marlin

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8 years, 346 days

MaplePrimes Activity


These are questions asked by marlin

Here is a Maple 2020 worksheet that ran fine on Maple 2020, but runs slower on Maple 2022, especially when plots[display] is used it seems to take much longer?

with(NumberTheory);
with(plots);
NULL;
NULL;
theta := [14.134725, 21.022039, 25.010858, 30.424876, 32.935062, 37.586178, 40.918719, 43.327073, 48.00515, 49.773832, 52.970321, 56.446248, 59.347044, 60.831779, 65.112544, 67.079811, 69.546402, 72.067158, 75.704691, 77.144840, 79.337375, 82.91038, 84.735493, 87.425273, 88.809111, 92.491899, 94.651344, 95.870634, 98.831194];
theta := [14.134725, 21.022039, 25.010858, 30.424876, 32.935062, 

  37.586178, 40.918719, 43.327073, 48.00515, 49.773832, 

  52.970321, 56.446248, 59.347044, 60.831779, 65.112544, 

  67.079811, 69.546402, 72.067158, 75.704691, 77.144840, 

  79.337375, 82.91038, 84.735493, 87.425273, 88.809111, 

  92.491899, 94.651344, 95.870634, 98.831194]

y[1] := x -> -2*sqrt(x)*cos(theta[1]*ln(x) - argument(0.5 + theta[1]*I))/(abs(0.5 + theta[1]*I)*ln(x));
y[1] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[1\

  ]*ln(x)-argument(.5+I*theta[1]))/(abs(.5+I*theta[1])*ln(x)) 

   end proc

plot(y[1](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 14.134725*i');

y[2] := x -> -2*sqrt(x)*cos(theta[2]*ln(x) - argument(0.5 + theta[2]*I))/(abs(0.5 + theta[2]*I)*ln(x));
y[2] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[2\

  ]*ln(x)-argument(.5+I*theta[2]))/(abs(.5+I*theta[2])*ln(x)) 

   end proc

plot(y[2](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 21.022040*i');

y[3] := x -> -2*sqrt(x)*cos(theta[3]*ln(x) - argument(0.5 + theta[3]*I))/(abs(0.5 + theta[3]*I)*ln(x));
y[3] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[3\

  ]*ln(x)-argument(.5+I*theta[3]))/(abs(.5+I*theta[3])*ln(x)) 

   end proc

plot(y[3](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 25.00858*i');

y[4] := x -> -2*sqrt(x)*cos(theta[4]*ln(x) - argument(0.5 + theta[4]*I))/(abs(0.5 + theta[4]*I)*ln(x));
y[4] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[4\

  ]*ln(x)-argument(.5+I*theta[4]))/(abs(.5+I*theta[4])*ln(x)) 

   end proc

plot(y[4](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 30.424876*i');

y[5] := x -> -2*sqrt(x)*cos(theta[5]*ln(x) - argument(0.5 + theta[5]*I))/(abs(0.5 + theta[5]*I)*ln(x));
y[5] := proc (x) options operator, arrow; -2*sqrt(x)*cos(theta[5\

  ]*ln(x)-argument(.5+I*theta[5]))/(abs(.5+I*theta[5])*ln(x)) 

   end proc

plot(y[5](x), x = 20 .. 100, title = 'Fig1*(S &G theta) = 1/2 + 32.93502*i');

T[1] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[1]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[1] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[1])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[1](x), x = 20 .. 100, title = 'T[1]');

T[2] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[2]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[2] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[2])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[2](x), x = 20 .. 100, title = 'T[2]');

T[3] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[3]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[3] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[3])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[3](x), x = 20 .. 100, title = 'T[3]');

T[4] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[3]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[4] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[3])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[4](x), x = 20 .. 100, title = 'T[4]');

T[5] := x -> -2*sum(Moebius(n)*Re(Ei((0.5 + theta[5]*I)*ln(x)))/n, n = 1 .. trunc(ln(100)/ln(2)) + 1);
T[5] := proc (x) options operator, arrow; -2*(sum(NumberTheory:-\

  Moebius(n)*Re(Ei((.5+I*theta[5])*ln(x)))/n, n = 1 .. 

