restart;
Fig:=proc(t)
local a,b,c,A,B,C,Oo,P,NorA,NorB,NorC,lieu,Lieu,dr,tx:
uses plots, geometry;
a := 11:b := 7:
c := sqrt(a^2 - b^2):

point(A, a*cos(t), b*sin(t)):
point(B, a*cos(t + 2/3*Pi), b*sin(t + 2/3*Pi)):
point(C, a*cos(t + 4/3*Pi), b*sin(t + 4/3*Pi)):
point(Oo,0,0):
lieu:=a^2*x^2+b^2*y^2-c^4/4=0:
Lieu := implicitplot(lieu, x = -a .. a, y = -b .. b, color = green):

line(NorA, y-coordinates(A)[2] =((a^2*coordinates(A)[2])/(b^2*coordinates(A)[1]))*(x-coordinates(A)[1]),[x, y]):
line(NorB, y-coordinates(B)[2] =((a^2*coordinates(B)[2])/(b^2*coordinates(B)[1]))*(x-coordinates(B)[1]), [x, y]):
line(NorC, y-coordinates(C)[2] =((a^2*coordinates(C)[2])/(b^2*coordinates(C)[1]))*(x-coordinates(C)[1]),[x, y]):
intersection(P,NorA,NorB):

ellipse(p, x^2/a^2 + y^2/b^2 - 1, [x, y]);

tx := textplot([[coordinates(A1)[], "A"],[coordinates(A2)[], "B"], [coordinates(C)[], "C"], [coordinates(Oo)[], "O"],#[coordinates(P)[], "P"]], font = [times, bold, 16], align = [above, left]):
dr := draw([p(color = blue),NorA(color=red,NorB(color=red),NorC(color=red),p(color=blue),
Oo(color = black, symbol = solidcircle, symbolsize = 8), P(color = black, symbol = solidcircle, symbolsize = 8)]):
display(dr,tx,Lieu,scaling=constrained, axes=none,title = "Les triangles inscrits dans une ellipse ont leur centre de gravité en son centre . Lieu du point de concours des perpendicalaires issues des sommets", titlefont = [HELVETICA, 14]);
end:

Error, `:=` unexpected
plots:-animate(Fig, [t], t=0.1..2*Pi, frames=150);
 

Let X₁, ...X_N  names of RandomVariable type and R a random variable defined as a function of  X₁, ...X_N.
(In Maple type(R, RandomVariable) returns false as R doesn't inherit the RandomVariable type.)

Given an expression of R I would like to determine if R is :

• either a linear combination of X₁, ...X_N ,
  example R = a*X₁ + X₂ + 1
  (I know how to handle this situation)
   
• or a linear combination of products of the X₁, ...X_N ,
  example R = a*X₁*X₂ + b*X₃
  (I feel I know how to handle this situation too)
   
• or a linear combination of functions, or products of functions, of  X₁, ...X_N .
  example R = a*f(X₁, X₂) + b*X₃*g(X₄) + c*X₁ + d*X₁*X₂
  (here I've no idea at all)

In the command hastype(R, some_type), how can I construct type some_type in order it returns an answer which matches the reqierements above?

RV_Type.mw

Thanks in advance for any suggestion

page 37 of book Symmetry Methods for Differential Equations by Hydon gives this example

When I wanted to verify it using Maple., symgen did not find these symmetries. Only when I give it using HINT the exact form it find them.  

Download why_no_syms_feb_10_2025.mw

Is this expected? Should it not have found them on its own?

Is it possible Maple internally does not automatically try Ansatz  of polynomials higher than quadratic to keep computation time low?   If so, I wonder if there is a way to tell it to try cubic or higher orders (like tryhard) option but for symgen?  I will search help more to see if there is a way to do this...

In trying to evaluate the accuracy of an asymptotic approximation, I asked evalf to return the numerical value of the difference of two expressions.  It evaluated each expression but would not take their difference (see line 6).  Any idea what's going on?

Download asyapprox.mw

I am working with an expression in Maple that involves complex terms and an integral. After applying the simplify command, some terms remain unsimplified, even though they seem reducible (see (7)). Additionally, an integral in my expression remains unevaluated (see (9)).
 

