## if only on parameter of 2D is to be shown in 3D

Mathematica

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• 1. what is my error?
eqns = {mr + mp == 13, fr + fp == 19, mr + fr == 15, mp + fp == 17}NSolve[eqns, {mr, mp, fr, fp}] gives {{mr->-4.+1. fp,mp->17.-1. fp,fr->19.-1. fp}} The solution is {mr->8, mp->5, fr->7, fp->12} if mr,mp,fr,fp are greater than zero -- Richard Palmer
• 2. Documentation
I guess I have been rather slow but I am gradually coming round to the view that Mathematica's documentation leaves something to be desired. For example: ?CoefficientDomain CoefficientDomain is an option for GroebnerBasis and PolynomialReduce. Valid choices are Integers, Rationals, RationalFunctions, or Polynomials[var]. However: ?InexactNumbers InexactNumbers is a setting for the CoefficientDomain option of GroebnerBasis and PolynomialReduce. InexactNumbers are mentioned in the main documentation: Possible settings for CoefficientDomain are InexactNumbers, Rationals, RationalFunctions and Polynomials[x]. but this is still quite hopeless as documentation as there is nothing to tell the user that the proper usage is: GroebnerBasis[polys, vars, CoefficientDomain -> InexactNumbers[n]] where n is precision. No wonder that I am yet to meet a person that has heard of numerical Groebner basis in Mathematica never mind anyone actually using it. Andrzej Kozlowski Chiba, Japan
• 3. Replacing expressions with smaller atoms
If I define an atom eg L=x^2+x+1, is there a way to rewrite an expression with these atoms? For example: L=x^2+x+1 M=x+(x(x^2+x+1))^(1/2) I would like some way to express this as x+(xL)^(1/2). Is this possible?
• 4. 1GB Kernel Memory Limit
Hi, all, I'm currently working on a problem that requires a whole lot of memory to complete. Sometimes, depending on the specific parameters being used, I will receive the dreaded, "No more memory available," message. Doing my best to track memory usage with MemoryInUse[], MaxMemoryUsed [] and the Windows Task Manager, I find that the kernel quits when it hits a limit of around one gigabyte. I'm using Version 7.0 on 32-bit Windows XP without the /3GB switch active; neither switching to a 64 bit OS nor activating the /3GB switch are possibilities. However, I was under the distinct impression that even without the /3GB switch active I should have a per-process memory limit of 2GB, not 1GB. Is there some other reason the kernel might quit, due to either Mathematica settings or OS settings? As for modifying my program I've done obvious things like setting \$HistoryLength = 0, Clear[]ing things that are no longer needed, and none of them have done the trick in all cases I've needed to deal with. I've also done an array of not-so-obvious things that haven't worked either. Any suggestions would be greatly appreciated. Thanks Pillsy

### Re: if only on parameter of 2D is to be shown in 3D

```Hi Bob,

Thanks. I wish to be able to see either the red lines or the blue
lines, but not both of them together showing small surface cells. Each
surface element should appear with very long aspect ratio, as
rectangles, but never mind.

After the above, opaque surface is required to be shown, usually as in
default Option .

Regards
Narasimham

```

### Re: if only on parameter of 2D is to be shown in 3D

```
----
Hi Bob,

I did not want to  watch parameter increments, but suppression of
either u or v lines in each display.

With your full  indicating several variations to pick out from, I got
it right here:

For u lines,

UU = Show[ Table[ParametricPlot3D[{u + v, u - v, v*u}, {v, -4, 2},
PlotStyle -> Directive[Blue]], {u, -2, 4, .2}]]

If v lines are needed,

VV = Show[ Table[ParametricPlot3D[{u + v, u - v, v*u}, {u, -4,
2},      PlotStyle -> Directive[Red]], {v, -2, 4, .2}]]

Show[UU, VV] ,  if both are to be seen in different colors.

Now remains only the requirement for showing opaque shaded surface
option.

Thanks  again,

Narasimham

```

### Re: if only on parameter of 2D is to be shown in 3D

```to suppress the lines just use the Mesh option.

Row[ParametricPlot3D[{u + v, u - v, v*u},
{u, -4, 4}, {v, -4, 4},
ImageSize -> 200,
Mesh -> #] & /@
{Full, {15, 0}, {0, 15}}]

Bob Hanlon

=============

----
Hi Bob,

I did not want to  watch parameter increments, but suppression of
either u or v lines in each display.

With your full  indicating several variations to pick out from, I got
it right here:

For u lines,

UU = Show[ Table[ParametricPlot3D[{u + v, u - v, v*u}, {v, -4, 2},
PlotStyle -> Directive[Blue]], {u, -2, 4, .2}]]

If v lines are needed,

VV = Show[ Table[ParametricPlot3D[{u + v, u - v, v*u}, {u, -4,
2},      PlotStyle -> Directive[Red]], {v, -2, 4, .2}]]

Show[UU, VV] ,  if both are to be seen in different colors.

Now remains only the requirement for showing opaque shaded surface
option.

Thanks  again,

Narasimham

```