by Google AI

PARI/GP is a computer algebra system primarily used for number theory, and its code consists of commands and functions to perform calculations like factoring, elliptic curve operations, and linear algebra. Examples of PARI/GP code include initializing an elliptic curve with ellinit and plotting a function, finding a non-trivial linear combination of vectors using lindep, or performing arithmetic operations on integers and polynomials. You can run PARI/GP code in a web browser, on the command line, or through a Python extension. 

Examples of PARI/GP code

• Elliptic curve analysis:
  • E=ellinit("11a1"); L=lfuninit(E,[0,100]); ploth(x=0,100,lfunhardy(L,x))
• Finding linear dependencies:
  • lindep(v, {flag = 0}) is used to find a small, non-trivial integral linear combination between the components of a vector v.
• Modular arithmetic:
  • chinese(x, {y}) combines elements in the same residue class modulo different moduli, which can also be applied recursively to vectors and matrices, as shown in this PARI/GP arithmetic function documentation.
• Matrix operations:
  • K=matkerint(Mat(concat([vector(23,i,2*i+1),51,145]))); M=matdiagonal(vector(25,i,if(i==25,-1,1))); L24 = K~*M*K 

How to run PARI/GP code

• Online: You can use an online compiler to run PARI/GP code directly in your web browser, as demonstrated on TutorialsPoint.
• Command line: After installation, you can open a terminal and type gp to launch the calculator, as explained in this PARI/GP reference card.
• From Python: You can use a Python extension to call PARI/GP functions from your Python scripts, according to a Stack Overflow post.