Dear All

In following I tried to find symmetries of certain partial differential equation taken from paper "Group classification and exact solutions of generalized modified Boussinesq equation". But the determining equations are not matching with equations obtained in paper.

Download [1116]_Symmetries_Determination.mw[1116]_Group_classification_and_exact_solutions_of_generalized_modified_Boussinesq_equation.pdf

Regards

Still a little unclear what this error means tho

Download dispatchTOshillCORE.mw

yep the errors recieved using some packages are very very specific for maple, for example, the one i got today using the ODE package was profoundly helpful:

Error, (in ODEtools/info) unable to handle derivatives as {diff(1/(ln(X)-Psi(1-f(X))-Psi(f(X))), [`$`(X, n-k[1]-k[2])]), diff(1/f(X), [`$`(X, n-k[1]-k[2])]), diff(Psi(1-f(X)), [`$`(X, k[2])]), diff(Psi(f(X)), [`$`(X, k[2])]), diff(f(X), [`$`(X, k[1])])} while solving w.r.t f(X)

im refering to the reason why a maple andriod application hasnt shown up or at least one of the big ones (preferably a java based on since thats the only thing i know for making any apps fluently) but yep cannot be the only one who has felt that need to get out of the house but wants to keep mathing when there is nothing to do which is pretty much always for me anyway

most effective built in operator code award goes to ppl that wrote the code for the union and intercect set operations for maple. Very important simple example below of  one of its applications.

When i work with algorithms, probably one of my most primary ports of enquiry (figuratively jeez skynet)  is to set up and if statement triggered to terminate the loop once the operations performed for any further cycles is INDEMPOTENT. this doesnt always mean your output is convergent in every case but it allows you to minimize the amount of time the cpu needs to collect data( ie the point at which it would produce that same set as it did in the last most loop)

Download idempotency.mwidempotency.mw

How can one find out when a Maple command or package became part of Maple? i.e. which Maple version first had this command or package?

For example, I'd like to know when applyrule https://www.maplesoft.com/support/help/Maple/view.aspx?path=applyrule was introduced. But this applies really to any command I see.

In Mathematica, this is easy to find out, since it is documented in the help page for the command, at the botton of each page when the command was added. Is there a command or a web page that shows this type of information about Maple commands and packages?

I have some data

> X:=[291.3301386,349.9410125,420.7945287,490.0836935,558.1365585,623.6824877,688.6344191,752.1359797,814.1871695,874.7879884,933.8452525,991.0023402,1047.88822,1102.687556,1156.036521,1207.200419]:

>
> Y:=[0.008923638,0.010336322,0.012031554,0.013676089,0.01527851,0.016809936,0.018315901,0.019777093,0.021194266,0.022568158,0.023897399,0.025174796,0.026437267,0.027645069,0.02881302,0.029925828]:

to which I am trying to fit a function

U:=(m,d,Theta,T)-> (((3*(6.62607e-34)^2*T)/(4*Pi^2*m*1.36085e-23*Theta^2))*((T/Theta)*int(x/(exp(x)-1),x=0..Theta/T) + (Theta/(4*T))))/1e-10^2 +d^2;

where Theta≈200 and d≈0.035. T, Theta, d, m > 0

 When I try and solve

> NonlinearFit(U(0.15036/6.022e23,d,Theta,T),X,Y,T,initialvalues=[Theta=200, d=0.035]);

I get the error "Error, (in Statistics:-NonlinearFit) complex value encountered"

I can plot the function with Theta=200 and d=0.035, I get approximately the right curve and no errors about complex values.

How can I solve for Theta and d without encountering this error?

Hello,

Lets say I have some expression F that is a function of n and N like, F=n+N-1 and I want to express that in terms of x, where x=n/N. How would I do this in maple? Thanks in advance. 

Hi, I am trying to plot a parabola in spherical coordinates using the command spacecurve, using 

>with(plots);

>spacecurve([cot(phi)/sin(phi), 1.61, phi], phi = -3.14 .. 3.14, numpoints = 3000, axes = normal, coords = spherical, color = red, linestyle = dash, axes = normal)

(I know it is easier in Cartesian coords, but I am doing this as a first version of a more complicated curve, given by the sol. of a system of differential equations). 

Maple plots the parabola correctly but it joins the initial and the final points of the plot with a straight line, yielding something that looks like a U with a bar on top (I cannot upload the image). Is there any way to get rid of the line?

This came up in another language. I tried to solve it in Maple, but I am newbie so did not know how to.

The problem is to remove all products of  "a^n*b^m" that shows up in an expression, including any powers of "n,m". For example, given these three expressions

f0 := a^4+4*a^3*b +6*a^2*b^2+4*a*b^3+ b^4;
f1 := 3*(a*b -2*c);
f2 := (a*b -2*c)/(c - a*b);

Then applying the transformation needed, will result in

f0:= a^4+b^4;
f1:=-6*c;
f2:=-2;

Becuase the transformation will detect any a^n*b^m and simply replace this product by zero 
from the resulting expression. So "a*b^2 + 2" will become "2", and so on.

I assume a function such as "patmatch"  or "match" is needed. I tried, but could not figure how. 
I also tried algsubs. How would this be coded in Maple?

Hi,

1st post. I'm trying to integrate the following function:

h:=t->(2*t-1)*cos*sqrt(3*(2*t-1)^2+6)/(sqrt(3*(2*t-1)^2+6));

h:=t->(2*t-1)*cos*(sqrt(3*(2*t-1)^2+6))/(sqrt(3*(2*t-1)^2+6));

h:=t->(2*t-1)*(cos*(sqrt(3*(2*t-1)^2+6)))/(sqrt(3*(2*t-1)^2+6));

h:=t->((2*t-1)*(cos*(sqrt(3*(2*t-1)^2+6))))/(sqrt(3*(2*t-1)^2+6));

int(h(t),t); ** Integration command. I've also replaced the "h(t)" with the entire function.

