Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2000
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

Questions about RoxReduce

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23871] Questions about RoxReduce
  • From: jmcornil <jmcornil at club-internet.fr>
  • Date: Thu, 15 Jun 2000 00:51:09 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

I have a few questions about the function RowReduce.

Please see the attached NoteBook

Thank You for answer

J.M. CORNIL

(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 4.0,
MathReader 4.0, or any compatible application. The data for the notebook 
starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do one of 
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the 
word CacheID, otherwise Mathematica-compatible applications may try to 
use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info at wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[      6966,        203]*)
(*NotebookOutlinePosition[      7874,        230]*)
(*  CellTagsIndexPosition[      7830,        226]*)
(*WindowFrame->Normal*)



Notebook[{
Cell["\<\
I have a few questions about the function RowReduce, please see the atthached \
NoteBook.
\
\>", "Text"],

Cell[CellGroupData[{

Cell["First question : ", "Subsection"],

Cell["\<\
The function RowReduce perform a Gauss-Jordan reduction putting
1 on the \"diagonal\" and 0 elsewhere so long it is possible. But is there 
an other function (or an option for RowReduce) performing a simple
Gauss reduction i.e. putting 0  ONLY UNDER the first diagonal ?

By the way I saw there is an option \"Method\" for the function.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Options[RowReduce]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`{Method \[Rule] Automatic, Modulus \[Rule] 0, 
      ZeroTest \[Rule] Automatic}\)], "Output"]
}, Open  ]],

Cell["and I did not found any help on it. How to use it ? ", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Second question : ", "Subsection"],

Cell[TextData[{
  "I did not foud any function to perform a \"limited\" Gauss reduction, i.e. \
a function performing\na reduction up to a column number .  Such an option \
woud be useful in a case as follows \nto get equations of the image of a \
matrice. \n\nIf you let RowReduce working as it will, you also reduce the \
last column (since for\nformally the polynoms in  ",
  Cell[BoxData[
      \(TraditionalForm\`y\_i\)]],
  " are not ZERO) and you cannot get the equations."
}], "Text"],

Cell[BoxData[{
    \(\(n = 5;\)\), "\[IndentingNewLine]", 
    \(\(m = 
        Table[\((i + j - 1)\)^2, {i, n}, {j, 
            n}];\)\), "\[IndentingNewLine]", 
    \(\(v = Table[y\_i, {i, n}];\)\), "\[IndentingNewLine]", 
    \(\(<< LinearAlgebra`MatrixManipulation`;\)\), "\[IndentingNewLine]", 
    \(mv = AppendRows[m, Transpose[{v}]]\)}], "Input"],

Cell[BoxData[
    FormBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"1", "4", "9", "16", "25", \(y\_1\)},
            {"4", "9", "16", "25", "36", \(y\_2\)},
            {"9", "16", "25", "36", "49", \(y\_3\)},
            {"16", "25", "36", "49", "64", \(y\_4\)},
            {"25", "36", "49", "64", "81", \(y\_5\)}
            }], "\[NoBreak]", ")"}], TraditionalForm]], "Output"],

Cell[CellGroupData[{

Cell[BoxData[
    \(RowReduce[mv]\)], "Input"],

Cell[BoxData[
    FormBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"1", "0", "0", "1", "3", "0"},
            {"0", "1", "0", \(-3\), \(-8\), "0"},
            {"0", "0", "1", "3", "6", "0"},
            {"0", "0", "0", "0", "0", "1"},
            {"0", "0", "0", "0", "0", "0"}
            },
          ColumnAlignments->{Decimal}], "\[NoBreak]", ")"}], 
      TraditionalForm]], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Third and (last) question : ", "Subsection"],

Cell[TextData[{
  "So I qickly wrote some lines to get my aim. But I am just beginning to \
program with ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  "\nand it is written as with Pascal and other classical languages.\nIs ther \
a mean to write such a function using more pattern-matching ? "
}], "Text"],

