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2016-11-04 09:12:14 -0500 | commented question | Speeding up power_mod @Mafra Thank you for your replies! I have tested and compared a few methods of computing modular powers. Apart from SageMath's power_mod, I have tried Python's pow, GMP's .powermod and SageMath's modular integer rings. The latter three have noticably outperformed power_mod, but all of them gave improvements of order of 30%, as opposed to 70% provided by Julia (tested using JuliaBox if that makes any difference) (to be precise: 63 seconds for power_mod, ~45s for other three, and 18.5s for Julia). By the way, do you think it makes any difference that I am using SageMathCloud as opposed to having it downloaded? I can't test right now because I don't have Sage on the machine I'm using now. |

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2016-10-28 15:00:30 -0500 | asked a question | Speeding up power_mod Recently I've been working a bit with modular arithmetic and big numbers. An incredibly useful tool for that is modular exponentiation by repeated squaring, implemented using power_mod function. Earlier I was using Julia for that (together with BigInt there), and I was quite disappointed to find out that in Sage modular exponentiation is noticably slower for (very) large moduli - slowdown by a factor of 3 modulo 10^5000 and by a factor of almost 10 modulo 10^50000 (I didn't test larger ones). I don't know if the reason for this is that Julia uses some faster modular exponentiation algorithm (I didn't manage to find how it is implemented), or whether it is because the BigInt makes it that significantly easier for CPU to work with these. So my question is, is there some way to speed up the modular exponentiation in Sage? |

2016-10-02 03:34:09 -0500 | commented answer | Plotting point when coordinate involves symbolic and numerical values Hello, sorry for a late reply, I was away from home. I am using SageMathCloud, and I'm not sure what version it's running (my guess is 7.3, latest stable). I also have version 7.2 downloaded on a Windows machine, but I didn't try running the code there, and I don't know where I could download beta versions. Anyways, using RDF fixed the problem, so I am willing to accept this answer. |

2016-09-25 13:21:03 -0500 | asked a question | Plotting point when coordinate involves symbolic and numerical values Consider the following single piece of code: When trying to compile it, I get the following error message: Is there some simple way to fix this? Interesting note: I have played around with this error, and it is very unclear to me when it does or doesn't appear. Here are some examples of when the error Here are some examples where it (edit: the error doesn't seem to ever occur if we give the zeta function a real argument) I'd be interested if someone figured out under what conditions the error appears or not, because I fail to see any pattern. Thank you in advance. |

2016-09-21 16:05:06 -0500 | commented answer | Errors when plotting zeta function parametrically Thank you very much! I am relatively new to both Python and Sage, so any help is appreciated. |

2016-09-21 16:04:54 -0500 | commented answer | Errors when plotting zeta function parametrically Thank you very much! I am relatively new to both Python and Sage, so any help is appreciated. By the way (although this isn't strictly relate to my overall question), do you know of a way to make the the plot non-monochromatic? I am thinking of making the hue of the line changing as |

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2016-09-21 10:04:03 -0500 | asked a question | Errors when plotting zeta function parametrically I have the following piece of code: It should be moderately clear what I'm trying to do - I want to produce a plot of Riemann zeta function on the line Re(z)=1 using parametric plotting. However, when I try to plot this, I get an error It's worth noting that trying to plot function f(x) I get the same error with Thanks in advance. |

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