Download simplify.mw

is(cos(x)=sqrt(1-sin(x)^2) or cos(x)=-sqrt(1-sin(x)^2)) assuming real;

                                          false  

In a simpler situation the result is correct

is(x=0 or x<>0) assuming real;

                                           true         

SymPy can handle the following query to its assumption system:

>>> from sympy import Q, ask
>>> from sympy.abc import x, y, z
>>> ask(Q.zero(x*y*z), Q.zero(x*z) & Q.real(y))
True
>>> ask(Q.zero(x*y*z), (Q.zero(x) | Q.zero(z)) & Q.real(y))
True
>>> ask(Q.zero(x*y) | Q.zero(y*z), Q.zero(x*z) & Q.real(y))
True

Mathematica can handle an equivalent query:

In[21]:= Assuming[{x*z == 0}, Refine[x*y*z == 0]]
Out[21]= True

However, it can't handle a similar type of query:

In[25]:= Assuming[{x == 0 || z == 0}, Simplify[x*y*z == 0]]
Out[25]= x y z == 0

In[28]:= Assuming[{x*y == 0}, Refine[x*z == 0 || z*y == 0]]
Out[28]= x z == 0 || y z == 0  

It seems that Maple can't handle this type of query at all:

> with(RealDomain);
> is(x*y*z = 0) assuming (x*z = 0, y::real);
FAIL   

However, Maple can handle simpler assumptions like x = 0:

> is(x*y*z = 0) assuming (x = 0, y::real, z::real);
true

Is there some way to use Maple's assumption system to reason about assumptions like x*y=0? I believe that's not possible. If Maple can infer either x=0 or y=0 from x*z=0, its assumption system doesn't seem to be capable of dealing with this sort of assumption.

Based on a paper by Weibel and Gonnet (1993), it doesn't seem like Maple can reason about assumptions that are disjunctions of properties for more than one variable, such as "property p holds for x OR property p holds for y."

SymPy can handle these sorts of queries because it uses a SAT solver as part of its assumption system. However, there is no mention of a SAT solver—or any method of checking multiple possibilities—in the referenced paper or related papers on Maple's assumption system.

Am I correct that Maple's assumption system is not capable of handling this sort of query?

Weibel, T., Gonnet, G.H. (1993). An assume facility for CAS, with a sample implementation for Maple. In: Fitch, J. (ed) Design and Implementation of Symbolic Computation Systems. DISCO 1992. Lecture Notes in Computer Science, vol 721. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57272-4_27

By the way, is there some way to use markdown for these questions? I made the above post by asking chatgpt to convert markdown into html. 

How do i plot / graph a limt? The plot must have a hole at 2 because it is undefined.

Download graph-a-limit.mw

i want to get zero of this function i did all part true but i don't know why my pde not getting zero after substitute each parameter and part 

Download test.mw

Could you explain me why the three forms of patmatch behave identically (which seems natural) but the three forms of type do not.
Is there a way to define the type in type such that this latter returns the same thing for a*f(x)+b, f(x)*a+b, b+a*f(x), b+f(x)*a ?

Download type_vs_patmatch.mw

TIA

Recently, Maple has become almost unuseable. Whatever I do, it suddenly becomes non-reponsive, the cursor stops blipping and nothing happens for about a minute, although I can still move the cursor around and the page slider works, suggesting that the kernel has gone mad.

Then suddenly it comes back to life, executes where it left off, which in most cases happens while I am typing input. A minute later it's back to sleep. When I look at the CPU usage while it is non-responsive, I can see CPU usage is about 30% (there is nothing else significant running), disk usage is about 1% and there is plenty of memory (everything in total wants about 10GB and I have 32GB).

I have the -nocloud parameter set and finally disconnected the network connection, but that didn't help.

It all seems to have started with the most recent upgrade, although I'm not 100% sure of that.

Is anyone else seeing something like this, or better yet, does anyone have a suggestion to make this behaviour stop?

How does one downgrade to 2024.1?

Thank you.

the second ode is giving me zero also when we back to orginal under the condition by using them must the orginal ode be zero but i don't know where is mistake , when Orginal paper use some thing different but i think they must have same results i don't know i use them wrong i am not sure at here just , when U(xi)=y(z) in my mw

Download ode.mw

this is my first time something like that   coming up my equation after taking integral exponential coming up why?

g1.mw

the series is so complicated but have a strange pattern if you watch the index of parameter  they are not repeated 

Hi,

I am looking for a simpler way to find the equation of a parabola passing through 3 points. I see that using the Geometry package requires defining the parabola with 5 distinct points. Thank you for your guidance.QuestionParabole.mw