I want to find coodinates of the point A, B, C, D and X of a problem 6 at IMO 2018 https://www.imo-official.org/problems.aspx

I tried 

 

restart:
 with(Student:-MultivariateCalculus):
 A := [0, 0]; 
B := [5, 0]; 
C := [3, 4]; 
DD := [a, 2]; 
solve([Distance(B, A)*Distance(C, DD) = Distance(B, C)*Distance(A, DD)], [a]);

How can I get coordinate X lies inside life request?

Hi,

I'm trying to implement Kernal PCA, I've got a large kernal matrix for which I have checked the elements are of floating point type, however when I try to run the Determinant operation on the matrix all of the coefficients say float(undefined).

In the same worksheet, there I have implemented the standard PCA routine, for which the determinant operation works fine. You can see this operation functioning corrrectly in it's testing section.

If anyone has any idea why this might be occuring I'd be really grateful for some advice.

Thanks

FUML.mw

Hello !

I want to plot its steamlines and Isotherms for different parameters. Anyone can help me for this issue.

eq1:=diff(f(eta),eta,eta,eta)+f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta)^2)-M*diff(f(eta),eta)=0:
eq2:=(1+R)*1/Pr*diff(theta(eta),eta,eta)+f(eta)*diff(theta(eta),eta)=0:
bc:=D(f)(0)=1,(f)(0)=0,(D)(f)(N)=0,theta(0)=0,theta(N)=1:
Pr:=1:R:=0.5:M:=0.5:N:=10:

Hello World (again);

For your edification, look at  a file.

L

fine_semiprime_2.mw

For what it's worth

Regards,

Matt

Can anyone explain the reasoning that went into the programming decisions that led Maple to give these results?

restart:
is(-infinity, complex); #expected: false
                             false 
is(-infinity-I*infinity, complex); #expected: false
                              true
exp(-infinity - I) = limit(exp(x-I), x= -infinity); #expected: 0=0
                         infinity*I = 0
is(exp(x)<>0) assuming x::complex; #expected: true
                             false
is(exp(x)<>0) assuming x::real; #expected: true
                              true
coulditbe(exp(x)=0) assuming x::complex; #expected: false
                              true

I got my maplet and there error occurs when I try to display it - Error, (in Maplets:-Display) BoxCell contains an element (_Maplets_reference_1235) that cannot be placed in a layout.
Please correct Maplet definition.

How to fix it?

with(Maplets[Elements]);

mpt := Maplet(Window("Точка выше или ниже прямой", [[[ToggleButton[TB1]("Tt", 'group' = 'tb1')], [ToggleButton[TB2]("Tt", 'group' = 'tb1')]], ButtonGroup['tb1']()]));

Display(mpt);

Hi I want to generate dihedral group of order 8.I have given the commands
with (GroupTheory):

GroupTheory(DihedralGroup);

DihedralGroup(8, s);
                              D[8]
Elements(DihedralGroup(8, s));
{(), (12345678), (14725836), (16385274), (18765432), 

  (1357)(2468), (1753)(2864), (13)(48)(57), (15)(24)(68), 

  (17)(26)(35), (28)(37)(46), (12)(38)(47)(56), (14)(23)(58)(67), 

  (15)(26)(37)(48), (16)(25)(34)(78), (18)(27)(36)(45)}
but I need symmetric and rotation matrices like 

R0=[1,0;0 1],R1=[0,-1;1,0], R2=[-1,0;0,1], R3=[0 1;-1,0],S0=[1 0;0 -1], S1=[0 1 ;1 0], S2=[-1,0;0,1]; S3=[0,-1;-1,0]
 Can any one help me how to generate these matrices

I am trying to check to see if two equations are equivalent, subject to rearrangment and scalar multiplication. For example, I would to have a procedure that would determine that each of the following equations are the equivalent:

(a) (1/2)*y*exp(-y)+2*y^3 - x*ln(x) +x^2 = 10
(b) (1/2)*y*exp(-y)+2*y^3 +x^2 = 10 + x*ln(x)

(c) y*exp(-y)+4*y^3 - 2*x*ln(x) +2*x^2 = 20

Is there a systematic way to go about doing this? Thanks!

I have a vector v= [1 ,1,0]
M=[1 2 3; 5 4 3; 7 9 0];

c=v.M

whats wrong with this. error is in the last statement

Hi

I have a solution obtained using

sol:=pdsolve(PDE,BC);

"sol" is a function depend on variable x,

how can I differentiate this sol ( which a function ) then plot it

many thanks

How to find 

a:=[8, 9 ,9 ,7 ,9 ,10 ,5]^-1 mod 11

Hello I want to multiply two vectors like

X=[x₁ ,x₂,...x₁₀]

G=[g₁,g₂,...g₁₀]

y=[x₁*g₁,x₂*g₂, ........, x₁₀*g₁₀]

How to perform this transformation in maple?

