MaplePrimes Questions

Hi

I need to express some discrete functions with domain in the natural numbers.

Is there a command like the 'AllSolutions' which is used for int?

As an example, how we can express all possible values of first derivative of chebyshev polynomial for various orders in terms of a piecewise function at origin ?

The following commands do not return a suitable answer, in this case!

f:=diff(ChebyshevT(n, r), r):

g:=simplify(eval(f, r = 0), symbolic) assuming(n::integer);

`assuming`([convert(g, piecewise, n)], [n::integer]);

Hello people in mapleprimes,

I installed maple 2018 Japanese version.
And, with solve(x^2-1,x), its solution is expressed as _EXPSEQ(1, -1)

I know this expression is an internal represantation.
How can I have maple answer as 1, -1?

Thanks in advance.

Addition: my pc is mac osx 10.13.6.
 

 

 

Hello,

I'm trying to solve  inverse trigonometric equation:

EQ := sqrt(3)*arctan(x/sqrt(3))-arctan(x) = 1;

sol := solve(EQ, {x});

#sol := {x = sqrt(3)*tan(RootOf(-tan(sqrt(3)*_Z-1)*sqrt(3)+3*tan(_Z)))}

evalf(sol);

#{x = 13.24164497} OK. one Real solution.

sol2 := evalf(allvalues(sol));

#sol2 := {x = -.1141310781-1.108044977*I}, {x = -.1141310781+1.108044977*I}, # {x = 1.142681884}, {x #= -2.379974990}, {x = 13.24164497}

Check:

seq(evalf(eval(EQ, sol2[k])), k = 1 .. nops([sol2]));

#.99999999991340592650+1.61960960*10^(-11)*I = 1., .99999999991340592650-#1.61960960*10^(-11)*I = 1., .15821278548775934290 = 1., -.4580182246463005988 = 1., #.9999999996233630663 = 1.

1.Can someone explain to me where did Maple find these Additional roots like: {x = 1.142681884}, {x = -2.379974990}?

2.It's a Bug or normal behavior ?

 

I have three questions

1:= If I have summation over i from 0 to 100 how do I prevent maple from unpacking the sum and set it like it is?

2:= Does the comand evalf give me an imaginary evaluation if we apply it in a sum and how do I avoid that?

3:= For infinite sum, Maple evaluates it with term hyper geometry and can't after that evaluate the diffrentation how do I prevent that?

Good morning, I'm trying to solve this very simple problem : plot a graph starting from the origin. The problem is that the x_axis is located at the lower value of my function, but i want it to go through the point (0,0). Let's see this example:

plot(piecewise( x<5, 100, x>5,200), x=0..10); As you can se the X-axis passes through y=100.

Now with this option I obtain:

plot(piecewise( x<5, 100, x>5,200), x=0..10, y=0..200); 

The problem is taht I need to specify the upper bound of the range for each function (200). Is there an automatic way? Any help is appreciated.


 

Hi.

I want to use canonical analysis or any other method to get vlaue of X1,X2.

How do I get  x 1, x 2 value?

please help!!

Hi.

Is possible to pdsolve these equations via maple.

Functions f1(x) and f2(x) and g(x) are aviable and only  phi and p1(x,z) and p3(x,z) are unknown.

I want to determine phi and p1(x,z) and p3(x,z).

 Also other parameter suvh as h-alpha-beta-beta1 -beta3 and L,..  are aviable and are not unknown.

