## modification of an expression...

Hello people in maple primes,

I have an expression,

e1_1:=-gamma*r*theta/(w*beta*(theta-1))

, which I want to put in order as

gamma*r*theta/(w*beta*(1-theta))

Isn't there any ways to do the modification above?

I am very glad if you answer to my question.

taro

## Can't solve arctan equation...

Trying to solve:

solve (arctan((2*x^2-1)/(2*x^2+1)) = 0, x);

The answer I get is the original function:

arctan((2*x^2-1)/(2*x^2+1))

This example is from the Maple book by Keck, and he shows the Maple V answer as

1/2 sqrt(2) -1/2 sqrt(2)

Suggestions?

## Separating positive, negative and indeterminate t...

Suppose that I have an expression of the form  eq:=a*x^2+b*y^2+c*x*y, where x,y are real numbers, a>0, b<0, and c>0. Is there a relatively simple way to separate the positive, negative, and indeterminate terms from such an expression. In other words, I want to get

eq_positive=a*x^2,

eq_negative=b*y^2,

eq_indeterminate=c*x*y.

Thanks

## problem with simple ODE...

Dear Community,

I try to solve the following very simple ODE symbolically with the ODE Analyzer assistant, yet Maple says "unble to obtain solution". :-/

If I try to slove it with dsolve, nothing happens. Is it really so difficult?

diff(p(h),h)=A/(B+C*p(h)), p(h0)=p1

A, B, C, h0 and p1 are constants. I use Maple 2016.

best egards

Andras

## Error when specifying the optimality tolerance opt...

Hi everyone,

I have a strange problem with the LSSolve function. I get an error when specifying an optimality tolerance as an option for LSSolve function : "unexpected parameters: optimalitytolerance = 1/1000" (see attached). When I remove the option, the LSSolve function works and returns something. Why ?

This is a problem for me because in my program I automatically generate lots of equations and I need to solve them using the same parameters.  "list1" is an example of a list that makes LSSolve to return an error and therefore it makes my program stop.
Is it possible, when LSSolve returns an Error, to re-run the function without the optimalitytolerance option ?

 (1)

 >

worksheet_help.mw

Lilian

## Matrix monomial orders in Maple...

In the Maple help to use a matrix defined monomial order it is said to define a matrix and a list of variables and then typing 'matrix'(M,V). But I fail to use it. A very simple example:

```M:=<<1,0>|<0,1>>;
V:=[x,y];

But Maple shows this error:

