## Difficultu with pointplot...

restart;
with(LinearAlgebra);
with(plots);
NULL;

EqBIS := proc(P, U, V) local a, eq1, M1, t, PU, PV, bissec1; a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2); M1 := P + a*t; eq1 := op(eliminate({x = M1[1], y = M1[2]}, t)); RETURN(op(eq1[2])); end proc;
NULL;
A := <4, 8>;
B := <4, 2>;
C := <1, 4>;
EqBIS(A, B, C);
NULL;

Cen := proc(M, N, R) local eq1, eq2, sol; eq1 := EqBIS(M, N, R) = 0; eq2 := EqBIS(N, M, R) = 0; sol := simplify(solve({eq1, eq2}, {x, y})); RETURN([subs(sol, x), subs(sol, y)]); end proc;
Cen(A,B,C):

CircleParm := t -> [(-t^2 + 1)/(t^2 + 1), 2*t/(t^2 + 1)];
P1 := Transpose(convert(CircleParm(1/4), Vector));

P2 := Transpose(convert(CircleParm(5), Vector));
P3 := Transpose(convert(CircleParm(-1/10), Vector));
P4 := Transpose(convert(CircleParm(-3/2), Vector));

C1 := Transpose(convert(Cen(P1, P2, P3), Vector));
Pts := [P1, P2, P3, P4, C1];

display(implicitplot([x^2 + y^2 - 1], x = -2 .. 2, y = -4 .. 2, colour = [blue], scaling = constrained), pointplot(Pts, symbolsize = 16));
Error, (in plots:-pointplot) incorrect number of coordinates in points data
NULL;Why this error. Thank you.

## What is generating the R[0] term, and how do I rem...

I'm using Maple 2021, and my Euler-Lagrange equation is coming out with a R[0] term that should not be there. I want to know what is causing this error and how I can fix it.

Lagrangian

 (1.1)

Time Equation

 (2.1)

## Font-size of caption, labels and axes on plots sma...

Maple 2021.
I expect after exporting to pdf view of page with plot like on fig. 1.

It means with font=[TIMES, ROMAN, 12] as in maine text.
But I obtaned this view of page on pdf (fig. 2) with smaller font-size.

In previouse versions there are no the problem like this.
Dear community, how to fix this annoying inconvenience?

fig. 1.  fig. 2.

## Why does Maple give sometimes erroneous results wh...

Consider the following integral, shown below in this image.

>> Link to the Maple sheet: example.mw <<

Why does Maple provide erroneous results? Is there a bug in the software? I use Maple 2021.

## Maple Bombs While Entering Text...

Hi.  I am using the linux version of Maple.  I seem to experience more bombs in Maple/Linux vs MathCad/Windows.  The program just froze as I was entering text.  Just text.  It is not a disaster since I make very frequent saves.  But it is very annoying.  I was a heavy user of MathCad from about 2005 to 2019.  In the early days, it bombed a lot.  But I do not recall that it ever bombed when I was entering text.  Any suggestions?  Would there be a limition on the number of text characters?  Is it Linux?  Other than this problem, it is a great program.

## resolution of the equation of degree 3...

restart:
eq := a*x^3 + b*x^2 + c*x + d;
s := x1 + x2 + x3 = -b/a;
sp := x1*x2 + x1*x3 + x2*x3 = c/a;
p := x1*x2*x3 = -d/a;
sol:=solve({eq, p, s, sp}, {x1, x2, x3},explicit);
a := 1;
b := -5;
c := 6;
d := -1;
sol;

why is not successfull ?   Thank you.

## unable to implicit plot a procedure...

I have a problem in plotting bellow function. actually because my main program is not working so I decided to do it in simple way. I found that my program in maple can't plot the function I introduced it as a procudure and is an implicit function. can you help me please?

>EQ := proc(x, t) local y, m, func;
m := 3;
func := m*x^2 + t*y^2 = 4;
end proc;

>eq := EQ(x, 10);
eq := 3*x^2  + 10*y^2  = 4

>implicitplot(eq, x = -1 .. 1, y = 0 .. 2)
Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {y}

## Maple's WeierstrassP vs Weierstrass' P-function...

What is the [explict] relation between Maple's WeierstrassP and Weierstrass' P-function (e.g. https://en.wikipedia.org/wiki/Weierstrass_elliptic_function) ?

## How to have Maple solve this simple ODE?...

The worksheet here shows a couple of failed attempts at coaxing Maple to calculate the general solution of a pretty simple second order ODE.  I have also included the expected solution which I  have calculated by hand.  Perhaps I am missing a key trick.  Any ideas?

The ODE that I am actually interested in is significantly more complex. The one in the worksheet is a much simplified "bare bones" specimen that exhibits the issue that I am facing.