Thanks

with(Maplets);
with(Elements);
with(plots);
with(DocumentTools);

 I use GetProperty("d", value) = "true"  to check if checkbox is checked but it does not work. How can I check if checkbox is checked?

workk := proc(g)

if GetProperty("d", value) = "true" then

print("true");

else print("False");

end if;

end proc;

mpt := Maplet(Window("aaaa", [[Plotter[f]()],

["Scalar", CheckBox[d]()],

[Button("Add", Evaluate(f = 'workk(1)')),

Button("OK", Shutdown())]]));

Display(mpt);
 

All of his should work very readily
 

Download DISGUSTING.mw

Hey,

Is anyone of you capable of simplifying this expression

f1:=(-3*sin(8*x) + 3*sin(8*x + 2*y) - 3*sin(8*x + 6*y) + 3*sin(8*y + 8*x) + 3*sin(8*y + 6*x) + 3*sin(8*y) - 18*sin(8*y + 4*x) + 3*sin(8*y + 2*x) - 45*sin(6*y + 6*x) + 87*sin(4*y + 6*x) - 3*sin(6*x - 2*y) - 87*sin(6*x + 2*y) + 18*sin(4*x - 4*y) - 93*sin(4*x + 4*y) + 93*sin(4*x + 6*y) - 51*sin(2*x - 4*y) - 342*sin(2*x + 4*y) - 3*sin(-6*y + 2*x) + 51*sin(6*y + 2*x) - 93*sin(-2*y + 4*x) + 342*sin(-2*y + 2*x) + 639*sin(2*x + 2*y) - 639*sin(2*x) + 45*sin(6*x) + 93*sin(4*x) + 231*sin(4*y) - 225*sin(2*y) - 63*sin(6*y) - 57*sqrt(3)*cos(2*x) - 375*sqrt(3)*cos(2*y) + sqrt(3)*cos(8*y + 8*x) - 5*sqrt(3)*cos(8*x + 6*y) - 7*sqrt(3)*cos(8*y + 6*x) + sqrt(3)*cos(8*x) + 192*sqrt(3)*cos(2*y + 4*x) + 43*sqrt(3)*cos(-2*y + 4*x) - 7*sqrt(3)*cos(6*x + 2*y) + 7*sqrt(3)*cos(-6*y + 2*x) - 5*sqrt(3)*cos(6*y) - 149*sqrt(3)*cos(4*x + 4*y) - 149*sqrt(3)*cos(4*x) - 65*sqrt(3)*cos(6*y + 2*x) + 126*sqrt(3)*cos(2*x + 4*y) - 65*sqrt(3)*cos(2*x - 4*y) - 5*sqrt(3)*cos(8*x + 2*y) - sqrt(3)*cos(8*y) + 7*sqrt(3)*cos(8*y + 2*x) + 6*sqrt(3)*cos(8*x + 4*y) - 57*sqrt(3)*cos(2*x + 2*y) + 125*sqrt(3)*cos(4*y) + 126*sqrt(3)*cos(-2*y + 2*x) - 7*sqrt(3)*cos(6*x - 2*y) + 19*sqrt(3)*cos(6*x) + 43*sqrt(3)*cos(4*x + 6*y) + 19*sqrt(3)*cos(6*y + 6*x) - 7*sqrt(3)*cos(4*y + 6*x) + 246*sqrt(3))/(2*(-261*sin(4*x + y) - 297*sin(2*x + 3*y) - 48*sin(5*y + 6*x) + 126*sin(5*y + 2*x) + 9*sin(5*y + 8*x) + 12*sin(7*y + 6*x) - 9*sin(7*y + 4*x) - 36*sin(5*y + 4*x) + 261*sin(3*y + 4*x) + 9*sin(-3*y + 4*x) + 297*sin(-y + 2*x) - 135*sin(3*y) - 21*sin(5*y) - 147*cos(y)*sqrt(3) - 9*sqrt(3)*cos(7*y + 4*x) - 3*sqrt(3)*cos(5*y + 8*x) - 3*sqrt(3)*cos(3*y + 8*x) + 54*sqrt(3)*cos(6*x + 3*y) + 5*sqrt(3)*cos(-5*y + 2*x) + 5*sqrt(3)*cos(7*y + 2*x) - 2*sqrt(3)*cos(6*x - y) - 20*sqrt(3)*cos(6*x + y) - 69*sqrt(3)*cos(4*x + y) + 68*sqrt(3)*cos(4*x - y) + 2*sqrt(3)*cos(8*x + y) + 2*sqrt(3)*cos(7*y + 8*x) - 20*sqrt(3)*cos(5*y + 6*x) - 2*sqrt(3)*cos(7*y + 6*x) + 68*sqrt(3)*cos(5*y + 4*x) - 9*sqrt(3)*cos(-3*y + 4*x) - 69*sqrt(3)*cos(3*y + 4*x) - 171*sqrt(3)*cos(2*x + 3*y) - 35*sqrt(3)*cos(5*y) + 171*sqrt(3)*cos(3*y) - 171*sqrt(3)*cos(-y + 2*x) + 354*sqrt(3)*cos(2*x + y) + sqrt(3)*cos(7*y) + 639*sin(y) - 9*sin(3*y + 8*x) - 12*sin(6*x - y) + 3*sin(7*y) - 9*sin(7*y + 2*x) + 9*sin(-5*y + 2*x) + 48*sin(6*x + y) + 36*sin(4*x - y) - 126*sin(2*x - 3*y)))

into

cos(y-Pi/3).

PS: Actually I managed by expanding the thing out and converting to exp then expanding again and using radnormal. In essence I leave the question, because maybe somebody can explain to me why radnormal seems to be superior (sometimes) to simplify which I thought of as the USEALL choice. Thanks