## Second order slope field...

Hey

Is it possible to draw a slope field for a second order differential equation with initial conditions?

## .eps figures produced by Maple are often excessive...

Why 3D .eps figures produced by Maple 2020 are often excessively large?

So, it´s a little heavy to the viewer and to compile to PDF.

• How could we reduce the size without losing any quality?

## show steps for isolate function...

as i can see there are functions to show steps of a calculation

such as ExpandSteps() and ShowSolution()

but would it not be possible to use these or some other function to show steps of the function called isolate()

it should be trivial since most online calculators are able to do this. and so does maple in the back - we just don't see the steps only the result

thanks regards mikkel

## Solving vorticity equation...

Hello,

I'm having some difficulty solving a set of equations. For example

dn/dt = Const*(phi - n)

ds/dt= Const*(phi-n)

s = d2 phi/dx2 + d2 phi/dy2

How do you solve a system like this? It is 2 equations with 2 unknowns, but it is the s variable that is evolved, i.e. ds/dt, instead of phi.

Anyone know of some code that could do this? (periodic boundary conditions)

Better yet, how do you formulate this as a regular ODE for n and phi?

## Some queries in matrix evaluation ...

Dear Users!

Hope everyone fine here. I have following three quires that need to be fix.

1. I want to collocate Vector IntXYZ1 and IntXYZ2 present in file Q1 in such a way that the first M1M2 + 2(M3-1)M2 + 2(M3-1)(M1-2) rows are zero and other rows are collocated at x=(i-1)/(M1-1), y=(j-1)/(M2-1), t=(k-1)/(M3-1) for i = 2,3,…,M1-1, j = 2,3,…,M2-1, k = 2,3,…,M3 as given as XX (of order 27 by 27 with first 25 rows are zero) for M1=M2=M3=3

2. Next, in file Q2 we have a Vector b with some entries which are actually the values of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2] in such a following way

(Vector(8, {(1) = chi[1, 1, 1], (2) = chi[1, 1, 2], (3) = chi[1, 2, 1], (4) = chi[1, 2, 2], (5) = chi[2, 1, 1], (6) = chi[2, 1, 2], (7) = chi[2, 2, 1], (8) = chi[2, 2, 2]})) = (Matrix(8, 1, {(1, 1) = 0, (2, 1) = 0, (3, 1) = 0, (4, 1) = 0, (5, 1) = 1.000000000, (6, 1) = 1.000000000, (7, 1) = 1.000000000, (8, 1) = .3678794412}))

Matrix B given in file Q2 have entires which are the linear cobiniation of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2]. I want to evaluate matrix B at the values of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2] which are obtained in vector b.

3. I want to recall a vector B in file Q3 at highlighted portion and B matrix is present in Q4. Which is the command to recall or export a matrix which contain in some other file like in file Q4.

I shall be very grateful for your support.

## Proof of an inequality...

``` Let d an integer ">=5 " and
"lambda  in ]-(1)/(2),-(1)/(d+1)[. "
Put
> gamma[s+1,d]=((s+1)[d]((d+1)lambda+s))/(2^(d+1)(lambda+s)[d+1]).;
We need to show that
> gamma[s+1,d]>=-(1)/(2^(s+1)),;
for
> s=1,...,[(d+1)/(2)].;

a[k] designates the pochhammer symbol.
```

Thanks a lot

## How can I constrain/set an asymptote at y = 1 for ...

If you could assist; I am trying to set something like an asymptote or upper limit such that my plot below approaches asymptotically (below y =1 ) from negative infinity:

## how to get types to show up in command completion?...

command completion (when hitting the ESC key) in Maple could be made more useful. It does not seem to support type names for example.

What shows up on the command completion window are  possible commands that start with that partial text.

It does not list other known names by Maple, such as type names and other options.

This makes it hard to use in many places, where one have to remember type names exactly instead of the system helping them by listing all possible type names that start with that string.

Is there a way around this? Will Maple next version support smarter and more complete command completion menu?

## how do i solve a partial differential equation in...

AoA....

sir how we solve partial differential equation by Adomian Decomposition method in maple? plz send me maple code..

