Mr. Roman Pearce

## 1683 Reputation

19 years, 299 days
CECM/SFU
Research Associate

I am a research associate at Simon Fraser University and a member of the Computer Algebra Group at the CECM.

## symbolic linear algebra...

As far as I know, this functionality doesn't exist in Maple.

## solve...

solve converts all the floating point numbers to exact rationals producing the following system:
```sys := {-194000-75000*x+5550*x^2+10000*x^3-25*x^4-3*x^5+500*y, 6800-2120*y+174*y^2-4*y^3+x};
```
solve notices that the last equation is linear in x, and substitutes
``` x = -6800+2120*y-174*y^2+4*y^3;
```
To obtain a degree 15 polynomial in y. The polynomial (call it p) is irreducible, so the proper thing to do is to declare the following to be the solution:
```{y=RootOf(p,y),  x = -6800+2120*y-174*y^2+4*y^3}
```
However this is where things take a turn for the worse. We somehow enter solve/rec and solve/rec2 and start applying linear transformations. It does try to factor the polynomial but when it doesn't factor it just keeps going with other methods. For what it's worth, the following input takes 37 seconds on my 1GHz iBook:
```p := -67923175392176599500*y-66270720*y^13+668160*y^14-3072*y^15+5757954385686159800*y^4-1159603769167725600*y^5+171252983206568800*y^6-18894385084992000*y^7+1571418646431600*y^8-98615035315200*y^9+4636705360672*y^10-160596365760*y^11+3971256320*y^12+47938232092490490000*y^2-20292994655276788000*y^3+43561409537141806000:
solve(p,{y});
```
The factor command takes .039 seconds, which is what we should expect.

## use fsolve...

You have no hope of solving this system directly with solve, and even fsolve will choke, however if you have Maple 10.04 you can try the following:
```sys := map(convert, {eq1,eq2,eq3}, rational):  # convert to rational numbers
sys := map(numer, map(lhs-rhs, sys)):  # get numerators = 0
kernelopts(opaquemodules=false):  # access internal commands
F, R, M, V := PolynomialIdeals:-substitute_everything(sys):  # magic
sys2 := subs(F, sys) union {op(M)};
```
The result is an equivalent system with 6 equations and 6 unknowns. All radicals are removed and replaced by variables. I would not recommend trying to solve this system exactly, however fsolve can find a numerical solution.
```Digits := 30:   # set desired precision
sol2 := fsolve(sys2);
sol := `union`(seq(solve(i,indets(i,'name')), i=subs(R,sol2)));  # replace variables in solution
```
I got {A = 0., zp = -1., zh = 551489.3617} with Digits=10.
```subs(sol, sys);  # check result
```

## try a table...

Try using a table with a while loop, and then making a list at the end.
```data := table();
N := 0;
while something do
N := N+1;
x := ...;
y := ...;
data[N] := [x,y];
end do:
data := [seq(data[i], i=1..N)]:
```

## diagonal matrix...

Matrix(B, shape=diagonal);

## are all of your commands broken ?...

Do all of the above commands actually work ? For example, try /bin/ls in your home directory. Does it produce the error reported above ? If so, then your Linux installation has a problem. If not, then something is very odd with Maple's install process.

## restart clears everything...

The restart command clears everything, including loaded packages.

## linear algebra over generic domains...

This functionality is not currently implemented, however there has been work in this direction by Simon Lo (shown at the Maple Conference) so you should watch for something in a future release of Maple. This paper gives an overview.

## plotdevice...

See the help pages for ?plotsetup and ?plotdevice. Basically you enter plotsetup('gif'); but there are a number of other options you may be interested in. On a related note, when I am working in command line Maple I use plotsetup(x11) to plot nice X11 plots. I have the following line in my .mapleinit file:
```if not IsWorksheetInterface() then plotsetup(x11) end if:
```
It might be useful if you want to preview the plots.

## contact Maplesoft support...

Firewall is the only thing I can think of, and you mentioned turning that off. You should contact Maplesoft's tech support (see http://www.maplesoft.com/support/).

## Linux versions...

There is actually only one Maple installer for 32-bit Linux, and it should work on Ubuntu. Redhat, Suse, etc are the only platforms with official support however.

## I couldn't figure this out...

I couldn't figure out how to do this either and it is really annoying.

## mws...

Old Maple worksheets should have the extension .mws. Newer versions of Maple will open and save .mws files, and you can of course save them as .mw files instead. I don't think there is a tool available for batch conversion of worksheets however. You would have to open and save them one by one.

## numerical products...

Numerical products are simplified automatically by the kernel, so without rewriting large parts of diff, the answer is no. However, if all of your expressions are restricted to a particular form it should be possible to set up what you want. Presumably you are trying to generate some sort of system of equations. Can you explain a little more and perhaps provide an example ?

## networks draw bug...

This is a bug in the drawing code and you should contact Maplesoft's support. Tell them that the problem is in the `draw/concentric` routine, which should ignore vertices not in the graph (but leave space for them on the circle). That way when you delete vertices in the graph the drawing doesn't change.
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