I was working through an old text book, trying to understand a different problem.  I came across this problem in an exercise set and thought it was simple.  Until I tried it.

The difficlty I had was in using subs to substitute all values.  I had to use subs 2 or 3 times to get all substitutions.  How can I avoid this?

## Prove if F is the fibonacci sequence,
restart;
with(combinat, fibonacci):
F := n -> fibonacci(n);  ## F(n+1) = F(n)+F(n-1); F(1) = 1;
## the problem
P := n-> F(n+1)*F(n+2) - F(n)*F(n+3);
##
check_low := proc(n)
    local idx;
    for idx to n do
        print(P(idx),(-1)^idx);
    end do;
end proc;
check_low(1);
check_low(2);
check_low(3);
check_low(4);

## Assume true for n=k
A := P(k) = (-1)^k;

notation := { F(k)   = a,
              F(k+1) = b,
              F(k+2) = c,
              F(k+3) = d,
              F(k+4) = e };

## some fibonacci definitions
fibs := [ e = c + d,  d = b + c, c = a + b ];

eq1 := subs(notation,A);
eq1 := subs(fibs,eq1);
eq1 := subs(fibs,eq1);  ## have to repeat to get only a and b in the expression

eq2 := subs(notation,P(k+1));
eq2 := subs(fibs, eq2);
eq2 := subs(fibs, eq2);
eq2 := subs(fibs, eq2);  ## have to repeat to get only a and b in the expression
## Reduce eq2 to (-1)^(k+1)
simplify(eq2 = -lhs(eq1));
verify(eq2, -lhs(eq1), equal);
evalb(eq2); simplify(%);  ## Ah, this is why I need equal in verify.
evalb(-lhs(eq1)); simplify(%);

testeq(eq2, -lhs(eq1));

Hello,

I'm compiling a maple procedure to a C code with the Compiler command. I was wondering if it is possible to change the optimization flag, for example -03  for gcc? Is there a way to maybe change a file in the Maple directory that specifies the compiler options?

Second Try:

f:= c/(c - 1) - c*(Pi^2 - 12*ln(c))*(1 + c)/(12*(c - 1)^3*n) + (((144*c^3 + 1584*c^2 + 1584*c + 144)*ln(c)^2 - 24*Pi^2*(1 + c)*(c^2 + 10*c + 1)*ln(c) + (-96*c^3 - 288*c^2 + 288*c + 96)*Zeta(3) + Pi^2*((Pi^2 + 24)*c^3 + (11*Pi^2 + 72)*c^2 + (11*Pi^2 - 72)*c + Pi^2 - 24))*c)/(288*(c - 1)^5*n^2)

This expression is already arranged with respect to n. However, the nominator of each term is not collected with respect to c. So naturally I thought

collect(f,[n,c]) or collect(f,[n,c],simplify)

would work. But now he messes up the nominator i.e. he can not factor and simplify. Note that the single variable case collect(f,n,simplify) works in not messing up, but this is not what I want, since the nominator of each n-term is not in c-collected form.

collect(f,[n],u->collect(u,[c],...))

also does not work, since he messes up again.

By c-collected form I mean the following:

The n^0 and n^{-1} term are actually fine. The factorization in the second term is ok. But for the third term

f2:=(144*c^3 + 1584*c^2 + 1584*c + 144)*ln(c)^2 - 24*Pi^2*(1 + c)*(c^2 + 10*c + 1)*ln(c) + (-96*c^3 - 288*c^2 + 288*c + 96)*Zeta(3) + Pi^2*((Pi^2 + 24)*c^3 + (11*Pi^2 + 72)*c^2 + (11*Pi^2 - 72)*c + Pi^2 - 24)

what I mean by c-collected is

collect(f2,c,simplify)

This is the nominator of the n^{-2} term.

I sort of managed by the following to procedings:

of:=[op(f)];
add(`~`[`/`](collect~(numer~(of), c, factor), ` $`, denom(of)));
add(collect~(of, c, simplify));

but the first one seems cumbersome for such a trivial thing that should be handled by collect. It also does not factor out the e.g. 12*ln(c)-Pi^2. This seems to be a general behaviour

g:=a*x*(x+1);
collect(g,x) does not factor out the a as in a*(x^2+x).

With the second method I'm more or less happy, but I didn't manage to completely collect the c terms i.e. the n^{-1} term is still c*(c+1) and not c^2+c.

 Hello everyone!

 I want to find all solutions of  following equations :

I used Maple 2019: 

The output is:

So we have two solutions. But when I use Matlab 2018, 
four solutions are returned.

It is easy to check that  first two in Maple and Matlab are  same.

Who is right? Does Maple miss complex solutions?

Hi forum

I got a problem:

When i use these lines:

with(plots);
implicitplot(y = a*x + b, x = -10 .. 10, y = -10 .. 10, axis = [gridlines = [10, color = blue]]);



The vertical axis dosent stretches as far as i want it to.

The 'Axis Gridlines Properties' match the plot.

But the 'Axis Properties' dosent:


I can change the 'range' manually, by checking off the 'use data extend' box.
- But i need to use these plotting commands, very often.
Is it possible to write something in the plot-function, so i dosent need to do these corrections manually, every time i plot something?

Thank you in advance
Dan

I'm working along in Maple 2019 and then all of a sudden it freezes.  Anyone else have this?

Maple 2018 and earlier displayed an Array like this

In Maple 2019 I get this

How do I display Arrays in Maple 2019 like Maple 2018?

How Do I set the Command Line Font in Maple 2019?

The default font is strange.  eq is displayed as a a lower case char like '8' followed by 'q'.

I would like to have something like courier 10, etc.