## trapezoid rule using loop...

Dear all

I tried to compute an integral using trapezoidal rule using two differents methods but I get two different results
trap.mw

## Matlab has a great package. Why can' t we create a...

Matlab has some great functions package which accomplishes:

• This function saves a figure or single axes to one or more vector and/or bitmap file formats, and/or outputs a rasterized version to the workspace, with the following properties:
- Figure/axes reproduced as it appears on screen
- Embedded fonts (pdf only)
- Improved line and grid line styles
- Anti-aliased graphics (bitmap formats)
- Render images at native resolution (optional for bitmap formats)
- Transparent background supported (pdf, eps, png, tiff)
- Semi-transparent patch objects supported (png, tiff)
- RGB, CMYK or grayscale output (CMYK only with pdf, eps, tiff)
- Variable image compression, including lossless (pdf, eps, jpg)
- Optional rounded line-caps (pdf, eps)
- Optionally append to file (pdf, tiff)
- Vector formats: pdf, eps
- Bitmap formats: png, tiff, jpg, bmp, export to workspace

• Why don't we all together in this forum create a package like that? :) At least I  hope we can create for most important of the functions like cropping border etc. Many Maple users need a code like that.

• I don't know whether we can quickly convert these codes to maple codes or not.  But maybe we use all code in this forum about this and create a new package.

Best regards.

## How to get Grid Run execute in parallel?...

Hi,

I was hoping to run two procs: tgf3 and tgf4 in parallel using Grid, Run and get a faster execution time. As I understood the description of Grid Run, the first call to Grid Run will run in the background and before it is finished the second call Grid Run will start. I do not believe I have that situation in my script. I am not understanding Grid Run. How can this problem be fixed? Here is just a portion of the script using Grid Run:

Use Grid Run 0 for tgf3 and 1 for tgf4. Determine the real time and compare times. The Grid Runs do not appear to run in parallel.

rgt := time[real]();
Grid:-Run(0, `~`[tgf3@op](convert(L, listlist)), 'assignto' = ans3roots);
Grid:-Run(1, `~`[tgf4@op](convert(L, listlist)), 'assignto' = ans4roots);
ans3roots;
ans4roots;

GridRunTime := time[real]() - rgt;
GridRunTime := 44.074

Here is my script:

Grid_Run_2.mw

## Problem in maple built in FGb method of calculatin...

When I am using

Polynomialdeal package:

sys:=[p31,p32,p33];

as in the end of the post. (for one to reproduce)

`J := PolynomialIdeal(sys, characteristic = p)`

and calculate the corresponding Groebner basis.

It report this "Error, (in Groebner:-Basis) Segmentation Violation occurred in external routine".

Does anyone know how to fix this error?

Here is the output details.

infolevel[GroebnerBasis] := 5;

GB:=Groebner[Basis](sys,IdealInfo[DefaultMonomialOrder](J),method=fgb);

memory used=712.9MB, alloc=103.8MB, time=4.48
memory used=779.3MB, alloc=111.8MB, time=4.89
-> MGb
domain: rat_int_cof
F4 algorithm
1: prime=2132425153
deg  pairs  taken         matrix                                        found
6     20      1         8 x 1018       238.5 per row,     0.0 MB      1 new,      0 zero     0.007 sec
8     22      3       310 x 20321      288.7 per row,     0.7 MB      3 new,      0 zero     0.035 sec
9     28      5       818 x 38796      397.2 per row,     2.5 MB      5 new,      0 zero     0.069 sec
10     37     18      5118 x 220200     532.9 per row,    20.8 MB     16 new,      2 zero     0.386 sec
11     83     52     21117 x 653954     835.4 per row,   134.7 MB     35 new,     17 zero     1.844 sec
12    218    153     84758 x 2148937   1314.0 per row,   850.0 MB    100 new,     53 zero    14.546 sec
13    690    551    336032 x 6779582   2133.6 per row,  5471.1 MB    310 new,    241 zero   222.741 sec
14   2256   1875   1144460 x 18963907  3811.9 per row, 33288.2 MB    732 new,   1143 zero  2407.556 sec
15   5978   5202  error in FGb
Error, (in Groebner:-Basis) Segmentation Violation occurred in external routine