```Error, invalid input: Groebner:-LeadingMonomial expects its 2nd argument, tord, to be of type {MonomialOrder, ShortMonomialOrder}, but received matrix(Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 1) = 0, (2, 2) = 1}), [x, y])
```

What is wrong?

## How to solve and plot system differential equation...

How to solve this problem? I want to display plot of differential equation system

Thank you :)

## Weird results from LSSolve when adding constraints...

Hi everyone,

I am desperatly trying to find a reason to those weird results I get using LSSolve. It could really help me to understand, maybe I am using the function the wrong way.
I have a system of equations which is overdetermined that I wrote using an electrical simulation and kirchoff's laws.
I am trying to resolve it using the LSSolve function. Here is the list of residuals :

`list := [-0.444299277411586e-2+(270.100000000000-Phi12_18)*D18, -.264819908561346+(627.030000000000-Phi23_18)*D18, .191242220011840+(-259.080000000000-Phi34_18)*D18, 0.269723795794403e-1+(-40.5060000000000-Phi45_18)*D18, 0.674200455699644e-2+(-10.1270000000000-Phi56_18)*D18, .109534122562258+(-197.290000000000-Phi67_18)*D18, 0.481462872723211e-3+(-2.41420000000000-Phi78_18)*D18, -0.346014532189641e-4+(-2.53290000000000-Phi89_18)*D18, -0.402474969346295e-4+(-2.94150000000000-Phi910_18)*D18, -0.632005430249463e-3+(-8.57100000000000-Phi1011_18)*D18, -0.105749265697549e-1+(-37.6580000000000-Phi1112_18)*D18, -0.116305497595306e-1+(-55.3250000000000-Phi1213_18)*D18, -0.581547498854927e-3+(-2.76630000000000-Phi1314_18)*D18, -0.371408130367776e-2+(-22.0900000000000-Phi1415_18)*D18, -0.886173700610320e-2+(-56.4810000000000-Phi1516_18)*D18, -0.478846208996643e-1+(262.447651185421-Phi12_18)*D29+(262.447651185421-Phi12_24)*D36, .348429199898355+(62.3165310883292-Phi23_18)*D29+(62.3165310883292-Phi23_24)*D36, .237294781239637+(41.8563477700905-Phi34_18)*D29+(41.8563477700905-Phi34_24)*D36, 0.356987380524040e-1+(6.12136413036823-Phi45_18)*D29+(6.12136413036823-Phi45_24)*D36, 0.892515544035472e-2+(1.53042068810978-Phi56_18)*D29+(1.53042068810978-Phi56_24)*D36, .163733792213247+(26.7554245920538-Phi67_18)*D29+(26.7554245920538-Phi67_24)*D36, 0.917897899527287e-3+(-0.110562085900856e-3-Phi78_18)*D29+(-0.110562085900856e-3-Phi78_24)*D36, 0.242480164562623e-4+(-.283316330467957-Phi89_18)*D29+(-.283316330467957-Phi89_24)*D36, 0.281967728090880e-4+(-.329007391842407-Phi910_18)*D29+(-.329007391842407-Phi910_24)*D36, -0.812318100863302e-3+(-1.22850243118112-Phi1011_18)*D29+(-1.22850243118112-Phi1011_24)*D36, -0.174002698946928e-1+(-9.57006175329410-Phi1112_18)*D29+(-9.57006175329410-Phi1112_24)*D36, -.125540933056649+(-44.2197489328973-Phi1213_18)*D29+(-44.2197489328973-Phi1213_24)*D36, -0.627722694977691e-2+(-2.21106159188713-Phi1314_18)*D29+(-2.21106159188713-Phi1314_24)*D36, -0.739424545575381e-1+(-24.8403831529913-Phi1415_18)*D29+(-24.8403831529913-Phi1415_24)*D36, -.203976357415920+(-68.0132712014090-Phi1516_18)*D29+(-68.0132712014090-Phi1516_24)*D36, 0.196522429267177e-1+(197.940000000000-Phi12_24)*D27, 0.368371276889244e-2+(57.8900000000000-Phi23_24)*D27, 0.144256702539785e-2+(48.4450000000000-Phi34_24)*D27, -0.115630146715321e-3+(10.-Phi45_24)*D27, -0.283028527731083e-4+(2.50010000000000-Phi56_24)*D27, -0.300476205822746e-2+(66.2640000000000-Phi67_24)*D27, -0.653509876948917e-3+(2.69040000000000-Phi78_24)*D27, -0.126753046978926e-2+(4.44790000000000-Phi89_24)*D27, -0.147212636486122e-2+(5.16530000000000-Phi910_24)*D27, -0.484316181019253e-2+(16.6000000000000-Phi1011_24)*D27, -0.298854531528585e-1+(96.8770000000000-Phi1112_24)*D27, -.120604432493978+(315.410000000000-Phi1213_24)*D27, -0.603334119632106e-2+(15.7700000000000-Phi1314_24)*D27, -0.664471982996522e-1+(167.170000000000-Phi1415_24)*D27, 0.786913003105101e-1+(-326.760000000000-Phi1516_24)*D27] `

I know that all D values must be positive. When resolving the system without any constraints (D >= 0), i get the values I expected (knowing the input I used in the simulation), with a really low error :

`result := LSSolve(list);`