Hi, I am using the GroupTheory package and I wanted to created the following group in Maple:

I stumbled across this link https://www.maplesoft.com/products/maple/features/grouptheory.aspx and then tried to use the following commands to define this group in Maple:

1. First a defined a 12x12 matrix:

2. Then I tried to define my  group using:

However this doesn't work because I get the following error:

Error, (in GroupTheory:-Group) invalid input: arguments to GroupTheory:-Group, [Matrix(12, 12, {(1, 1) = e, (1, 2) = p, (1, 3) = q, (1, 4) = r, (1, 5) = s, (1, 6) = t, (1, 7) = u, (1, 8) = v, (1, 9) = w, (1, 10) = x, (1, 11) = y, (1, 12) = z, (2, 1) = p, (2, 2) = q, (2, 3) = e, (2, 4) = y, (2, 5) = u, (2, 6) = w, (2, 7) = z, (2, 8) = r, (2, 9) = x, (2, 10) = t, (2, 11) = v, (2, 12) = s, (3, 1) = q, (3, 2) = e, (3, 3) = p, (3, 4) = v, (3, 5) = z, (3, 6) = x, (3, 7) = s, (3, 8) = y, (3, 9) = t, (3, 10) = w, (3, 11) = r, (3, 12) = u, (4, 1) = r, (4, 2) = z, (4, 3) = t, (4, 4) = s, (4, 5) = e, (4, 6) = y, (4, 7) = v, (4, 8) = x, (4, 9) = p, (4, 10) = ...  (12, 8) = s, (12, 9) = u, (12, 10) = y, (12, 11) = x, (12, 12) = e})], do not match any of the accepted calling sequences

I don't know what's going wrong. It doesn't give a 2D Plot. Thanks in advance.

Download temperature24hr.mw

I'm using variable names that have subscripts, not as a table index but literal i.e. R__1 as a unique variable name.  It seems whenever I make assumptions on variables that have subscripts, when I use them the variables that have subscripts are printed twice:

Can anyone explain why this happens and how to get around it?

Thanks in advance.

alternatingseries.mw
I have a double about this alternating series.
According to maple this series converges:

evalf(sum((-1)^(n+1)*(ln(n)/n+1),n=1..infinity))
                          0.3401310963

However limit ln(n)/n + 1 does not equal to zero, it equals 1. Therefore the series should diverge.

Also while I am on the subject of series and limits, why is limit (-1)^n  as n goes to infinity a range between -1-I and 1 + I.

limit((-1)^(n), n=infinity)
                        -1 - I .. 1 + I

Hello, I am having a bit of difficulty simplifying some calculations in Maple 2019. In short, in order to verify that the tensors that I am trying to use are indeed inverses of each other, I am simply trying to multiply component wise, for example the tensor component e[2,~2] with the tensor component f[~2,2], since they are essentially inverses of each other, i.e. the matrix defining f is actually the inverse of the matrix e, i.e. f=e^(-1), should give back 1 as an answer. Nonetheless, when I attempt to take this simple multiplication Maple does not reduce it, but rather just gives multiplies the terms with no simplification. Is there anything I can do so that Maple may simplify its calculations? I have already tried the "eval" calling sequence but that didn't do the trick, and I fear that when escalating the calculations I will get a bunch of long expressions rather than concise solutions. Thank you for your help in advance,
 

Christoffel_symbols_of_de_Sitter_metric_research.mw

restart;
with(LinearAlgebra);
G := Matrix([[beta1^2, 0, -beta2^2, 0], [0, beta1*(b^2 - beta1^2), 0, beta2*(b^2 + beta2^2)], [beta1^2*cosh(beta1*l), beta1^2*sinh(beta1*l), -beta2^2*cos(beta2*l), -beta2^2*sin(beta2*l)], [beta1*sinh(beta1*l)*(b^2 - beta1^2), beta1*cosh(beta1*l)*(b^2 - beta1^2), -beta2*sin(beta2*l)*(b^2 - beta2^2), beta2*cos(beta2*l)*(b^2 + beta2^2)]]);
NULL;
NULL;
S := Determinant(G);
S := simplify(S);
S1 := S/(beta1^2*beta2^2);
F := Pi*d^2/4;
Q := F*d^2/8;
u := E/(2*(1 + v));
lambda := sqrt(w^2/c^2);
j := v*d*lambda/sqrt(8);
y1 := 1 - j^2 + sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
y2 := 1 - j^2 - sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
b := 2*(1 + v)*(8/(v^2*d^2) - w^2/c^2);
beta1 := sqrt(y1);
beta2 := sqrt(-y2);
S;
d := 24.8;
c := 5100;
v := 0.34;
l := 2000;
E := 2.1*10^5;
p := 7700;
S;
plot(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error

Error, (in plot) incorrect first argument (-HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I)*(HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I+(HFloat(2.918216722364015e-174)+HFloat(7.045198389075166e-174)*I)*(HFloat(1.2899139595562734e220)+HFloat(1.2899139595562734e220)*I+(HFloat(2.345679734289597e162)+HFloat(9.71612358926469e161)*I)*(.3015529528-0.1030372934e-6*w^2)^2)+(HFloat(2.739493386336394e-116)+HFloat(2.739493386336394e-116)*I)*(HFloat(1.5009648027561687e-231)-HFloat(2.757556062608314e294)*I+(-HFloat(5.478986772672788e-116)+HFloat(5.478986772672788e-116)*I)*(.3015529528-0.103 ... HFloat(2.739493386336394e-116)*I)*(.3015529528-0.1030372934e-6*w^2)^4)

w1 := fsolve(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error 

Error, (in fsolve) Digits cannot exceed 38654705646
 

Is it italic when copied and pasted?  Is it bold when copied from maple 8?  I just ahve not been able to work it out.