Dr. Banana's profile - activity

I'm trying to do this: (sqrt(10*y*(10-y))+sqrt(1000)*acos(sqrt(y/10))-15*sqrt(2*6.673*10^(-11)*50000000000)).roots( ring=RealField(100)) Unfortunately I get the error in the title. Also any other way of solving the above equation numerically would be appreciated. I was able to do it in maxima using find_root but was hoping for a better function (one that doesn't require specifying an interval). I couldn't use find_root in sage because it returns the error 'unable to simplify to float approximation' and ofcourse solve doesn't return explicit solutions.

Cannot evaluate symbolic expression to a numerical value I'm trying to do this: (sqrt(10*y*(10-y))+sqrt(1000)*acos(sqrt

So I tried solving this in wxmaxima: eq: 'diff(y, x, 2)=-G*M/y^2 sol2: ode2(eq, y, x) bc2(sol2, x=0, y=1000, x=pi*sqrt(

Maxima wants to know whether %k1 is positve or negative I tried to do this in sage: sage: de=-diff(y,x,2)-G*M/y^2 sage

I'm getting the same issue as well. Are you using arch linux by any chance?

@slelievre I compiled sagemath using march=native -O3 -fno-plt and unfortunatlely I have to say that sage is now slower (I think). The thing you have to know is, sagemath speeds up if I use schedutil as my scaling governor. Unfortunately I can't remember whether I was using schedutil or powersave when I was testing the binary version (probably powersave though). So I downloaded the binary version again (turns out out you can have both installed side-by-side)(it's kind of creepy that the binary version remembers my previous inputs). Here are results from old the binary version:

Running benchmark 0 Benchmark 0:
   Factor the following polynomial over
       the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1) Time: 0.2822810000000002 seconds
   Running benchmark 1 Find the
   Mordell-Weil group of the elliptic
   curve 5077A using mwrank Time:
   0.4469660000000002 seconds Running benchmark 2 Some basic arithmetic
   with very large Integer numbers:
   '3^1000001 * 19^100001 Time:
   0.01994899999999955 seconds Running benchmark 3 Some basic arithmetic
   with very large Rational numbers:
   '(2/3)^100001 * (17/19)^100001 Time:
   0.028340999999999728 seconds Running benchmark 4 Rational polynomial
   arithmetic using Sage. Compute
   (x^29+17*x-5)^200. Time:
   0.009201000000000015 seconds Running benchmark 5 Rational polynomial
   arithmetic using Sage. Compute (x^19
   - 18*x + 1)^50 one hundred times. Time: 0.10662800000000017 seconds
   Running benchmark 6 Compute the
   p-division polynomials of y^2 = x^3 +
   37*x - 997 for primes p < 40. Time:
   0.05905899999999997 seconds Running benchmark 7 Compute the Mordell-Weil
   group of y^2 = x^3 + 37*x - 997.
   Time: 0.37592800000000004 seconds
   Running benchmark 8 %time
   sum(1/(x^2), x,1,100000) CPU times:
   user 1min 11s, sys: 1.14 s, total:
   1min 12s

Wall time: 27.9 s

Here are results from the new binary version (powersave):

Running benchmark 0
Benchmark 0: Factor the following polynomial over
    the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: 0.2790720000000002 seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: 0.4314460000000002 seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: 0.019366999999999912 seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: 0.028370000000000672 seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: 0.008942000000000228 seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: 0.106522 seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: 0.05832100000000029 seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: 0.3272319999999995 seconds
Running benchmark 8

From compiled version (powersave):

Running benchmark 0
Benchmark 0: Factor the following polynomial over
    the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: 0.3547199999999995 seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: 0.43139200000000066 seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: 0.019306000000000267 seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: 0.028086999999999307 seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: 0.008855999999999753 seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: 0.10795900000000103 seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: 4.499999999918458e-05 seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: 2.1000000000270802e-05 seconds
Running benchmark 8

What's interesting is that the compiled version is slower in benchmark 0. Could this be due to a missing dependency or something? Also the compiled version is faster at benchmarks 7 and 8. Now for my own test: the time it takes to compute sum(1/(x^2), x,1,100000):

Binary version (powersave):
CPU times: user 1min 11s, sys: 1.1 s, total: 1min 12s
Wall time: 27.4 s

Compiled version (powersave):
CPU times: user 1min 23s, sys: 1.3 s, total: 1min 25s
Wall time: 28.5 s

So the compiled version is slower in this regard.

Binary version (schedutil):
Running benchmark 0
Benchmark 0: Factor the following polynomial over
    the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: 0.14427600000000007 seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: 0.1471680000000002 seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: 0.0064669999999997785 seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: 0.009400999999999993 seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: 0.00301399999999985 seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: 0.03593299999999999 seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: 3.0999999999892225e-05 seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: 1.2999999999596668e-05 seconds
Running benchmark 8

Compiled version (schedutil):

Running benchmark 0
Benchmark 0: Factor the following polynomial over
    the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: 0.17197400000000007 seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: 0.14492799999999972 seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: 0.006648000000000209 seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: 0.009484000000000048 seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: 0.0030330000000002855 seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: 0.0348070000000007 seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: 5.2999999999858716e-05 seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: 1.1999999999900979e-05 seconds
Running benchmark 8

My own tests:

Binary version (schedutil):
CPU times: user 40.2 s, sys: 547 ms, total: 40.8 s
Wall time: 12.1 s

Compiled version (schedutil):
CPU times: user 46.3 s, sys: 621 ms, total: 46.9 s
Wall time: 12.6 s

P.S. I didn't delete the .sage directory before compiling.

Basically the thing that annoys me about sage is the slow start-up time. It takes about 13 seconds to get to the prompt. Now, I had compiled sage before, but I mistakenly did that with the -march=generic flag. Now, if I compile it with the -march=native (znver1 in my case) and -03 flags, will it start up faster? Has anybody else compiled it with -03? Any other flags I should be aware of?

Thank you very much.

I know that if I press the up arrow key, I can cycle through the previous inputs. Is there a similar hotkey/shortcut for cycling through the previous outputs?