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MathGroup Archive 1999

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Re: Manipulation of equations and inequalities in "high-school style"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19598] Re: Manipulation of equations and inequalities in "high-school style"
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sat, 4 Sep 1999 01:34:30 -0400
  • Organization: University of Western Australia
  • References: <7q9hdf$o62@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Silvano D'Orazio wrote:

> Does anybody know a Mathematica (3 or 4) package which allows
> manipulaton of equations and inequalities like high-school students
> are supposed to do?
>
> For example
>
> 2x+a = x-b      subtract a
>   2x = x-b-a    divide by 2, subtract x
>    x = -b-a
>
> or
>
>  (2^x-1)^(1/2) = 5b                 log both sides
> (1/2)(x-1)log2 = log5 + logb        multiply by 2, divide by log2
>
>                  2(log5 + logb)     add 1
>            x-1 = --------------
>                      log2
>
> and so on.

Here is a short Notebook which illustrates one way of doing this.

Notebook[{
Cell[TextData[{
  "If you modify ",
  Cell[BoxData[
      FormBox[
        StyleBox["Equal",
          "Input"], TraditionalForm]]],
  " (following Maeder) so that ",
  Cell[BoxData[
      FormBox[
        StyleBox["Listable",
          "Input"], TraditionalForm]]],
  " operations are automatically applied to both sides of any equality,"
}], "Text",
  CellTags->{"Equal", "Listable"}],

Cell[BoxData[
    \(TraditionalForm\`\(Unprotect[Equal];\)\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`listableQ(f_) :=
      MemberQ(Attributes(f), Listable)\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`Equal /: \
      lhs : f_Symbol?
            listableQ[___, \ _Equal, \ ___]\  := \n\ \ \ \ \ \ \ \ Thread[\
        Unevaluated[lhs], \ Equal\ ]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`\(Protect[Equal];\)\)], "Input"],

Cell[TextData[{
  "you can directly manipulate equations, ",
  StyleBox["e.g.",
    FontSlant->"Italic"],
  ","
}], "Text"],

Cell[BoxData[
    \(TraditionalForm\`\(a + 2\ x == x - b;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`% - a\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`2\ x == \(-a\) - b + x\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`% - x\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`x == \(-a\) - b\)], "Output"]
}, Open  ]],

Cell["or", "Text"],

Cell[BoxData[
    \(TraditionalForm\`\(\ at 2\^\(x - 1\) == 5\ b;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    FormBox[
      RowBox[{"Simplify", "[",
        RowBox[{\(log(%)\), ",",
          RowBox[{"x", "\[Element]",
            TagBox["\[DoubleStruckCapitalR]",
              (Reals&)]}]}], "]"}], TraditionalForm]], "Input"],

Cell[BoxData[
    \(TraditionalForm\`1\/2\ \((x - 1)\)\ \(log(2)\) ==
      log(5\ b)\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "Note that ",
  Cell[BoxData[
      FormBox[
        RowBox[{"x", "\[Element]",
          TagBox["\[DoubleStruckCapitalR]",
            (Reals&)]}], TraditionalForm]]],
  " is required here. Then we can proceed:"
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`2  %\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`\((x - 1)\)\ \(log(2)\) ==
      2\ \(log(5\ b)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`%\/\(log(2)\)\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`x -
        1 == \(2\ \(log(5\ b)\)\)\/\(log(2)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`% + 1\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`x == \(2\ \(log(5\ b)\)\)\/\(log(2)\) +
        1\)], "Output"]
}, Open  ]]
}
]

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________




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