(g o f ) o alpha =g o (f o alpha)
restart;alpha := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -1
g := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -(1/3)*(y/x+sqrt(-2*y^2/x^2))*x/y
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help. 

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

Hello!

I am trying to create a Fortran routine that creates and populates a large 2D array, using Maple's codegen or CodeGeneration capabilities. I would like Maple to create the Fortran code so that the column-major ordering is respected: I would like Maple to populate mat(1,1), mat(2,1), mat(n,1) before moving on to mat(1,2)... Unfortunately, codegen and CodeGeneration seem to only produce row-major code.

Any idea on how to proceed, or an option of the code generation that I would have missed?

Thanks for your help!

Etienne

soslve('(cosh(C + cosh(C))/cosh(C) = 2') gives me a "Waning, solutions may have ben lost" message and no answer.

Write a procedure which inverts a given 2x2 matrix ie
Given a list of 4 numbers (a,b,c,d) return numbers (x,yz,w) such that
Matrix(a,b,c,d)(Matrix(x,y,z,w)) =Identity matrix

Trying to write a procedure to just reduce the vales of x.. 

restart: 

proc_r:= proc(x :: numeric) 

local x0:

x := x0: 

#reducing the value to between -Pi and Pi

do 

 if ( x0 <= evalf(Pi) ) then 

  break: 

 end if: 

 x0 := x0 - 2*evalf(Pi)

end do: 

do 

 if (x0 >= evalf(-Pi) ) then

  break: 

 end if:

 x0 := x0 + 2*evalf(Pi)

end do: 

#using the symmetry of sin to reduce to between -Pi/2 and Pi/2 

 if (x0 <= evalf(Pi/2) ) then  

 break:

end if: 

x0 := evalf(Pi) - x0:

if (x0 >= evalf(-Pi/2) ) then 

 break:

end if: 

x0 := evalf(-Pi) - x0:

return x0:

end proc:

proc_r(7);  

Error, (in proc_r) illegal use of a formal parameter

 

Why do i get this error message... 
How do i fix it? 

Hi there!

I wrote a piece of code which spits out the numerical datapoints (x,y(x)) corresponding to a function y(x). So that the result is accurate, I need quite a lot of data points - currently I am working with 5k.

In order to work with this function later, I interpolated it with a Spline. For instance, I would like to sample the function values on a fifferent grid, etc.. However the evaluation of this function really takes up hell of a lot of time, and the reason seems to be, that it, being a spline on 5k nodes, is simply a huge expression.

Is there a better way to do this? Are other fitting functions than a spline maybe better suited?

Thanks for help!

I have defined the following procedure, S(x,a,b,s), in Maple with the goal of creating an exportable two column, multi-row array, containing the least positive real root of a high order polynomial f(x,y)=0 in the 2nd column, and a parameter y in the first column.

The procedure takes four numerical arguments (x,a,b,s) and varies parameter y from the initial non-negative value of a, by stepsize s, until the value min(b,1) is reached.

Unfortunately, the output 4x2 array only has the last calculated [y,solution] entries in the first row. Successive rows are filled with zeros.

Is there anyone kind enough to point out the error in the way I have defined this procedure? Many thanks in advance. Procedure is:

S := proc (x, a, b, s) 
   global R, y;
   for y from a by s to b while y < 1
     do R := Array(1 .. ceil((min(b, 1)-a)/s), 1 .. 2, [[y, FindMinimalElement(select(type, [fsolve(f(x) = 0)], positive))]])
     end do;
     end proc;

I have a nested list a := [[1,2,3],[4,5,6],[7,8,9]]: and would like to apply a function f to the 1st elements in nested list, e.g. [[f(1),2,3],[f(4),5,6],[f(7),8,9]]. How can I achieve this?

Thanks in advance.

Congratulations to Andriy Andrusyk, from the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, who won last quarter’s Möbius Challenge with his application Heat Equation.  Dr. Andrusyk won a DSLR Camera Prize Pack.

Remember that you have until Mar. 31 to enter your Möbius Apps for a chance to win the next prize, an Xbox One!   Visit Möbius App Challenge for full contest details.

eithne

what is the difference between endomorphism and identity map?

http://mathfaculty.fullerton.edu/mathews//n2003/hornermod.html

i find a program above, 

if no general method, how about specific to convert it

if have general method, how is it?

I have defined a function by doing

f:= (x1,x2,x3) -> sum( [complicated expression], [summation ranges]),

which Maple converts to an explicit polynomial in x1,x2,x3.

However, it seems Maple does not quite think of f as this polynomial, but always remembers the original definition of f. How should I do in order for Maple to really define f to be this explicit polynomial?

I'm trying to animate transparency, here's are the plots:

A :=tranz-> plot3d(-2/sqrt(x^2+y^2)+5/sqrt((x-1.6)^2+y^2), x = -5 .. 5, y = -5 .. 5, view = [-5 .. 5, -5 .. 5, -5 .. 5], transparency = tranz) end proc;
B := sphere([0, 0, 0], 2*(1/10), color = magenta, style = patchnogrid):
C := sphere([1.6, 0, 0], 5*(1/10), color = green, style = patchnogrid);
E := plot3d(0, x = -5 .. 5, y = -5 .. 5, view = [-5 .. 5, -5 .. 5, -5 .. 5], style = wireframe, shading = zgrayscale):

here I am displaying them without a problem:

display(A(.5), B, C, E, scaling = constrained, view = [-5 .. 5, -5 .. 5, -5 .. 5], axes = normal)

here I am trying to animate the transparency in plot A to no avail :( :

animate(display, [A(tranz), B, C, E, scaling = constrained, view = [-5 .. 5, -5 .. 5, -5 .. 5], axes = normal], tranz = 0.1 .. 0.9)
Error, (in plot3d) expecting option transparency to be of type {"default", realcons} but received tranz

if you guys could help me find where I'm going wrong I'd be super grateful :D

thanks everyone.

Best,

-Mike

I have an equation with the following structure:

sin(a)-sin(b)=0;

Maple can solve this:

solve(%,[b]);

[[b=a]]

so it misses the 2nd solution (b=π-a). I can use the allsolutions qualifier:

solve(%,[b],allsolutions);

and now Maple returns an expression that, while correct, is really not conducive to further work without fairly massive substition work (_Z10 has to be 0 and the solutions wanted have _B10 0 and 1). In a classroom settng this is not helpful. Try as I might using the options to solve I have not found a way to make this into a list of the two solution I want without extensively mucking around with the expression. Is there any way to coerce solve to return something simpler?

I really want something like

[b=a,b=π-a]

TIA,

Mac Dude.