Cell[BoxData[
    \(\(\(gaussElim[m_, 
        jmax_]\)\(:=\)\(\[IndentingNewLine]\)\(Module[{}, \
\[IndentingNewLine]mm = 
          m; \[IndentingNewLine]nl = \(Dimensions[
              mm]\)[\([1]\)]; \[IndentingNewLine]nc = \(Dimensions[
              mm]\)[\([2]\)]; \[IndentingNewLine]For[i0 = 1; 
          j0 = 1, \[IndentingNewLine]\ \ \ \ \ \ i0 <= nl; 
          j0 <= Min[nc, 
              jmax], \[IndentingNewLine]\ \ \ \ \ \ \ \(i0++\)\ ; \(j0++\)\ , \
\[IndentingNewLine]\ \ \ \ \ \ ip = i0; \[IndentingNewLine]\ \ \ \ \ \ While[
            ip < nl && 
              mm[\([ip, j0]\)] == 
                0, \(ip++\)]; \[IndentingNewLine]\ \ \ \ \ \ If[
            mm[\([ip, j0]\)] \[Equal] 0, \(i0--\); 
            Continue[]]; \[IndentingNewLine]\ \ \ \ \ \ \n\ \ \ \ \ \ \
{mm[\([i0]\)], mm[\([ip]\)]} = {mm[\([ip]\)], 
              mm[\([i0]\)]}; \n\ \ \ \ \ \ \ \ \ \[IndentingNewLine]\ \ \ \ \ \
For[i = i0 + 1, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ i \[LessEqual] 
              nl, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \(i++\), \
\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ mm[\([i]\)] = 
              Simplify[
                mm[\([i]\)] - 
                  mm[\([i, j0]\)]/mm[\([i0, j0]\)]*
                    mm[\([i0]\)]]];\[IndentingNewLine]]; \
\[IndentingNewLine]mm]\)\(\[IndentingNewLine]\)\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(gaussElim[mv, 5]\)], "Input"],

Cell[BoxData[
    FormBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"1", "4", "9", "16", "25", \(y\_1\)},
            {"0", \(-7\), \(-20\), \(-39\), \(-64\), \(y\_2 - 4\ y\_1\)},
            {"0", 
              "0", \(8\/7\), \(24\/7\), \(48\/7\), \(\(17\ y\_1\)\/7 - \(20\ \
y\_2\)\/7 + y\_3\)},
            {"0", "0", "0", "0", 
              "0", \(\(-y\_1\) + 3\ y\_2 - 3\ y\_3 + y\_4\)},
            {"0", "0", "0", "0", 
              "0", \(\(-3\)\ y\_1 + 8\ y\_2 - 6\ y\_3 + y\_5\)}
            }], "\[NoBreak]", ")"}], TraditionalForm]], "Output"]
}, Open  ]]
}, Open  ]],

Cell["Thanks very much for answer,", "Text"],

Cell["\<\
Jack-Michel CORNIL                    

VERSAILLES-FRANCE\
\>", "Subsubtitle"]
},
FrontEndVersion->"4.0 for Microsoft Windows",
ScreenRectangle->{{0, 800}, {0, 527}},
CellGrouping->Manual,
WindowSize->{671, 459},
WindowMargins->{{Automatic, 31}, {18, Automatic}},
StyleDefinitions -> FrontEnd`FileName[{ParentDirectory[ParentDirectory[]], \
"Program Files", "Wolfram Research", "Mathematica", "4.0", "SystemFiles", \
"FrontEnd", "StyleSheets"}, "Default.nb", CharacterEncoding -> "WindowsANSI"]
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of 
the file.  The cache data will then be recreated when you save this file 
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{
Cell[1717, 49, 114, 4, 52, "Text"],

Cell[CellGroupData[{
Cell[1856, 57, 39, 0, 47, "Subsection"],
Cell[1898, 59, 360, 7, 128, "Text"],

Cell[CellGroupData[{
Cell[2283, 70, 51, 1, 30, "Input"],
Cell[2337, 73, 131, 2, 29, "Output"]
}, Open  ]],
Cell[2483, 78, 68, 0, 33, "Text"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2588, 83, 40, 0, 47, "Subsection"],
Cell[2631, 85, 492, 9, 128, "Text"],
Cell[3126, 96, 355, 7, 110, "Input"],
Cell[3484, 105, 398, 8, 99, "Output"],

Cell[CellGroupData[{
Cell[3907, 117, 46, 1, 30, "Input"],
Cell[3956, 120, 406, 10, 99, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[4411, 136, 50, 0, 47, "Subsection"],
Cell[4464, 138, 315, 7, 71, "Text"],
Cell[4782, 147, 1368, 25, 430, "Input"],

Cell[CellGroupData[{
Cell[6175, 176, 49, 1, 30, "Input"],
Cell[6227, 179, 573, 12, 109, "Output"]
}, Open  ]]
}, Open  ]],
Cell[6827, 195, 44, 0, 33, "Text"],
Cell[6874, 197, 88, 4, 89, "Subsubtitle"]
}
]
*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)


  • Prev by Date: Re: Integral evaluation bug?
  • Next by Date: I wish Descending Order Result
  • Previous by thread: RE: Re: Functional Expression Meaning (was:A Functional Expression Trick)
  • Next by thread: Re: Questions about RoxReduce