[Math] Tool to draw graphs when input points are given

graphing-functionsmath-software

I am writing a dissertation and I have a two collections of data from my research which I would like to compare using graphs. I have the values for abscissa and ordinate and I am looking for some sort of tool into which I can input the values I have and which will plot and trace the graph so I can show the variations in both samples. Just something simple nothing very complicated.

I have been searching the Internet for something like this for hours and I can't seem to find one. What I have found so far are tools which take a function before drawing the graph, but what I need is something which can take the values directly in order to draw the graph connecting them. I don't know whether my search terms are not accurate enough to describe what I need so I hope someone here may be able to help me out.

Please, does anyone know a simple tool which I can use to achieve this? (Windows or – eventually – Linux would be highly appreciated)

Best Answer

One option is gnuplot, which handles a lot of graph formats.

More flexible in format (and easier to integrate with LaTeX) is asymptote, but then you have to use a library, and defining the graph is more work.

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[Math] ny maths software to help determine the formulas of given curves

It sounds like you're talking about drawing Bézier patches. Lots of programs let you draw these (e.g. essentially every graphic design program) and all of them would have an internal representation of the equation, although I'm not sure how to get most of them to tell it to you. But that should tell you what to Google.

I found this thing online:

http://cs.jsu.edu/~leathrum/gwtmathlets/mathlets.php?name=bezier

See the "notes" tab.

PHI function to list relative primes

This is an easily solved problem, and doesn't require any sort of advanced tools. As Peter said, Euler's Totient is only for computing the number of coprimes for a given n. To actually calculate them, I guarantee that website is doing exactly what Peter suggested: checking the GCD of each possibility. That shouldn't take very long.

Here's a complete Python program to do that, for numbers passed as arguments to the script. (i.e. you'd call it like python3 coprimes.py 47 87 to list the coprimes for, separately, 47 and 87). It'll list the results, and then give the quantity and time required to produce them, for each argument in turn.

It's quite fast. I tried it with the value 4636436, which has 1987032 coprimes. It took my Linux machine 8 seconds to compute and list them all. And honestly, the time spent printing them to the terminal takes up roughly half of that time.

#!/usr/bin/python3
import sys
import time
from pprint import pprint
from math import gcd

def coprimes(n):
    return list([x for x in range(1, n) if gcd(x, n) == 1])

def main(args):
    for n in args:
        t1 = time.monotonic()
        cp = coprimes(int(n))
        pprint(cp, compact=True)
        t2 = time.monotonic()
        print(f"Found {len(cp)} coprimes for {n} in {(t2 - t1):.6f} seconds")
        if n is not args[-1]:
            print("\n")

if __name__ == "__main__":
    main(sys.argv[1:])

The output:

$ python3 coprimes.py 47 87
[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]
Found 46 coprimes for 47 in 0.000209 seconds


[1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 31, 32,
 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 59, 61, 62, 64,
 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86]
Found 56 coprimes for 87 in 0.000224 seconds

Best Answer

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[Math] ny maths software to help determine the formulas of given curves

PHI function to list relative primes

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