p31:=-2*(a2^3*A20 + a2^2*a3*(2*A20 - A40) + a1^2*(A20*a3 - a3*A30 + a2*(A20 - A40) - a3*A40 + A10*(a3 - a5) - A20*a5) - a4*(A10*a3*(a3 + a4) + A40*a5*(a4 + a5) + A20*(a3 - a5)*(a3 + a4 + a5)) + a1*(A20*a3^2 - a3^2*A30 + 2*a3*A30*a4 + a2^2*(2*A20 - A40) - a3^2*A40 + 2*a3*a4*A40 + 2*a3*A30*a5 + 2*a3*A40*a5 - A20*a5^2 + a2*(2*A10*a3 + 3*A20*a3 - a3*A30 - 2*a3*A40 + 2*a4*A40 - A20*a5) + A10*(a3^2 - a5^2)) - a2*(A40*(a3^2 - 2*a3*a5 - 2*a4*a5) + A20*(-a3^2 + a3*a4 + a4^2 + a4*a5 + a5^2)));

p32:=1/8 + 2*(-(a2^3*A21) + A11*a3^2*a4 + A21*a3^2*a4 + A11*a3*a4^2 + A21*a3*a4^2 - A21*a4^2*a5 + a4^2*A41*a5 - A21*a4*a5^2 + a4*A41*a5^2 - A10*a3^2*b1 - A20*a3^2*b1 + a3^2*A30*b1 - 2*a3*A30*a4*b1 + a3^2*A40*b1 - 2*a3*a4*A40*b1 - 2*a3*A30*a5*b1 - 2*a3*A40*a5*b1 + A10*a5^2*b1 + A20*a5^2*b1 - A20*a3^2*b2 + A20*a3*a4*b2 + A20*a4^2*b2 + a3^2*A40*b2 + A20*a4*a5*b2 - 2*a3*A40*a5*b2 - 2*a4*A40*a5*b2 + A20*a5^2*b2 + 2*A10*a3*a4*b3 + 2*A20*a3*a4*b3 + A10*a4^2*b3 + A20*a4^2*b3 + a2^2*(-2*A21*a3 + a3*A41 - 2*A20*b1 + A40*b1 - 3*A20*b2 - 2*A20*b3 + A40*b3) + A10*a3^2*b4 + A20*a3^2*b4 + 2*A10*a3*a4*b4 + 2*A20*a3*a4*b4 - 2*A20*a4*a5*b4 + 2*a4*A40*a5*b4 - A20*a5^2*b4 + A40*a5^2*b4 - A20*a4^2*b5 + a4^2*A40*b5 - 2*A20*a4*a5*b5 + 2*a4*A40*a5*b5 + a1^2*(-(A21*a3) + a3*A31 + a3*A41 + a2*(-A21 + A41) + A21*a5 + A11*(-a3 + a5) - A20*b2 + A40*b2 - A10*b3 - A20*b3 + A30*b3 + A40*b3 + A10*b5 + A20*b5) + a1*(-(A21*a3^2) + a3^2*A31 - 2*a3*A31*a4 + a3^2*A41 - 2*a3*a4*A41 + a2^2*(-2*A21 + A41) - 2*a3*A31*a5 - 2*a3*A41*a5 + A21*a5^2 + A11*(-a3^2 + a5^2) - 2*A10*a3*b1 - 2*A20*a3*b1 + 2*a3*A30*b1 + 2*a3*A40*b1 + 2*A10*a5*b1 + 2*A20*a5*b1 - 2*A10*a3*b2 - 3*A20*a3*b2 + a3*A30*b2 + 2*a3*A40*b2 - 2*a4*A40*b2 + A20*a5*b2 - 2*A10*a3*b3 - 2*A20*a3*b3 + 2*a3*A30*b3 - 2*A30*a4*b3 + 2*a3*A40*b3 - 2*a4*A40*b3 - 2*A30*a5*b3 - 2*A40*a5*b3 - 2*a3*A30*b4 - 2*a3*A40*b4 - 2*a3*A30*b5 - 2*a3*A40*b5 + 2*A10*a5*b5 + 2*A20*a5*b5 + a2*(-2*A11*a3 - 3*A21*a3 + a3*A31 + 2*a3*A41 - 2*a4*A41 + A21*a5 - 2*A20*b1 + 2*A40*b1 - 4*A20*b2 + 2*A40*b2 - 2*A10*b3 - 3*A20*b3 + A30*b3 + 2*A40*b3 - 2*A40*b4 + A20*b5)) + a2*(a3^2*A41 - 2*a4*A41*a5 + A21*(-a3^2 + a3*a4 + a4^2 + a4*a5 + a5^2) - 2*a4*A40*b1 + A20*a5*b1 + A20*a4*b3 - 2*A40*a5*b3 + 2*A20*a4*b4 + A20*a5*b4 - 2*A40*a5*b4 + A20*a4*b5 - 2*a4*A40*b5 + 2*A20*a5*b5 + a3*(-2*A41*a5 - 2*A10*b1 - 3*A20*b1 + A30*b1 + 2*A40*b1 - 4*A20*b2 + 2*A40*b2 - 2*A20*b3 + 2*A40*b3 + A20*b4 - 2*A40*b5)));