`[1.82130325886306*10^(-8), [D10 = 0.200009334740825e-2, D11 = 0.666620509302803e-3, D14 = 0.222215208246154e-2, D15 = 0.128202791383597e-2, D17 = 0.499886140344411e-2, D19 = 0.302925526676043e-3, D2 = 0.100002349341980e-2, D20 = 0.142849446596938e-3, D22 = 0.111121127122156e-1, D23 = 0.222228054119820e-2, D25 = 0.714293621502836e-3, D26 = 0.833326349912537e-3, D28 = 0.217396531719902e-3, D3 = 0.400217567900069e-3, D6 = 0.166878862202449e-3, D7 = 0.999969828547956e-2, Phi1011_17 = -1.22850243118112, Phi1011_19 = -20.5335193736012, Phi1011_21 = -104.090964313150, Phi1011_23 = 19.2144499395683, Phi1112_17 = -9.57006175329410, Phi1112_19 = -81.6848630234903, Phi1112_21 = -242.149849175388, Phi1112_23 = 109.001351349915, Phi1213_17 = -44.2197489328973, Phi1213_19 = -92.8267195929548, Phi1213_21 = -204.444165890808, Phi1213_23 = -61.4447612788985, Phi12_17 = 262.447651185421, Phi12_19 = 262.149192406679, Phi12_21 = 256.248405276737, Phi12_23 = 246.521172863223, Phi1314_17 = -2.21106159188713, Phi1314_19 = -4.64255435896474, Phi1314_21 = -10.2212158757032, Phi1314_23 = -3.07798400495386, Phi1415_17 = -24.8403831529913, Phi1415_19 = -30.5944507718603, Phi1415_21 = -45.5847025259923, Phi1415_23 = -77.3297680041818, Phi1516_17 = -68.0132712014090, Phi1516_19 = -74.2023324471993, Phi1516_21 = -95.1952296374558, Phi1516_23 = -132.328467080565, Phi23_17 = 62.3165310883292, Phi23_19 = 200.804225452845, Phi23_21 = 130.018791598707, Phi23_23 = 73.7043262431720, Phi34_17 = 41.8563477700905, Phi34_19 = 343.409987932231, Phi34_21 = 159.593996060841, Phi34_23 = 62.6564757702407, Phi45_17 = 6.12136413036823, Phi45_19 = 12.3839171939746, Phi45_21 = 46.0005281797016, Phi45_23 = 13.1665796516893, Phi56_17 = 1.53042068810978, Phi56_19 = 3.16614687399595, Phi56_21 = 11.4998114891963, Phi56_23 = 3.29093394692614, Phi67_17 = 26.7554245920538, Phi67_19 = -244.288977944524, Phi67_21 = 376.351493538080, Phi67_23 = 88.4830465193635, Phi78_17 = -0.110562085900856e-3, Phi78_19 = -6.28061380389266, Phi78_21 = 43.7035845962372, Phi78_23 = 3.35123473697264, Phi89_17 = -.283316330467957, Phi89_19 = -6.18811507913178, Phi89_21 = -13.9258224376815, Phi89_23 = 5.20325572546379, Phi910_17 = -.329007391842407, Phi910_19 = -7.18580970783931, Phi910_21 = -16.1669897128450, Phi910_23 = 6.04291224185087]] `

When adding the constraints that D should be positive (and that are actually positive in the previous result), I get a worse result in term of precisions :

`LSSolve(list, {D10 >= 0, D11 >= 0, D14 >= 0, D15 >= 0, D17 >= 0, D19 >= 0, D2 >= 0, D20 >= 0, D22 >= 0, D23 >= 0, D25 >= 0, D26 >= 0, D28 >= 0, D3 >= 0, D6 >= 0, D7 >= 0});`

`[0.667302976414869964e-1, [D10 = 0.240199442379079e-2, D11 = 0.666577572133538e-3, D14 = 0.222218786790062e-2, D15 = 0.128192441757651e-2, D17 = 0.278678889056743e-2, D19 = 0.200473317719685e-3, D2 = 0.109938538155804e-2, D20 = 0.840721762649974e-4, D22 = 0.685770482726534e-3, D23 = -1.387530857*10^(-312), D25 = 0.714397733627028e-3, D26 = 0.833201232339238e-3, D28 = 0.204319731851617e-3, D3 = 0.419994015872111e-3, D6 = 0.191996909862889e-3, D7 = 0.103884505319047e-1, Phi1011_17 = -.709707335593168, Phi1011_19 = -15.7863975896827, Phi1011_21 = -151.171843708558, Phi1011_23 = 19.2211409030343, Phi1112_17 = -8.90604676283968, Phi1112_19 = -75.8627539382983, Phi1112_21 = -311.423930967299, Phi1112_23 = 109.002880650927, Phi1213_17 = -54.9212365194647, Phi1213_19 = -89.9790565093006, Phi1213_21 = -250.971671756001, Phi1213_23 = -61.5160003335629, Phi12_17 = 251.480872515883, Phi12_19 = 255.977573006508, Phi12_21 = 254.397100891354, Phi12_23 = 246.524672366158, Phi1314_17 = -2.74614386328796, Phi1314_19 = -4.48401822538664, Phi1314_21 = -12.5381572344771, Phi1314_23 = -3.08154491280567, Phi1415_17 = -31.8947514252141, Phi1415_19 = -30.8090400512349, Phi1415_21 = -51.0499196769535, Phi1415_23 = -77.3268969229600, Phi1516_17 = -87.7947790488482, Phi1516_19 = -75.5403005246575, Phi1516_21 = -101.763771364478, Phi1516_23 = -132.314524393221, Phi23_17 = 94.0093590848714, Phi23_19 = 86.4429757025976, Phi23_21 = 108.554765004168, Phi23_23 = 73.7072279431268, Phi34_17 = 87.6938924370977, Phi34_19 = 82.3922347753764, Phi34_21 = 88.5582078636840, Phi34_23 = 62.6604078051191, Phi45_17 = 13.1910198060107, Phi45_19 = 69.3008595136787, Phi45_21 = 15.5530983566712, Phi45_23 = 13.1677681559684, Phi56_17 = 3.29792072169498, Phi56_19 = 17.4003349272078, Phi56_21 = 3.88187632917493, Phi56_23 = 3.29123115133383, Phi67_17 = 60.0045707036166, Phi67_19 = 54.3070868626015, Phi67_21 = 87.9421288802858, Phi67_23 = 88.4929920125095, Phi78_17 = .279952186311827, Phi78_19 = -3.50632712699693, Phi78_21 = -20.3872167203319, Phi78_23 = 3.35213748642018, Phi89_17 = -0.991299169828910e-1, Phi89_19 = -4.44636683843093, Phi89_21 = 297.888811926331, Phi89_23 = 5.20500671661437, Phi910_17 = -.115101700555720, Phi910_19 = -5.16603761776826, Phi910_21 = 346.033351291632, Phi910_23 = 6.04494564310825]] `

I also get the warning "limiting number of major iterations has been reached".
Can someone explain me?

It may not seem important at first sight, but sometimes when using my program I get wrong values and a negative D, which is not possible. Therefore I try to add a positive constraint, but the LLSolve function doesn't return anything except the error "no improved point could be found", which is weird because when I manually substitute the value I consider correct, i get a really low error. I can show you the related list of equations if you are interested...

Lilian

## Problem with instruction subs of Maple...

Hi, i have a problem with subs instruction. I'd like to change a function D(s) with symbol d/ds d(t), but i won't to calculate derivate, I want only change symbol. Thanks a lot.

## How can I display an arbitrary spherical cap?...

What coding will display a spherical cap of an arbitrary sphere (an arbitrarily located centre and arbitrary radius) where the cap covers an arbitrary solid angle and the radius to the cap's centre is any arbitrary radius of the sphere?

Assume the sphere is defined by its radius and its azimuth and polar angles.

## how can I display long equations or configure mapl...

how can I print my equation or configure maple so that they don't try to autofit themselves in the window? and what would the best way to export them to MATLAB be? I know there's the codegeneration command.

For example, I noticed that the output of some commands like StateSpace prints the equations in a way that if they are too long, they won't try tu fit, but rather it lets you scroll to the right:

## Elements and length of a PolynomialIdeal!...

When one uses the PolynomialIdeals package, then how should he ask the elemnts in an ideal or the number of generators?

An idea can be writing a proc getting a polynomialideal and returning a list with the generators as its elements in this way. Converting the polynomialideal to a list, then deleting its three last entries. But I'm wondering if there is any other way to do this? It's reasonable to be able to ask generators of an ideal of result of some computations in polynomialideal package.

## How to program a for loop inside a procedure and m...

I'm trying to program a procedure that will return me a list of positions defining equally spaced points (planets) around a circumference, for example:
PSI := [0, Pi]; # Location of 2 planets
PSI := [0, ((2/3)*Pi) , ((4/3)*Pi) ]; # For 3 Planets
I'm new to maple so most commands are new to me, I tried building the size of the list with [0 \$ n] because I want the first position to always be at 0 degrees. The first problem is that I get this error:

 > nplanets := 2;
 (1)
 > make_PSI := proc(nplanets); local n,psin,i,PSI: n = nplanets; psin  :=(pi*2)/n; PSI := [0 \$ n]; for i from 1 to n do  angle :=(psin*i);  op(i,PSI) := angle; end do; end;
 >
 >

Any advice would be appreciated!

## 3d contourplot (3 variables not 3d view of contour...

When we have a two variable function f(x,y), Maple can plot f-inverse of a value with contourplot. But how about contourplot of a three variable function? for example f-1(0) which can be a surface in the 3 dimensional space. The contourplot3d is just the contourplot (2-dimensional) which also shows the value of f(x,y) on the third axis. So this is not what I want.

## Command for blow ups...

Is there any command or package in Maple that computes blow ups? I didn't find blow up in the help.

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