Kitonum

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11 years, 269 days

MaplePrimes Activity


These are replies submitted by Kitonum

You need to formulate your question more clearly. For example, I did not understand:

1. What partitions are we talking about, into 2 summands or to any number of summands starting from two?
2. Should all terms in the partition be prime numbers?
3. What is Q(n)  and  {phi}  means?
4. What is the specific feature of the numbers 63 and 161?

@Abdoulaye  I won’t be able to help you until you figure out what each line of your code does (after that, help is no longer needed). If you do not want to understand this, then you can just use my code.

@findoc  This is not difficult. We simply project this solution (the red dot) on the coordinate axes with black dashed lines:

restart; with(plots):
sys := [p+x+.6*y-15, p+.3*x+.2*y-10, p+.5*x+y-14]:
sol:=solve(sys, [x, y, p])[];
A:=implicitplot3d(sys, x = 0 .. 10, y = 0 .. 10, p = 0 .. 10, style=surface, color=["LightBlue","LightGreen","Yellow"]):
B:=pointplot3d(eval([x,y,p],sol), color=red, symbol=solidsphere, symbolsize=15):
C:=plottools:-line(eval([x,y,p],sol),eval([x,0,0],sol),color=black,linestyle=3),plottools:-line(eval([x,y,p],sol),eval([0,y,0],sol),color=black,linestyle=3),plottools:-line(eval([x,y,p],sol),eval([0,0,p],sol),color=black,linestyle=dash):
display(A,B,C, axes=normal, orientation=[-20,80], lightmodel=light4);

                    

 

@mathkid99  Compare the last lines of my and your codes.

@Carl Love  Here is it:


 

restart

Digits := 10

with(plots)

with(CurveFitting)

with(plottools)

v := .7

Disp := 15

esp := 800000

k := 0

"E(x,t):=(∫)[0.0]^(infinity)1/(Pi)*(e)^((-esp*w^(4)+Disp*w^(2)+k)*t)*cos(w*(x+v*t)) ⅆw;"

proc (x, t) options operator, arrow, function_assign; int(exp((-esp*w^4+Disp*w^2+k)*t)*cos(w*(x+v*t))/Pi, w = 0. .. infinity) end proc

(1)

E(4000, 3600)

0.6340566551e-11

(2)

simplify(int(exp(-2880000000*w^4+54000*w^2)*cos(6520.0*w)/Pi, w = 0 .. infinity))

0.6340566551e-11

(3)

"f(x):=20*(e)^((-(x-10000)^(2))/(900000))+17*(e)^((-(x-12000)^(2))/(900000));"

proc (x) options operator, arrow, function_assign; 20*exp(-(1/900000)*(x-10000)^2)+17*exp(-(1/900000)*(x-12000)^2) end proc

(4)

plot(f(x), x = 0 .. 15000)

 

"u(x,t):=(∫)[0.0]^(15000)E(x-xi,t)*f(xi) ⅆxi;"

proc (x, t) options operator, arrow, function_assign; int(E(x-xi, t)*f(xi), xi = 0. .. 15000) end proc

(5)

u(12000, 7200)

-0.3891737055e-4

(6)

 

uu3600 := [seq(evalf(Int(E(i-xi, 3600)*f(xi), xi = 0 .. 15000, method = _NCrule, epsilon = 10^(-6))), i = 0 .. 15000, 100)]

