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", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["x", "v"], "z"], TraditionalForm]]], " : allows all symbolic manipulations using standard algebraic functions, \ but becomes large and slow for small to moderate arguments, and quite unfit \ for human consumption.\nIt can however always be reduced to elementary S.P. \ by the standard \[OpenCurlyQuote]", StyleBox["SymmetricReduction", FontWeight->"Bold"], "\[CloseCurlyQuote] function.\n*\tcondensed format: ", Cell[BoxData[ FormBox[ SubscriptBox["\[CapitalSigma]", "i"], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ SubscriptBox["a", "i"], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["p", "n"], "i"], TraditionalForm]]], " where ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["p", "n"], "i"], TraditionalForm]]], " stands for the i-th partition of n in reverse lexicographic ordering. It \ codes the expanded format by ignoring the permutation of the \ (interchangeable) indices and extracting only the (orderless) exponents \ recast into a partition of n. This format loses the info on the actual number \ of variables used. It groups monomials according to the exponents : 5 ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox[ SubscriptBox["x", "1"], "3"], SuperscriptBox[ SubscriptBox["x", "3"], "2"]}], TraditionalForm]]], " becomes 5 ", Cell[BoxData[ FormBox[ SuperscriptBox[ SubscriptBox["p", "5"], "3"], TraditionalForm]]], " since {3,2} is the 3rd partition of 5. The info that there are 3 or more \ variables \[OpenCurlyQuote]in play\[CloseCurlyQuote] (as shown by the indices \ 1 and 3) is lost.\n*\tunevaluated format ", StyleBox["uu[ arg , ", FontWeight->"Bold"], "# of variables", StyleBox[" v ]", FontWeight->"Bold"], " which can be taken as argument for symbolic transformation functions. Only \ the basic definition ", StyleBox["uu[ partition, v ]==0 /; Length[partition]>v", FontWeight->"Bold"], " is coded for (one cannot distribute 5 exponents over 4 variables). 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", StyleBox["m", FontWeight->"Bold"], " (monomial) and ", StyleBox["s", FontWeight->"Bold"], " (Schur) do not share this property, and always need a partition as first \ argument. Transformations thus need a threading step in order to get \ acceptable arguments." }], "Text", CellMargins->{{66, 0}, {2, 10}}, CellChangeTimes->{{3.5777768190505104`*^9, 3.5777768826353064`*^9}, { 3.577776924801244*^9, 3.577777161105074*^9}, {3.5777793774672203`*^9, 3.5777794391871557`*^9}, {3.5777795416584992`*^9, 3.577779710506572*^9}, 3.5778054755086193`*^9, {3.577805577051427*^9, 3.577805588659091*^9}, { 3.5778059809685297`*^9, 3.577806001144684*^9}, 3.5810072698924417`*^9}], Cell[TextData[{ "Transformation Functions:\n", StyleBox["u[ arg , ", FontWeight->"Bold"], "# of variables", StyleBox[" v ]", FontWeight->"Bold"], " produces the expanded format \[CapitalSigma] a ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox[ SubscriptBox["x", "1"], "i"], " ", SuperscriptBox[ SubscriptBox["x", "2"], "j"]}], TraditionalForm]]], " ... 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