## 266 Reputation

19 years, 161 days

## For a system, the fsolve command compute...

According to the online documentation about fsolve (?fsolve), "For a general equation or system of equations, the fsolve command computes a single real root. " Now, you can tell Maple to look in a specific interval or to start the search at a specific value for one or more of the variables. For instance,
```restart;
e1 := 3*x^2+3*y-a*(2*x-6);
e2 := 3*y^2+3*x-a*(2*y-6);
e3 := x^2+y^2-6*x-6*y+9;
fsolve({e1, e2, e3});
fsolve({e1, e2, e3}, {a, x = 5, y = 5});

print(`output redirected...`); # input placeholder
2
e1 := 3 x  + 3 y - a (2 x - 6)
2
e2 := 3 y  + 3 x - a (2 y - 6)
2    2
e3 := x  + y  - 6 x - 6 y + 9
{a = -1.167261890, x = 0.8786796564, y = 0.8786796564}
{a = 22.16726189, x = 5.121320344, y = 5.121320344}

```
Regards, -- Jean-Marc

## Inverse matrix uploaded on MaplePrimes (...

I have uploaded the inverse matrix obtained with Mathematica as a CSV file compressed with GZIP on MaplePrimes, so you can import the matrix back into Maple. Download 97_mat.csv.gz
View file details HTH, -- Jean-Marc

## Assuming you run Windows...

Assuming you run Windows: "Start" -> "All Programs" -> "Maple 12" -> "Command-line Maple 12" Regards, -- Jean-Marc

## Example of a 5x5 matrix...

Could you post an example of what you did (actual commands you used). For instance, for Q2, a 5x5 matrix with the Maple commands and the output. It would be easier to check what's went wrong (Q2 suggests you made a mistake either in the matrix itself or in the command to manipulate it).
```    |\^/|     Maple 12 (IBM INTEL NT)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> with(LinearAlgebra):
> M := Matrix([[a, 0, f, 0, 0], [0, b, 0\
> , 0, 0], [0, 0, c, 0, 0], [0, 0, 0, d, 0], [0, 0, 0, g, e]]);
[a    0    f    0    0]
[                     ]
[0    b    0    0    0]
[                     ]
M := [0    0    c    0    0]
[                     ]
[0    0    0    d    0]
[                     ]
[0    0    0    g    e]

> MatrixInverse(M);
[                 f                 ]
[1/a     0     - ---      0       0 ]
[                c a                ]
[                                   ]
[ 0     1/b      0        0       0 ]
[                                   ]
[ 0      0      1/c       0       0 ]
[                                   ]
[ 0      0       0       1/d      0 ]
[                                   ]
[                          g        ]
[ 0      0       0      - ---    1/e]
[                         d e       ]

```
Regards, -- Jean-Marc

## What is your exact configuration?...

Could you be more specific about your configuration? You seem to imply that you are working on a 64-bit platform (assuming you are talking about 4 GB of physical RAM and not of virtual memory), while the error reported suggest that you are using a 32-bit version of Maple xx.x (not being able to go beyond 2 GB of memory). Details such as operating system, Maple version, 32- or 64- bit hardware, etc., might be crucial to answer your question. Regards, -- Jean-Marc

## NewtonsMethodTutor is an interactive int...

NewtonsMethodTutor is a visual and interactive interface to the Maple function NewtonsMethod. So, you should read the online help pages related to both function and ask, if needed, more specific question(s). (Note that from your post, it is not clear, at lest for me, whether you have difficulties with the tutor or with the understanding of how Newton's method works.)
```> help("Student,Calculus1,NewtonsMethod");
> help("Student,Calculus1,NewtonsMethodTutor");
> with(Student[Calculus1]);
> NewtonsMethodTutor();
```
Regards, -- Jean-Marc

## proTeXt - MiKTeX-based distribution for ...

If you use Windows and know nothing about LaTeX, it may be worthwhile to have a look at proTeXt.
proTeXt aims to be an easy-to-install TeX distribution for Windows, based on MiKTeX. After downloading, it guides the installation via a short pdf document (available in English, French, German, and Italian), which provides clickable links to install the various components, along with explanations.
See http://www.tug.org/protext/ for more information and download link. What is worth noting is that proTeXt guide you during the installation process thanks to a pdf file that acts simultaneously as documentation and installer (via links to the relevant piece of software) and it includes TeXnicCenter (a visual shell for all the tools and some tool bars and shortcuts to ease the typesetting) as well as Ghostscript and GSview (pdf and ps/eps viewer. Also, they can be used to create/convert pdf and ps files). HTH, -- Jean-Marc

