MaplePrimes Questions

How to create a double underscore in a macbook air.  

I type G__[], the underscore disappears even on 1-D math.  I am using maple 2019.1, Mojave 10.14.6

I am trying to follow an example on geodesics 

 

with(Physics);

Setup(mathematicalnotation = true);
Setup(coordinates = X);

g_[];

 

I cannot reproduce the example because I cannot even create the syntax.

 

 

Take any odd number k, with distinct odd prime divisors p_1,...p_k and ask the following question: What is the smallest even number which when added to each prime divisor p_i of k, gives another prime? Example: k= 119=7*17, so the smallest even number is 6 because 7+6=11 and 17+6=23. NB: some numbers (eg 105,195,231...) seem to have no solution. I would appreciate assistance with a code to calculate for every odd k, the even number in question, or to allocate 0 for numbers where no solution has been found up to some suitably convincing high number like N= 10^5 or 10^6, (a parameter I could change if desired). The idea would be to conjecture that the apparently no solution numbers (up to N) don’t actually have a solution. Any assistance much appreciated in advance. I have found the solutions up to k=781 by hand, but my hand is getting tired now.

cheers,

David.

ps: I would like to have the option (if possible) to output the numbers with solution =  0, and the numbers which are the smallest to have solution 2*n, as separate sequences, for n up to some arbitrary value (ie 3,7,23,69,93...). (n>=1). Hope this is not asking too much. 

How i convert the following mathematica code to Maple

f1[t^m_] := Gamma [m + 1] t^(m - a[t]) /Gamma[m + 1 + a[t]];
f1[t] := Gamma [2] t^(1 - a[t]) /Gamma[2 + a[t]];

f1[p_Plus] := Map[f1, p]
f1[c_*f_] := c*f1[f] /; FreeQ[c, t]
f1[c_] := 0 /; FreeQ[c, t]

f1[x^2*t^2 + t + x]

gives

t^(1 - a[t])/Gamma[2 + a[t]] + (2 t^(2 - a[t]) x^2)/Gamma[3 + a[t]]

In this worksheet I solve a system of differential-algebraic equations (DAEs) and then invoke a proc to evaluate the solution.  The trivial proc, called tryme, is reduced from a larger proc which I have cut down to focus on the error message.

I can't explain where the error originates.  Can someone shed light?  I don't insist on the output=operator option.  I tried other output options but always arrived at the same error message.

restart;

de1 := diff(x(t),t,t) = lambda(t)*x(t);

diff(diff(x(t), t), t) = lambda(t)*x(t)

de2 := diff(y(t),t,t) = 1 + lambda(t)*y(t);

diff(diff(y(t), t), t) = 1+lambda(t)*y(t)

eq := x(t)^2 + y(t)^2 = 1;

x(t)^2+y(t)^2 = 1

ic := x(0)=1, y(0)=0, D(x)(0)=0, D(y)(0)=0;

x(0) = 1, y(0) = 0, (D(x))(0) = 0, (D(y))(0) = 0

dsol := dsolve({de1,de2,eq,ic}, numeric, output=operator);