is there a way to set conjugate=true  to false as a default for BilinearForm?  This would be used inside a package.

restart;
with(LinearAlgebra);

v := <x, y>;
BilinearForm(v, v);
BilinearForm(v, v, conjugate = false);

I am trying to define a function f(x1+tau,x2)= (x1+tau)*a+x2*b. I need this to be able to take derivations w.r.t. the sum (x1+tau) and to only tau as well. Is there a way to do this?

I am presently working on bivariate functions defined this way

C := (u, v) -> (phi@@(-1))(phi(u)+phi(v));

phi is a function of specific expression named the "generator". Both u and v are assumed to be in the closed interval [0,1].

Here is an example:

restart
phi := u -> (u^(-theta)-1)/theta:
C := (u, v) -> (phi@@(-1))(phi(u)+phi(v)):
C(u, v)
                       / (-theta)        (-theta)    \
                      | u         - 1   v         - 1|
           @@(phi, -1)| ------------- + -------------|
                       \    theta           theta    /

This definition of C is correct providing that  theta in [-1, +infinity) \ {0}.
As you can see, the display of C(u, v) contains the inverse function phi@@(-1) which Maple doesn't seem to know what to do with.

What I would like is to get rid of  phi@@(-1) and get 

C(u, v);
        (-1+u^(-theta)+v^(-theta))^(-1/theta)

The only way I found to get this is to do that:

restart
phi := u -> (u^(-theta)-1)/theta:
(phi@@(-1)) := u -> solve(phi(x)=u, x): # explicit definition of (phi@@(-1))
C := (u, v) -> simplify((phi@@(-1))(phi(u)+phi(v))) assuming theta >= -1, theta <> 0:
C(u, v);
                                         /    1  \
                                         |- -----|
                                         \  theta/
             /      (-theta)    (-theta)\         
             \-1 + u         + v        /         

As you see I have been forced to tell Maple what the inverse function of phi was.
Is there another way do get this result without writting the bold red line?

Maple knows several inverse functions (trigonometric functions for instance), but how does it know that?
As Maple does not seem to use a (f@@(-1)) := u -> solve(f(x)=u, x) like definition, does it uses a correspondence table between functions and their inverse?
If it is so can we augment it?

Thanks in advance.

PS: the ultimate goal is to do something like this Download CAC.mw  for different generators.

For the moment I have defined my own table generator <--> inverse function  as I did above with the bold red line: this works but it is not very elegant.

Hi,
I have a problem and I haven't been able to solve it yet. I want to solve an ordinary diffrential equation similar to
                                                                                                   (dphi/dxi)^2+2*V(phi)=0
and plot phi versus xi for a the following conditions:
1) V(phi)=dphi/dxi=0 at (phi=0,phi_m) and
2) dV(phi)/dphi=0 at phi=phi_m and 
3) d^2V(phi)/dphi^2=0 at both phi=0 and phi=phi_m.
How can I do this by Maple?(see the attached file)
w1.mw

Has anyone else noticed that Mapleprimes response/loading/refreshing time has become relatively much slower in the past few weeks?

In MapleFlow lowerscript L is not easily available.  It should be accessible with the CRTL+space after typing L.

Or in a list of common symbols (that pallete is not available in Maple Flow)

I had to to use maple to discover how to enter it.

`&ell; produced the correct result and then deleting the quote I could achieve the desired result.

I tried

interface(warnlevel=0); infolevel[all]:=0;prinlevel:=0;kernelopts('printlevel'=0);

to suppress the warnings I get from this code

restart;
f:=z^3;
z_map:=proc(f,re,im) 
  if((re>0) and (im>0) and (im<1-re))then
    eval(f,z=re+I*im);
  else
    NULL;
  end if;
end proc;
p_re:=plots:-display(seq(plot([Re('z_map(f,re,im)'),Im('z_map(f,re,im)'),im=0..1]),re=0..10,0.1)):
p_im:=plots:-display(seq(plot([Re('z_map(f,re,im)'),Im('z_map(f,re,im)'),re=0..1]),im=0..10,0.1),color=green):
plots:-display(p_re,p_im,scaling=constrained)

The reason for the warnings is clear. The input lines are too long to be plotted. However, the resulting plot is exactly what I intended. Programatically truncating the lines would make the warning disappear, but it would make the code much more complicated.

