Product Perfect

PARI/GP is a computer algebra system with the main aim of facilitating number theory computations. Developed by Henri Cohen and his co-workers at Université Bordeaux I, France, it was first released in 1985. The software is written in C and comes with its own scripting language, GP. It is free software distributed under the GNU General Public License and is widely used by research mathematicians. Its development has been supported by the French National Institute for Computer Science and Automation (INRIA) since 2010.

Ask the right questions secure the right PARI/GP talent among an increasingly shrinking pool of talent.

First 20 minutes

General PARI/GP app knowledge and experience

The first 20 minutes of the interview should seek to understand the candidate's general background in PARI/GP application development, including their experience with various programming languages, databases, and their approach to designing scalable and maintainable systems.

How would you install PARI/GP on a Linux system?

First, you would download the source code from the PARI/GP website. Then, you would extract the files, navigate to the directory, and run './Configure' and 'make all' commands. Finally, run 'make install' to finalize the installation.

What are some of the functions provided by PARI/GP for number theory computations?

PARI/GP provides many functions for number theory computations, including prime number functions, functions for factorization, functions for handling modular forms, and functions for elliptic curves.

How would you use PARI/GP to compute the factorial of a number?

You can use the 'factorial' function in PARI/GP. For example, to compute the factorial of 5, you would enter 'factorial(5)' at the prompt.

What is the purpose of the 'ellinit' function in PARI/GP?

'ellinit' is used to initialize an elliptic curve. It takes as input the coefficients of the elliptic curve and returns an object representing the curve, which can then be used in further computations.

How would you define a function in PARI/GP?

Functions in PARI/GP are defined using the 'fun' keyword, followed by the function name, arguments in parentheses, and the function body enclosed in braces. For example, 'fun square(x) = { return x^2; }'.

The hiring guide has been successfully sent to your email address.

Oops! Something went wrong while submitting the form.

What you’re looking for early on

Does the candidate have a strong understanding of PARI/GP?

Has the candidate demonstrated problem-solving skills?

Is the candidate familiar with number theory and algebra?

Can the candidate work well in a team?

Next 20 minutes

Specific PARI/GP development questions

The next 20 minutes of the interview should focus on the candidate's expertise with specific backend frameworks, their understanding of RESTful APIs, and their experience in handling data storage and retrieval efficiently.

Describe the difference between the 'factorint' and 'factor' functions in PARI/GP.

Both 'factorint' and 'factor' functions perform factorization, but 'factorint' is used for factoring integers, while 'factor' can be used for factoring polynomials as well as integers.

What are some ways to improve the performance of PARI/GP scripts?

Performance can be improved by using vector operations instead of loops where possible, preallocating memory for large data structures, and using the inline version of functions when the overhead of a function call is significant.

How would you use PARI/GP to compute the sum of the first n terms of a geometric series?

You can use the 'sum' function in combination with the 'for' loop. For example, to compute the sum of the first n terms of the series 2^n, you would enter 'sum(n=1, N, 2^n)'.

What is the purpose of the 'forprime' function in PARI/GP?

'forprime' is a loop construct that iterates over all prime numbers in a given range. The body of the loop is executed for each prime number.

Describe the difference between the 'if' and 'ifelse' functions in PARI/GP.

'if' and 'ifelse' both perform conditional execution, but 'ifelse' is an expression that returns a value, while 'if' is a statement that does not.

The hiring guide has been successfully sent to your email address.

Oops! Something went wrong while submitting the form.

At this point, a skilled PARI/GP engineer should demonstrate strong problem-solving abilities, proficiency in PARI/GP programming language, and knowledge of software development methodologies. Red flags include lack of hands-on experience, inability to articulate complex concepts, or unfamiliarity with standard coding practices.

Digging deeper

Code questions

These will help you see the candidate's real-world development capabilities with PARI/GP.

What does the following PARI/GP code do?
factor(2021)
This code gives the prime factorization of the number 2021.
What will be the output of the following PARI/GP code?
a = vector(5, i, i^2); a
This code will output the first five squares: [1, 4, 9, 16, 25].
What does the following PARI/GP code do?
a = vector(5, i, i^2); vecsort(a, ,4)
This code creates a vector of the first five squares and then sorts this vector in ascending order based on the 4th entry.
What will be the output of the following PARI/GP code?
install(numtoperm, GG); numtoperm(5,3)
This code will output the 3rd permutation of 5 elements, which is [1,3,2,4,5].

Wrap-up questions

Final candidate for PARI/GP Developer role questions

The final few questions should evaluate the candidate's teamwork, communication, and problem-solving skills. Additionally, assess their knowledge of microservices architecture, serverless computing, and how they handle PARI/GP application deployments. Inquire about their experience in handling system failures and their approach to debugging and troubleshooting.

How would you use PARI/GP to compute the greatest common divisor of two numbers?

You can use the 'gcd' function in PARI/GP. For example, to compute the greatest common divisor of 12 and 18, you would enter 'gcd(12, 18)'.

What are the benefits of using PARI/GP for mathematical computation over other software?

PARI/GP has a number of benefits over other software, including its speed, its wide range of built-in functions for number theory, and the flexibility of its scripting language.

How would you implement the Sieve of Eratosthenes in PARI/GP?

You would create a list of numbers from 2 to the desired limit, then repeatedly remove multiples of the smallest remaining number, until no numbers are left. This can be implemented with a combination of 'for' loops and array operations.

PARI/GP application related

Product Perfect's PARI/GP development capabilities

Beyond hiring for your PARI/GP engineering team, you may be in the market for additional help. Product Perfect provides seasoned expertise in PARI/GP projects, and can engage in multiple capacities.

PARI/GP Consultive assessments

PARI/GP Application Conversion Assessment PARI/GP Application Integration Assessment PARI/GP Data & Database Integration Assessment

Custom PARI/GP development projects

Custom PARI/GP App Conversion PARI/GP Custom App Development Process App UI Design for PARI/GP Facelifts

Hiring guide for PARI/GP Engineers

PARI/GP Developer Hiring Guide

What you’re looking for early on

The ideal back-end app developer

What you’re looking to see on the PARI/GP engineer at this point.

PARI/GP Consultive assessments

Custom PARI/GP development projects