Attempt to solve with Heaviside

 > restart;
 > de := diff(u(x),x\$2) = Heaviside(x - a)*u(x);

dsolve fails:

 > dsolve(de);

Attempt to solve with piecewise

 > restart;
 > de := diff(u(x),x\$2) = piecewise(x < a, 0, 1)*u(x);

 > dsolve(de);

Error, (in dsolve) give the main variable as a second argument

 > dsolve(de, u(x));

Error, (in dsolve) give the main variable as a second argument

 >
 >

The solution is easy to calculate by hand

We just solve the (quite trivial) DE over the intervals  and x>a

separately, and patch the two solutions by requiring the continuity

of  and  at .  We get

 > sol := piecewise(x < a,         x*c[1] + c[2],         ((a*c[1] + c[1] + c[2])*exp(x))/(2*exp(a)) + ((a*c[1] - c[1] + c[2])*exp(-x))/(2*exp(-a)));

## How to built a pentagon...

restart;
with(plots);
with(plottools);
Vdot := proc (U, V)local i: add(U[i]*V[i], i = 1 .. 2) end proc:
dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end proc:
ngon := n -> local i; [seq([cos(2*Pi*i/n), sin(2*Pi*i/n)], i = 1 .. n)]:
theta := (2*Pi)/5;
poly := [seq([cos(k*theta), sin(k*theta)], k = 1 .. 5), datatype = float];
Ii := [0, 1/2]:
H := [-1/4, 0]:
r := dist(Ii, H):
theta := (2*Pi)/5:
p1 := pointplot([seq([cos(k*theta), sin(k*theta)], k = 0 .. 5)], symbol = solidcircle, color = red, symbolsize = 10):
p2 := textplot([seq([cos(k*theta), sin(k*theta), cat("M", k)], k = 0 .. 4)], align = ["above", "right"]):
cir1 := circle([0, 0], 1/2, color = green,dashdot:):
cir2 := circle([-1/4, 0], r, color = black):
cir3:=circle([0,0],1,color=red):
display([p1, p2, cir1, cir2, cir3,polygonplot(poly, thickness = 5, color = blue, transparency = 0.95)], axes = normal);
Why this error , Thank you.

## How do I solve a equation in Maple?...

y = ax^3 + bx^2 + cx + d this is curve and is passing through the points (−1,−4),(1,0),(2,0),(3,−4).
1) Find the values of 𝑎,𝑏,𝑐 and 𝑑.
2) Plot the curve and the points given on the same axis.

I tried solving with derivative of the curve but i didnt find the exact values.

## Difficulty with concatenation and indexing...

Why this error message ?
with(geometry);
vartheta := (2*Pi)/17;
x || k := cos(k*theta);
y || k := sin(k*theta);
xk := cos(k theta): yk := sin(k theta)
.M||k:=(point,x||k,y||k);
with(plots):
Points := pointplot([seq(M || k, k = 1 .. 16)], symbol = solidcircle, color = red, symbolsize = 10):
Error, (in plots:-pointplot) cannot convert data to an Array of datatype float[8]; Thank you for your answer..

## How do I put this linear transformation in Maple? ...

Hello, I have a question.

The exercise consists of defining the image in relation to a chosen base. For example, I choose {x^4,x^3*y,x^2*y^2,x*y^3,y^4} as a base. Then I want to calculate T(x^4), T(x^3*y),T(x^2*y^2),T(x*y^3),T(y^4) through maple but but maple won't calculate it.

Do you know what I'm doing wrong?

## How to solve a cubic assuming discriminant conditi...

Hi MaplePrimes.

I have a cubic with some parameters that I would like to solve and recieve 3 real solutions, however I cannot seem to find a way to get that to work while using assumptions. I always recieve 1 real and two complex conjugate answers. I have tried assuming the discrimant to be greater then zero but nothing seems to be working, and I have looked through a few posts on here but I cant seem to find anything out. In particular solve({f,conditions},{variable})

If I solve with a known set of paramters(which i determine graphically) that gives three solutions everything works fine. Also if I solve the cubic generally and recieve the two complex solutions and one real then substitute the paramters in I get the same correct answers, so I am slightly baffled. If I have missed something simple my apologies.

Any help would be greatly appreciated. File attached.

CubicSolve.mw

## How to label the DrawSubgroupLattice with the orde...

This is the default style about the group of `DrawSubgroupLattice`:
`DrawSubgroupLattice(SymmetricGroup(4))`
But I hope to label the `DrawSubgroupLattice` with the order of the subgroup but not the default index, is it possible? I can get the order with this code:
`GroupOrder~(SubgroupLattice(SymmetricGroup(4), output = list))`