Awgn78 [mailto:robynobile at]
To: mathgroup at

How i can obtain a list {x1_,x2_,x3_} from a list {x1, x2, x3}...
thank you for help and sorry for my bad english...i'm italian

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