[0.2640356212e-11, -0.1108781091e-12, -0.7053844499e-11, -0.1845238658e-10, -0.2870430935e-10, -0.2617757157e-10, 0.7489924448e-11, 0.8790949552e-10, 0.2087928058e-9, 0.3175706731e-9, 0.2925221097e-9, -0.2377850126e-10, -0.8340262606e-9, -0.2138294067e-8, -0.3514379232e-8, -0.3842895093e-8, -0.1252502369e-8, 0.6399275952e-8, 0.2012993073e-7, 0.3739977407e-7, 0.4910848252e-7, 0.3756975089e-7, -0.2170706349e-7, -0.1507077743e-6, -0.3489642690e-6, -0.5633570802e-6, -0.6555864928e-6, -0.3866033993e-6, 0.5502192383e-6, 0.2408268739e-5, 0.5148853923e-5, 0.8090576068e-5, 0.9527324272e-5, 0.6506086936e-5, -0.4918507300e-5, -0.2854609446e-4, -0.6563041430e-4, -0.1110888323e-3, -0.1487618170e-3, -0.1470895260e-3, -0.5777758241e-4, 0.1787589043e-3, 0.6166460360e-3, 0.1272412695e-2, 0.2075813396e-2, 0.2807102507e-2, 0.3032413409e-2, 0.2059661179e-2, -0.1050714518e-2, -0.7375478845e-2, -0.1786898766e-1, -0.3290878463e-1, -0.5161872477e-1, -0.7097541378e-1, -0.8475238668e-1, -0.8241585329e-1, -0.4814719802e-1, 0.3978168660e-1, .2090284137, .4923570097, .9257957277, 1.545713917, 2.384914613, 3.468023826, 4.806640403, 6.394857461, 8.205844853, 10.19016427, 12.27636194, 14.37415129, 16.38018293, 18.18604743, 19.68780939, 20.79609737, 21.44561031, 21.60287926, 21.27131250, 20.49266974, 19.34480434, 17.93561989, 16.39384319, 14.85751293, 13.46136107, 12.32439040, 11.53892853, 11.16227374, 11.21176417, 11.66373477, 12.45641909, 13.49644426, 14.66820628, 15.84512788, 16.90162688, 17.72457375, 18.22310020, 18.33582702, 18.03488582, 17.32648110, 16.24813056, 14.86308414, 13.25271127, 11.50782401, 9.719953626, 7.973516226, 6.339610604, 4.871920246, 3.604886928, 2.554030637, 1.718050170, 1.082178567, .6222005689, .3085617532, .1100942493, -0.2974156545e-2, -0.5690106712e-1, -0.7322384974e-1, -0.6836984356e-1, -0.5390561325e-1, -0.3721314207e-1, -0.2238439684e-1, -0.1115784729e-1, -0.3768833161e-2, 0.3617636955e-3, 0.2128724701e-2, 0.2425505772e-2, 0.1978153353e-2, 0.1289130816e-2, 0.6500209620e-3, 0.1885613416e-3, -0.7502365004e-4, -0.1776643672e-3, -0.1761267512e-3, -0.1239650374e-3, -0.6058189967e-4, -0.8824571996e-5, 0.2249289342e-4, 0.3404886445e-4, 0.3140587539e-4, 0.2138548593e-4, 0.9785502919e-5, 0.3533349704e-6, -0.5298950692e-5, -0.7218870018e-5, -0.6421118778e-5, -0.4231541408e-5, -0.1812895008e-5, 0.8028203365e-7, 0.1143237346e-5, 0.1425599206e-5, 0.1176212534e-5, 0.6930209081e-6]

(7)

uu7200 := [seq(evalf(Int(E(i-xi, 7200)*f(xi), xi = 0 .. 15000, method = _NCrule, epsilon = 10^(-6))), i = 0 .. 15000, 100)]

[-0.3744761506e-4, -0.3061074528e-4, -0.3562880683e-5, 0.5006874616e-4, 0.1310578434e-3, 0.2295286556e-3, 0.3201067843e-3, 0.3591667999e-3, 0.2866925165e-3, 0.3568747084e-4, -0.4488957762e-3, -0.1180927552e-2, -0.2096924939e-2, -0.3018643472e-2, -0.3626502642e-2, -0.3458659544e-2, -0.1940904845e-2, 0.1448545513e-2, 0.7137440632e-2, 0.1510046225e-1, 0.2401933137e-1, 0.3416115891e-1, 0.4087395636e-1, 0.4087043945e-1, 0.2927498296e-1, 0.9176113397e-3, -0.4882730067e-1, -.1225800173, -.2194075941, -.3327871975, -.4489698555, -.5450026823, -.5906084275, -.5445719781, -.3593723328, 0.1631881006e-1, .6330252755, 1.534757895, 2.752717835, 4.299101067, 6.161815855, 8.300941320, 10.64766161, 13.10617285, 15.55883081, 17.87419739, 19.91769061, 21.56351781, 22.70701433, 23.27580964, 23.23866895, 22.61057017, 21.45382420, 19.87409155, 18.01225305, 16.03239803, 14.10722537, 12.40228814, 11.06078974, 10.19023873, 9.852791823, 10.05982806, 10.77155435, 11.90154391, 13.32568257, 14.89452241, 16.44774962, 17.82919128, 18.90085972, 19.55464969, 19.72061422, 19.37115674, 18.52093699, 17.22281745, 15.56043307, 13.63850038, 11.57198094, 9.475334792, 7.452892932, 5.591400255, 3.954975910, 2.582959941, 1.490404379, .6707710951, .1002638273, -.2569308622, -.4432198526, -.5025497265, -.4762932676, -.4002463468, -.3028863191, -.2047938365, -.1190304482, -0.5222094186e-1, -0.6002797153e-2, 0.2139091196e-1, 0.3366004535e-1, 0.3521900087e-1, 0.3042084172e-1, 0.2244061650e-1, 0.1416874748e-1, 0.7057084217e-2, 0.1832480832e-2, -0.1401550340e-2, -0.2929069817e-2, -0.3214955945e-2, -0.2750432488e-2, -0.1954142835e-2, -0.1126737943e-2, -0.4447881405e-3, 0.2003006214e-4, 0.2700184373e-3, 0.3495690200e-3, 0.3181632039e-3, 0.2304723176e-3, 0.1339755847e-3, 0.5057270261e-4, -0.6508707749e-5, -0.3642982039e-4, -0.4462581427e-4, -0.3891813673e-4, -0.2676824271e-4, -0.1380329599e-4, -0.3359736758e-5, 0.3177658512e-5, 0.6182000430e-5, 0.6347503913e-5, 0.4916801140e-5, 0.2923262792e-5, 0.1105412852e-5, -0.1999773458e-6, -0.9040799916e-6, -0.1069658891e-5, -0.8990385008e-6, -0.5767712304e-6, -0.2460973866e-6, 0.5954590335e-8, 0.1484706340e-6, -0.4802506075e-5, 0.1652700506e-6, 0.1061920495e-6, 0.4460780963e-7, -0.2788334338e-8, -0.2897193877e-7, -0.3586378526e-7, -0.2952752366e-7, -0.1775696420e-7, -0.6092069243e-8, 0.2218359030e-8, 0.6252525670e-8, 0.6698874782e-8]