What else can be done to suppress this kind of warning.

For Mathematica  math software app,there is a plugin to use in chatGPT pro ( paid subscription ) and maybe this can be done for Maple too ? 

Haven't used the plugin for Mathematica yet, am curious about it.
Let me have the AI look at the Riemann Hypothesis :)  
Have a few books on it, but can't get through that math with all those special functions.

Why does the execution of procedure J2 in the attached file fire an error?
it looked to me as if I had built it the same way as J1.
 

Download integration_issue.mw

Can you help me fix this issue?

Thanks in advance

Hi,

How can I get y=x in output (4) when  g is equal to f?

Download inverse_f.mw

Thanks in advance

This is something I use a fair bit. I have procedures with alternative spelling options for the colours Red Green and Blue.
Have shown a single example copied from  an overloaded procedure. It there a nicer way of handling this than what I am doing?
There is a section in help under "Procedure Parameter Declarations" on "Indexed Keyword Parameters"  but I don't see how to use it here. These procedures are used inside a package.

Download Q_2024-02-09_Alternative_Spelling_in_Proc.mw

I just came across an issue when solving a simple thermodynamics problem. Steam enters a turbine at 140 psia and 1000 F and expands isentropically to 2psia. When I try to determine the exit temperature, the problem occurs. If I set the units for the problem to FPS, I get the answer in F. The problem is that the numerical value is wrong. The numerical value corresponds to degree R, not F. The numerical value given is 585 F, it should be 585 R.  If I set the problem to SI units, the answer is in K. The answer given is 325 K.  I can then convert it to degree F. This way I get the correct answer.

According to the Maple documentation, both commands can handle inequalities. I'm only interested in checking when a semialgebraic set is empty, so I thought SemiAlgebraicSetTools:-IsEmpty would be generally faster than computing the solutions with the SemiAlgebraic command. However, the following code shows otherwise:

Code 1:

```

restart;
with(SolveTools, SemiAlgebraic);

B_poly := -(x + 4)*(x + 3)*(x + 2)*(x + 1)*(x - 1)*(x - 2)*(x - 3)*(x - 4);
g := -1/100000*(x+4)*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)*(-1/670*(x+4)
*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)-669/670)^136+1/100000*(x+4)*(x+3)*(x
+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)*(1/670*(x+4)*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x
-3)*(x-4)-669/670)^136;
f := -4347225/87808*x^8 - 17375/392*x^7 + 629491375/395136*x^6 + 
   266375/252*x^5 - 200677775/12544*x^4 - 3174625/504*x^3 + 
   11067842125/197568*x^2 - 53625/98*x - 126496075/4116;

SemiAlgebraic(
  [B_poly >= 0, g - f >= 0], [x]);

```
 

Code 2:

```

restart;
with(RegularChains, SemiAlgebraicSetTools, PolynomialRing);

local R := PolynomialRing([x]);

B_poly := -(x + 4)*(x + 3)*(x + 2)*(x + 1)*(x - 1)*(x - 2)*(x - 3)*(x - 4);
g := -1/100000*(x+4)*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)*(-1/670*(x+4)
*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)-669/670)^136+1/100000*(x+4)*(x+3)*(x
+2)*(x+1)*(x-1)*(x-2)*(x-3)*(x-4)*(1/670*(x+4)*(x+3)*(x+2)*(x+1)*(x-1)*(x-2)*(x
-3)*(x-4)-669/670)^136;
f := -4347225/87808*x^8 - 17375/392*x^7 + 629491375/395136*x^6 + 
   266375/252*x^5 - 200677775/12544*x^4 - 3174625/504*x^3 + 
   11067842125/197568*x^2 - 53625/98*x - 126496075/4116;

SemiAlgebraicSetTools:-IsEmpty([B_poly >= 0, g-f >= 0], R);

```

My computer finishes 'Code 1' in about 20 seconds, while 'Code 2' doesn't terminate. Am I misunderstanding something about how to use these commands for my problem? I'd appreciate it if you could clarify why this is happening and when to use each command in each case. Thanks!

For example, given plot f(x)= x^5+x. plot the function given by g(x)= f(x-2)+3

Also, when plotting my graphs they look different than other graphing software.

How to rectify this error.

S-D_effect-RK.mw