## Putting assumptions on constants should ...

Looking at the worksheet you posted, I would be more worried by the occurance of a term defined as the limit for lambda approaching zero on the right. This smells fishy ;-) Nevertheless, assuming that the expression returned by Maple makes sense, you should be able to get rid of the polylogarithms by telling Maple that the names c, h, k, and T are positive constants. To do so, you could use either assume() or assuming. See ?assume and ?assuming for detailed information. HTH, -- Jean-Marc

## Use rhs to apply the substitution to the...

My understanding is that a name can be of one type only at a time. Either it is a symbol (i.e. non-indexed name) or it is an indexed (subscripted) name (see ?names). One possible way to do the transformation you want is the following (we use the rhs function to apply the substitution to the right-hand side only),
```> eq := m = m[0]*x;
m = m[0] x

> eq := m = subs(m = k, rhs(eq));

m = k[0] x
> eq;

m = k[0] x
```
HTH, -- Jean-Marc

## Creating Mathematical Documents (User Ma...

In addition to J. Tarr's reply, you may be interested in browsing chapter 6 of the User Manual, chapter titled, "Creating Mathematical Documents." You can load the User Manual as a worksheet within Maple (see below) or/and download it as a pdf file at http://maplesoft.com/documentation%5Fcenter/ Regards, -- Jean-Marc

## 2D-Math region within a text region seem...

I may have failed to understand you correctly, but 2D-Math region within a text region seems to work without interpreting the maths or preprocessing the maths. Now, since there exists different interfaces with more or less overlapping modes, it could be better if you post an example of what you did and what went wrong. The following non-imaginative sample document seems to display things as expected.

Say we have a function . If we compare it against , we see ...

>

>

>

This post was generated using the MaplePrimes File Manager

View file details

## Nested sequences...

Depending on whether u and v have different values or are equal, you could use two nested seq command or just one sequence with the arguments for x1, y1, and z1 duplicated, as illustrated by the following examples: ``` restart; with(plots): with(plottools): x1 := proc (u, v) options operator, arrow; sin(u*Pi)*cos(v*Pi) end proc; y1 := proc (u, v) options operator, arrow; sin(u*Pi)*sin(v*Pi) end proc; z1 := proc (u, v) options operator, arrow; cos(u*Pi) end proc; x2 := proc (u, v) options operator, arrow; 3*sin(u*Pi)*cos(v*Pi) end proc; y2 := proc (u, v) options operator, arrow; 3*sin(u*Pi)*sin(v*Pi) end proc; z2 := proc (u, v) options operator, arrow; 3*cos(u*Pi) end proc; p1 := plot3d([x1(u, v), y1(u, v), z1(u, v)], u = 0 .. 1, v = 0 .. 2, color = blue, axes = normal); points := {seq(seq([x1((1/50)*k, (1/150)*n), y1((1/50)*k, (1/150)*n), z1((1/50)*k, (1/150)*n)], k = 0 .. 314), n = 0 .. 314)}; display(p1, pointplot3d(points)); ``` ``` points := {seq([x1((1/50)*k, (1/50)*k), y1((1/50)*k, (1/50)*k), z1((1/50)*k, (1/50)*k)], k = 0 .. 314)}; display(p1, pointplot3d(points)); ``` Hope this helps, -- Jean-Marc

## Piecewise vs Parametric Form...

I do not have Maple 8 at hand, but the issue seems to be related to the structure of the result returned by both functions. Spline returns a piecewise function, whereas BSplineCurve returns a parametric function. So the first structure can be directly integrated. Here is what we can read in Maple 11 online help for Spline,
The Spline routine computes a degree d piecewise polynomial in variable v that approximates the points {(x0, y0), (x1, y1), ..., (xn, yn)}.
and for BSplineCurve,
The resulting curve is in parametric form [xf(v), yf(v), v=a..b], where xf(v) and yf(v) are piecewise functions of v, and a..b is the range over which the B-spline curve is defined.
```with(CurveFitting):
Spline([[0,0],[1,1],[2,4],[3,3]], v);

/       1     4  3         14   41     42  2      3
piecewise|v < 1, - v + - v , v < 2, -- - -- v + -- v  - 2 v ,
\       5     5            5    5      5

114   151     54  2   6  3\
- --- + --- v - -- v  + - v |
5     5      5       5   /

type(%, piecewise);
true

```
Does this match your problem with Maple 8? Regards, -- Jean-Marc

## The "less than" character of death strik...

Jacques, Your post (especially the piecewise function) has been victim of the "less than" character when it occurs in some HTML code posted on MaplePrimes. Replace any occurrence of "less than" by the HTML safe proof code "<" (without the quotation marks). Best regards, -- Jean-Marc

## The function applyrule may be more appro...

The function applyrule may be more appropriate to cleanly handle the example you provided.
```> applyrule([a*b = x, 1/(a*b) = 1/x], f);
c
- + d x
x

```
Regards, -- Jean-Marc
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