(8)

xx := [seq(i, i = 0 .. 15000, 100)]

p1 := plot(f(x), x = 0 .. 15000, color = blue, legend = [''t = 0''])

p2 := plot(xx, uu3600, color = red, legend = [''t = 3600''])

p3 := plot(xx, uu7200, color = blue, legend = [''t = 0''])

plots[display]({p1, p2, p3})

 

 

NULL


 

Download permanouuuuuuuuuuuuuuuuuun_new.mw

@JAMET  To get the curve equation from equations  and  t1  in the form  F(x,y)=0  you just need to eliminate the parameter  m   from these equations:

restart;  
t := y-m*x-p/(2*m) = 0; 
t1 := y+x/m+(1/2)*p1*m = 0; 
Sol:=eliminate({t,t1}, m);
Eq:=op(Sol[2])=0;
plots:-implicitplot(eval(Eq,[p=1,p1=-2]), x=-2..2,y=-2..2,color=red, scaling=constrained, size=[200,600]); 

     

 

@vv  I don’t understand where the discontinuous points come from? The integrand is obviously continuous. Isn't its antiderivative function to be continuous?

For example, if we plot  F , we see a continuous curve:

F:=Int(sqrt(1+((k*Pi)/l*cos((Pi*x)/l))^2), x=0..X):
plot(eval(F,[k=2,l=2]), X=0..6);

                  

 

 

@Mariusz Iwaniuk  Of course you're right. The integrand  sqrt(1 + k^2*Pi^2*cos(Pi*x/l)^2/l^2)  in the original integral is positive, therefore the definite integral  (if  b>a) is also positive. Maple seems to find this primitive function  F1 =  -csgn(sin(Pi*x/l))*Elliptic E(cos(Pi*x/l), I*k*Pi/l)*l/Pi  incorrectly.

@Carl Love  for this info. I fixed the procedure  P  code with this in mind.

@ActiveUser  Present here in text form code that does not work in Maple 12 (so that I can test it). The upper value for the variable  n  in the procedure  P  is not indicated , because it is unknown in advance and can be large enough if the numbers  a  and  b  are close.

PS. I slightly modified the procedure  P  code. Check again how it works.

@Stretto   I did not study all these options in detail, but I just offered you another way in which you first find all these points, and then consciously delete them. Of course, you yourself must choose the approach that you like best.

As for me, I always try to choose an approach where I clearly understand what is happening and it is easy for me to manage what is happening.

@Carl Love  Your code does not work in Maple 2018.2 and in older versions, at least since Maple 2015.

@Carl Love  Have you checked if this works?

restart;
r:= t->[t, t^2, t^3];
a:=1;
D(r)(a)*~(t-a)+~r(a);

 

@ActiveUser  If I understand correctly, then you can just take the arithmetic mean of any neighboring numbers.
For your example:
 

restart; 
sourcesamples :=[evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
n:=nops(sourcesamples);
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));

      

 

@ActiveUser  I am not familiar with all this issue.

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