   trunc(ln(100)/ln(2))+1)) end proc

plot(T[5](x), x = 20 .. 100, title = 'T[5]');

f10 := x -> Li(x) - 2*sum(Re(Ei((1/2 + theta[n]*I)*ln(x))), n = 1 .. 10) - ln(2) + int(1/(t*(t^2 - 1)*ln(t)), t = x .. infinity);
f10 := proc (x) options operator, arrow; Li(x)-2*(sum(Re(Ei((1/2\

  +I*theta[n])*ln(x))), n = 1 .. 10))-ln(2)+int(1/(t*(t^2-1)*ln(\

  t)), t = x .. infinity) end proc

R10 := x -> sum(Moebius(l)*f10(x^(1/l))/l, l = 1 .. 8);
R10 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f10(x^(1/l))/l, l = 1 .. 8) end proc

plot1 := plot(R10(x), x = 2 .. 100);

plot2 := plot(pi(x), x = 2 .. 100);

display([plot1, plot2]);

f29 := x -> Li(x) - 2*sum(Re(Ei((1/2 + theta[n]*I)*ln(x))), n = 1 .. 29) - ln(2) + int(1/(t*(t^2 - 1)*ln(t)), t = x .. infinity);
f29 := proc (x) options operator, arrow; Li(x)-2*(sum(Re(Ei((1/2\

  +I*theta[n])*ln(x))), n = 1 .. 29))-ln(2)+int(1/(t*(t^2-1)*ln(\

  t)), t = x .. infinity) end proc

R29 := x -> sum(Moebius(l)*f29(x^(1/l))/l, l = 1 .. 8);
R29 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f29(x^(1/l))/l, l = 1 .. 8) end proc

plot3 := plot(R29(x), x = 2 .. 100);

NULL;
display([plot1, plot2, plot3]);

R29(100);
R10(100);
pi(100);
                          25.25165721

                          25.28503922

                               25

RR10 := x -> sum(Moebius(l)*f10(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR10 := proc (x) options operator, arrow; sum(NumberTheory:-Moeb\

  ius(l)*f10(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end 

   proc

RR10(1000);
pi(1000);
                          168.1328341

                              168

RR29 := x -> sum(Moebius(l)*f29(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR29 := proc (x) options operator, arrow; sum(NumberTheory:-Moeb\

  ius(l)*f29(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end 

   proc

RR29(1000);
                          167.6113955

P1 := plot(RR29(x), x = 880 .. 930);

P2 := plot(pi(x), x = 880 .. 930);

display([P1, P2]);

f0 := x -> Li(x) - ln(2) + int(1/(t*(t^2 + 1)*ln(t)), t = x .. infinity);
f0 := proc (x) options operator, arrow; Li(x)-ln(2)+int(1/(t*(t^\

  2+1)*ln(t)), t = x .. infinity) end proc

RR0 := x -> sum(Moebius(l)*f0(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2)) + 1);
RR0 := proc (x) options operator, arrow; sum(NumberTheory:-Moebi\

  us(l)*f0(x^(1/l))/l, l = 1 .. trunc(ln(1000)/ln(2))+1) end proc

P3 := plot(RR0(x), x = 880 .. 930);

NULL;
display([P1, P2, P3]);

P4 := plot(RR10(x), x = 880 .. 930);

display([P1, P2, P3, P4], color = [green, blue, purple, yellow]);

evalf(Li(2)), evalf(ln(2));
                   1.045163780, 0.6931471806

evalf(li(2));
                             li(2)

evalf(Ei(2));
                          4.954234356

evalf(Int(1/ln(t), t = 0 .. 2));
                        Float(undefined)

evalf(Ei(ln(2)));
                          1.045163780

Li(1000.);
                          177.6096580

isprime, [$ (1 .. 100)];
isprime, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 

  17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 

  33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 

  49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 

  65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 

  81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 

  97, 98, 99, 100]

nops(select(isprime, [$ (1 .. 100)]));
                               25

theta[1];
                           14.134725

evalf(Ei((1/2 + theta[1]*I)*ln(x)));
             Ei((0.5000000000 + 14.134725 I) ln(x))

evalf(Ei(ln(1/2 + theta[1]*I)));
                  4.386989035 + 6.632175089 I

plot(Li(x), x = 0 .. 5);

I have an ipad air 16G running ios 7.0.4 and downloaded the MaplePlayer APP.  t seems to crash on several of the routines for example, "Approximaing Sphere" and "Linear System Tutor". The app was last updated in 2011.  Do you have plans to any upgrades plan in the near future?

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