Thanks

After calculations the integral contains infinity. what it resembles? Is it correct  answer?  Please check the file maple
 

restart

with(DifferentialGeometry):with(JetCalculus):NULL``

DGsetup([x, t], [u], E, 1):

``

 

 
E > 

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(1.1)
E > 

``

E > 

A := evalDG((-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))*`&w`(Dx, Dt)/((u[1]-u[2])^3*(u[1]+u[2])^3))

_DG([["biform", E, [2, 0]], [[[1, 2], -(3*t*u[1]^2*u[2]+t*u[2]^3-x*u[1]^3-3*x*u[1]*u[2]^2)*(2*u[]^2*u[1, 1]-2*u[]^2*u[2, 2]-2*u[]*u[1]^2+2*u[]*u[2]^2-u[1, 1]+u[2, 2])/((u[1]-u[2])^3*(u[1]+u[2])^3)]]])

(1.2)
E > 

simplify(HorizontalHomotopy(A))

_DG([["biform", E, [1, 0]], [[[1], -t*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((t*u[2]^6+(-3*x*u[1]-u[])*u[2]^5+(2*t*u[1]^2+3*u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4+(2*x*u[1]^3-2*u[]*u[1]^2-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1])*u[2]^3+18*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[1]^2*u[2]^2+(x*u[1]^5+3*u[]*u[1]^4-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1]^3)*u[2]+3*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity], [[2], x*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((x*u[1]^6+(-3*t*u[2]-u[])*u[1]^5+(2*x*u[2]^2+3*u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4+(2*t*u[2]^3-2*u[]*u[2]^2-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2])*u[1]^3+18*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[2]^2*u[1]^2+(t*u[2]^5+3*u[]*u[2]^4-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2]^3)*u[1]+3*u[]*(t*u[1, 2]+x*u[2, 2])*u[2]^4)/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity]]])

(1.3)
E > 

``

``

E > 

``

E > 

``


 

Download maple1.mw

1.mw maple1.pdf

Hi everybody, I have some programming difficulties on the maple, this is the algorithm and link article, hope everyone help me, please, thank you so much!!

Algorithm:

1: for Search every non-singular m × m matrix T with a few of XORs over F2. do

2: Find the minimum polynomial f(x) of T.

3: if f(x) = g(x)t(x) satisfying g(x) 6= 1, t(x) 6= 1 and g(x) is relatively prime with t(x). then

4: Find ri1(x), ri2 satisfying g(x)ri1 +t(x)ri2 = 1. Let pi1=g(x)ri1, pi2=t(x)ri2 = 1 . Sore pi1 and pi2.

5: end if

6: end for

7: for i from 1 to k. do

8: for Search a over F2[x]/(fi(x)). do

9: for Search b over F2[x]/(fi(x)). do

10: c = a + pi1(x), d = b + pi2.

11: if The circulant orthogonal matrix (a, b, c, d) is MDS. then

12: Store fi(x) and (a, b, c, d).

13: end if

14: end for

15: end for

16: end for

17: for Search every m × m non-singular matrix T with a few of XORs. do

18: for i from 1 to k. do

19: if fi(T) = 0. then

20: Substitute T into corresponding circulant orthogonal MDS matrix (a, b, c, d). Compute the sum of XORs of (a, b, c, d).

21: end if

22: end for

23: end for

Link: https://eprint.iacr.org/2017/371.pdf

i am trying to solve some equations ......but the comand f solve is not always work .i have two Question 
1:=is there any ather comand in maple solve the quations and looking for the answer in acetrtian region of real line other than f solve?

2:=iam trying to tell maple if you couldnt solve this equation assign another value of X as 
(if fsolve(Q[1])=Nill then X:=3;) but this comand desnt actually work in my loop

sol := dsolve([op(eqs), op(ICs)], numeric, range = 0 .. tmax, abserr = 10^(-3), relerr = 10^(-3), stiff = true, maxfun = 0);
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
can any one tell how to remove this error?

Good day 

Recently, I decided to learn Maple. So, I came across these exercises(uploaded) but I don't have any idea about the shooting method's Maple coding and how to compare especially representing it in tables.
 

What is the Maple coding needed?

How do I compare both results in a tabular form?

How do I calculate the error analysis? and

How do I plot the graph?

I believe with the knowldege gotten from the solutions of this exercises, I will be able to answer any question on shooting method.

Thank You. 

 

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