I've tried the following:

1. Changed the "t" to "x" throughout function.

2. Added parens around sqrt portion.

3. Added parens to include "cos" and then added to include the beginning (2*t-1).

4. I've added brackets around the numerator but this just causes Maple to reprint the function with the inegration sign in front of the function.

5. I've also tried using the Integration tutor. It returns that maple is unable to calculate.

6. Repeat all the above in Maple 2015, same answer.

I always get cos(t^2-t).

The math book claims the answer is 1/6*sin*sqrt(3*(2*t-1)^2+6). When I perform the inegration on paper I get the same answer.

Any suggestions or corrections would be great.

Thank you,

Jay.

hi every one...

how i can simplify this result (R_arm_F2 $  Twflex) via tringular relations.

where Ixflex & tetadot and other... are constants

thanks

matrix_f.mw

Download matrix_f.mw

updated:

i use 5 points trapezoid got RootOf  in result,

only 4 points is acceptable

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

moreover, i got a problem when i copy the area1 result into 

visual studio c# code, it has error Integral Constant is too large

i find area2 has

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

Download question4.mw

A prime producing polynomial.

Observations on the trinomial n² + n + 41.

by Matt C. Anderson

September 3, 2016

The story so far

We assume that n is an integer.  We focus our attention on the polynomial n^2 + n + 41.

Furthur, we analyze the behavior of the factorization of integers of the form

h(n) = n2 + n + 41                                          (expression 1)

where n is a non-negative integer.  It was shown by Legendre, in 1798 that if 0 ≤ n < 40 then h(n) is a prime number.

Certain patterns become evident when considering points (a,n) where

h(n) ≡ 0 mod a.                                             (expression 2)

The collection of all such point produces what we are calling a "graph of discrete divisors" due to certain self-similar features.  From experimental data we find that the integer points in this bifurcation graph lie on a collection of parabolic curves indexed by pairs of relatively prime integers.  The expression for the middle parabolas is –

p(r,c) = (c*x – r*y)² – r*(c*x – r*y) – x + 41*r².           (expression 3)

The restrictions are that 0<r<c and gcd(r,c) = 1 and all four of r,c,x, and y are integers.

Each such pair (r,c) yields (again determined experimentally and by observation of calculations) an integer polynomial a*z2 + b*z + c, and the quartic h(a*z2 + b*z + c) then factors non-trivially over the integers into two quadratic expressions.  We call this our "parabola conjecture".  Certain symmetries in the bifurcation graph are due to elementary relationships between pairs of co-prime integers.  For instance if m<n are co-prime integers, then there is an observable relationship between the parabola it determines that that formed from (n-m, n).

We conjecture that all composite values of h(n) arise by substituting integer values of z into h(a*z² + b*z + c), where this quartic factors algebraically over Z for a*z² + b*z + c a quadratic polynomial determined by a pair of relatively prime integers.  We name this our "no stray points conjecture" because all the points in the bifurcation graph appear to lie on a parabola.

We further conjecture that the minimum x-values for parabolas corresponding to (r, c) with gcd(r, c) = 1 are equal for fixed n.  Further, these minimum x-values line up at 163*c^2/4 where c = 2, 3, 4, ...  The numerical evidence seems to support this.  This is called our "parabolas line up" conjecture.

The notation gcd(r, c) used above is defined here.  The greatest common devisor of two integers is the smallest whole number that divides both of those integers.

Theorem 1 - Consider h(n) with n a non negative integer. 

h(n) never has a factor less than 41.

We prove Theorem 1 with a modular construction.  We make a residue table with all the prime factors less than 41.  The fundamental theorem of arithmetic states that any integer greater than one is either a prime number, or can be written as a unique product of prime numbers (ignoring the order).  So if h(n) never has a prime factor less than 41, then by extension it never has an integer factor less than 41.

For example, to determine that h(n) is never divisible by 2, note the first column of the residue table.  If n is even, then h(n) is odd.  Similarly, if n is odd then h(n) is also odd.  In either case, h(n) does not have factorization by 2.

Also, for divisibility by 3, there are 3 cases to check.  They are n = 0, 1, and 2 mod 3. h(0) mod 3 is 2.  h(1) mod 3 is 1. and h(2) mod 3 is 2.  Due to these three cases, h(n) is never divisible by 3.  This is the second column of the residue table.

The number 0 is first found in the residue table for the cases h(0) mod 41 and h(40) mod 41.  This means that if n is congruent to 0 mod 41 then h(n) will be divisible by 41.  Similarly, if n is congruent to 40 mod 41 then h(n) is also divisible by 41.

After the residue table, we observe a bifurcation graph which has points when h(y) mod x is divisible by x.  The points (x,y) can be seen on the bifurcation graph.

< insert residue table here >

Thus we have shown that h(n) never has a factor less than 41.

Theorem 2

Since h(a) = a^2 + a + 41, we want to show that h(a) = h( -a -1).

Proof of Theorem 2

Because h(a) = a*(a+1) + 41,

Now h(-a -1) = (-a -1)*(-a -1 +1) + 41.

So h(-a -1) = (-a -1)*(-a) +41,

And h(-a -1) = h(a).

Which was what we wanted.

End of proof of theorem 2.

Corrolary 1

Further, if h(b) mod c ≡ = then h(c –b -1) mod c ≡ 0.

We can observe interesting patterns in the “graph of discrete divisors” on a following page.