Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

Hello Maple community and others,

It has been proven that every positive
rational number can be represented in 
Egyptian Fraction form

See wikipedia on Egyptian Fractions

We have the fact that the harmonic series diverges
Let Hn = 1 + 1/2 + 1/3 + ... + 1/n.

Then the limit as n goes to infinity of Hn is unbounded.

It seems these two facts go hand in hand.

Is there a procedure in Maple that will give
Egyptian Fraction representation of an arbitrary
rational number?

I made a worksheet with some examples.

egyptian_fractions.mw

egyptian_fractions.pdf

 

Regards,
Matt

Hello again,   I'm trying to write a procedure to multiply quaternions.   We know that they can be represented as a vector of length 4.   See Wikipedia.   My try  -

qaa=[8,4,6,2] and qab =[2,,4,6,8]
mult:=proc(a,b)

end proc;

maybe needs some looping or data from a table.  

Regards,

Matt

Hi all,

We want to find a curve fit for an integer sequence.

We have n such that n^2+n+17 is a prime number.

See oeis.org/A007635 and comments.

Use the Maple CurveFitting package.

I tried with(CurveFitting).

We do not know if this is best represented by a polynomial or exponential curve fit.

 

n2_and_n_and_17_in_OEIS_007635.mw

n2_and_n_and_17_in_OEIS_007635.pdf

Regards,

Matt

The low-level command is "RTABLE". I have used it a million times. I use it with Maple 13 to replace expressions by tables.
For example,

print(`Hello! `*RTABLE(1,x^2+y^2));

will print: Hello! x^2+y^2. However, the main reason I am using it is to avoid Maple messing up the order of things like sums,
products, etc. However, this command has disappeared. It does not exist in Maple 2020. So, I cannot run my programs at the university which now has Maple 2020. Anybody knows if this command can still be used in another form the same way?

Thank you!
mapleatha

Since I am a mathematician, I am wondering how Maple goes about solving an identity for 3 functions.
Let's say we have af1(t)+bf_2(t)+cf_3(t) = 0 for all t. How does maple actually find a triplet a,b,c that works for all real t?
It does with solve(identity( ),[a,b,c]). But what is the theory behind it?
We know, of course, a priori, that such a triplet exists.

Thank you!

mapleatha

 



 

Please refer to this for the definition(s):

http://www.mrob.com/pub/math/largenum-3.html#hyper

The hy(a,n,b) recursion turns  into the following Maple code:

 

Unfortunately this code depends on x and y being explicit numeric values (x,y \in N), otherwise the recursion crashes (if I ask for example H(2,x,y) or H(2, x, 2))

Is there any way to transform the code so that the final construct can be shown symbolically?

I don't see anything obvious, especially since if y is not a specific natural number the recursion will crash. Can we maybe force Maple to not evaluate it for natural number arguments and return the final construct as either a sum, product or tower of the symbols for x and y (i.e. symbols of the digits of x and y like a tower of 2's 3's, etc)?

I do remember something about putting primes around functions prevents premature evaluation, but in this case it doesn't do anything like I'd want. This definition is not primitive recursive (like that of the Ackerman function), so I don't expect it to be able to be called abstractly (H(2,x,y) or something else such), but maybe we can turn it into something that shows the structure of the final construct as symbols of the digits of x and y?

Thanks.

Yannis

PS: One can improve the situation a bit, by implementing the extended definition as:

hy := proc (n, x, y) if n = 0 then y+1 elif n = 1 then x+y else if y = 1 then x else if n = 2 then x*y elif n = 3 then x^y elif n = 4 then x^hy(4, x, y-1) else hy(n-1, x, hy(n, x, y-1)) end if end if end if end proc

(which can be called abstractly for n=0,1,2,3,4 (hy(n,x,m) for natural m), but for higher n it crashes similar to H, since the definition falls back to the previous if n>4.

There are some answers up here, but they are for given known functions.
I need to place parentheses around functions that are automatically created.
For example, the function $f(x)$ takes many polynomial values during the execution
of a procedure. For examplle, it takes the values, 2x-1, x^2+3x+2, x^3-2x-3, etc.
How do I automatically place parentheses around these polynomials?
Thank you!
mapleatha

Why doesn't Maple 13 plot x^(1/3) for x negative?

Thank you.

mapleatha

I use "cat" to concatinate greek letters but the output is not correct.test_cat.mw
 

restart; with(linalg); QPT := proc (q) local nc, qp, qpp, i, p, pp; nc := vectdim(q); qp := Vector(nc); qpp := Vector(nc); for i to nc do qp[i] := cat(p, q[i]); qpp[i] := cat(pp, q[i]) end do; return qp, qpp end proc

q := convert([alpha, beta], Vector); QPT(q)

q := Vector(2, {(1) = alpha, (2) = beta})

 

Vector(2, {(1) = palpha, (2) = pbeta}), Vector(2, {(1) = ppalpha, (2) = ppbeta})

(1)

``


 

Download test_cat.mw

 

I use WINDOW 10 

for j from 1 to 3 do
pout := cat("C:/Users/Eli/Documents/Animation/", "file", j, ".bmp"):
print(pout):
plotsetup(bmp, plotoutput = pout):
# plot (...)
od:

I have 2   equations that must be zero, and 2 ODE's for phi and theta

Vector(2, {(1) = `ϕ`(tau)-1.5*sin(`ϑ`(tau)), (2) = -`ϕ`(tau)^2+1.5*cos(`ϑ`(tau))})

how can i implement this quations with event statment .  this dose't work

 

event1 := [[`and`(gln[1], gln[2]), halt]]

 

 

maple_event_test.mw

I want to catch the trigger time t[i]

f1 := 0.001;
f2 := 0.002;
c1 := 0.002;
c2 := 0.005;
w1 := 0.1;
W := 0.14;
p1 := 0.65;
p2 := 0.28;
p := 1.167;
r := 0.004;
alpha := 0.2;
ze := 0.14;
mu := 0.05;
ga := 0.01;
cp := 9.3;
Rp := 100;
sigma2 := 0;
l[1] := 3*W^2*(-1+W^2)/(4*(-1+4*W^2));
l[2] := Rp^2*w1^2*mu*ga*cp/(2*(Rp^2*w1^2*cp^2+1));
l[3] := (Rp.w1.mu.ga)/(2*(Rp^2*w1^2*cp^2+1));
l[4] := W*(-1-7*W^2+8*W^4)/(8*(-2+8*W^2));
eq1 := (-x*t+l[2]*x+l[1]*x*y^2+(3/2)*alpha*ze^2*x)^2+((1/2)*c1*x+l[3]*x)^2-(1/4)*f1^2;
eq2 := (-l[4]*y^3+l[1]*x^2*y)^2+(1/4)*y^2*c2^2-f2^2/(4*W^2);

I need to solve these two equation for the variable x and y in terms of  t because I want to plot x with a range for t 

and the same plot y with a range for t and if it is possible to plot x vs y for the previuos same range for t

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