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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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