p33:=2*(-(A11*a3^2*b1) - A21*a3^2*b1 + a3^2*A31*b1 - 2*a3*A31*a4*b1 + a3^2*A41*b1 - 2*a3*a4*A41*b1 - 2*a3*A31*a5*b1 - 2*a3*A41*a5*b1 + A11*a5^2*b1 + A21*a5^2*b1 - A10*a3*b1^2 - A20*a3*b1^2 + a3*A30*b1^2 + a3*A40*b1^2 + A10*a5*b1^2 + A20*a5*b1^2 - A21*a3^2*b2 + A21*a3*a4*b2 + A21*a4^2*b2 + a3^2*A41*b2 + A21*a4*a5*b2 - 2*a3*A41*a5*b2 - 2*a4*A41*a5*b2 + A21*a5^2*b2 - 2*A10*a3*b1*b2 - 3*A20*a3*b1*b2 + a3*A30*b1*b2 + 2*a3*A40*b1*b2 - 2*a4*A40*b1*b2 + A20*a5*b1*b2 - 2*A20*a3*b2^2 + a3*A40*b2^2 + 2*A11*a3*a4*b3 + 2*A21*a3*a4*b3 + A11*a4^2*b3 + A21*a4^2*b3 - 2*A10*a3*b1*b3 - 2*A20*a3*b1*b3 + 2*a3*A30*b1*b3 - 2*A30*a4*b1*b3 + 2*a3*A40*b1*b3 - 2*a4*A40*b1*b3 - 2*A30*a5*b1*b3 - 2*A40*a5*b1*b3 - 2*A20*a3*b2*b3 + A20*a4*b2*b3 + 2*a3*A40*b2*b3 - 2*A40*a5*b2*b3 + A10*a4*b3^2 + A20*a4*b3^2 + a2^2*(A41*(b1 + b3) - A21*(2*b1 + 3*b2 + 2*b3)) + A11*a3^2*b4 + A21*a3^2*b4 + 2*A11*a3*a4*b4 + 2*A21*a3*a4*b4 - 2*A21*a4*a5*b4 + 2*a4*A41*a5*b4 - A21*a5^2*b4 + A41*a5^2*b4 - 2*a3*A30*b1*b4 - 2*a3*A40*b1*b4 + A20*a3*b2*b4 + 2*A20*a4*b2*b4 + A20*a5*b2*b4 - 2*A40*a5*b2*b4 + 2*A10*a3*b3*b4 + 2*A20*a3*b3*b4 + 2*A10*a4*b3*b4 + 2*A20*a4*b3*b4 + A10*a3*b4^2 + A20*a3*b4^2 - A20*a5*b4^2 + A40*a5*b4^2 - A21*a4^2*b5 + a4^2*A41*b5 - 2*A21*a4*a5*b5 + 2*a4*A41*a5*b5 - 2*a3*A30*b1*b5 - 2*a3*A40*b1*b5 + 2*A10*a5*b1*b5 + 2*A20*a5*b1*b5 + A20*a4*b2*b5 - 2*a3*A40*b2*b5 - 2*a4*A40*b2*b5 + 2*A20*a5*b2*b5 - 2*A20*a4*b4*b5 + 2*a4*A40*b4*b5 - 2*A20*a5*b4*b5 + 2*A40*a5*b4*b5 - A20*a4*b5^2 + a4*A40*b5^2 + a1^2*(-(A11*b3) + A31*b3 + A41*(b2 + b3) - A21*(b2 + b3 - b5) + A11*b5) + a1*(-2*A21*a3*b1 + 2*a3*A31*b1 + 2*a3*A41*b1 + 2*A21*a5*b1 - 3*A21*a3*b2 + a3*A31*b2 + 2*a3*A41*b2 - 2*a4*A41*b2 + A21*a5*b2 - 2*A20*b1*b2 + 2*A40*b1*b2 - 2*A20*b2^2 + A40*b2^2 - 2*A21*a3*b3 + 2*a3*A31*b3 - 2*A31*a4*b3 + 2*a3*A41*b3 - 2*a4*A41*b3 - 2*A31*a5*b3 - 2*A41*a5*b3 - 2*A10*b1*b3 - 2*A20*b1*b3 + 2*A30*b1*b3 + 2*A40*b1*b3 - 2*A10*b2*b3 - 3*A20*b2*b3 + A30*b2*b3 + 2*A40*b2*b3 - A10*b3^2 - A20*b3^2 + A30*b3^2 + A40*b3^2 - 2*A11*a3*(b1 + b2 + b3) - 2*a3*A31*b4 - 2*a3*A41*b4 - 2*A40*b2*b4 - 2*A30*b3*b4 - 2*A40*b3*b4 - 2*a3*A31*b5 - 2*a3*A41*b5 + 2*A21*a5*b5 + 2*A10*b1*b5 + 2*A20*b1*b5 + A20*b2*b5 - 2*A30*b3*b5 - 2*A40*b3*b5 + A10*b5^2 + A20*b5^2 + 2*A11*a5*(b1 + b5) + a2*((-2*A11 + A31)*b3 + 2*A41*(b1 + b2 + b3 - b4) + A21*(-2*b1 - 4*b2 - 3*b3 + b5))) + a2*(-2*A11*a3*b1 + a3*A31*b1 + 2*a3*A41*b1 - 2*a4*A41*b1 - A20*b1^2 + A40*b1^2 + 2*a3*A41*b2 - 4*A20*b1*b2 + 2*A40*b1*b2 - 3*A20*b2^2 + 2*a3*A41*b3 - 2*A41*a5*b3 - 2*A10*b1*b3 - 3*A20*b1*b3 + A30*b1*b3 + 2*A40*b1*b3 - 4*A20*b2*b3 + 2*A40*b2*b3 - A20*b3^2 + A40*b3^2 - 2*A41*a5*b4 - 2*A40*b1*b4 + A20*b3*b4 + A20*b4^2 - 2*a3*A41*b5 - 2*a4*A41*b5 + A20*b1*b5 - 2*A40*b3*b5 + A20*b4*b5 - 2*A40*b4*b5 + A20*b5^2 + A21*(a3*(-3*b1 - 4*b2 - 2*b3 + b4) + a4*(b3 + 2*b4 + b5) + a5*(b1 + b4 + 2*b5))));

## simplification ...

I have this two expresions

e1 := (1/2)*P[psi]^2/(cos(`&vartheta;`)^2*Ix)

e2 := (1/2)*P[psi]^2/(cos(`&vartheta;`)^2*Ix)

simplify(e1-e2)=-(1/2)*(-P[psi]^2+P[psi]^2)/(cos(`&vartheta;`)^2*Ix)

but

simplify(-P[psi]^2+P[psi]^2)

is zero

why i dont obtain zero if i use simplify(e1-e2) ??