Evaluate a PARI/GP expression string.

Get the PARI/GP version string.

Returns: String describing the PARI version.

Example: >>> get_pari_version() 'GP/PARI CALCULATOR Version 2.15...'

Set the PARI default real precision in decimal digits.

Get the current PARI default real precision in decimal digits.

Returns: Current precision in decimal digits.

Example: >>> get_real_precision() 15

Set the PARI default real precision in bits.

Get the current PARI default real precision in bits.

Returns: Current precision in bits.

Example: >>> get_real_precision_bits() 53

Change the PARI stack size.

Get the current PARI stack size in bytes.

Returns: Current stack size.

Example: >>> stacksize() 8000000

Get the maximum PARI stack size in bytes.

Returns: Maximum stack size.

Example: >>> stacksizemax() 536870912

Set PARI's random number seed.

Get PARI's current random number seed.

Returns: The current random seed.

Example: >>> getrand() [1, 2, 3, ...]

Return prime numbers.

Return the nth prime (1-indexed).

Factor an integer.

Test if an integer is prime.

Compute the greatest common divisor of two integers.

Compute the least common multiple of two integers.

Compute the Bezout identity: gcd(a,b) = au + bv.

Compute Euler's totient function phi(n).

Compute the sum of k-th powers of divisors of n.

Compute the Möbius function mu(n).

Compute the Jacobi symbol (a/n).

Compute the Legendre symbol (a/p).

Compute the multiplicative order of x modulo n.

Compute the structure of (Z/nZ)*.

Compute the factorial n!.

Compute the binomial coefficient C(n,k).

Compute the nth Fibonacci number.

Compute the nth Lucas number.

Compute the nth cyclotomic polynomial.

Compute the nth Chebyshev polynomial of the first kind.

Compute the nth Legendre polynomial.

Compute the nth Hermite polynomial (probabilists' version).

Compute the complex roots of a polynomial.

Compute the roots of a polynomial modulo p.

Compute the p-adic roots of a polynomial.

Factor a polynomial over the p-adic numbers.

Compute the derivative of a polynomial.

Compute the integral of a polynomial.

Compute the resultant of two polynomials.

Compute the discriminant of a polynomial.

Compute the norm of a polynomial/algebraic number.

Compute the trace of a polynomial/algebraic number.

Substitute a variable in a polynomial.

Create a modular number or polynomial.

Lift a modular object (remove Mod wrapper).

Lift a modular object with centered representatives.

Initialize a number field defined by a polynomial.

Initialize a number field with Buchmann's algorithm.

Initialize a ray number field (class field).

Add two ideals in a number field.

Multiply two ideals in a number field.

Compute a power of an ideal.

Factor an ideal in a number field.

Initialize an elliptic curve.

Add two points on an elliptic curve.

Multiply a point on an elliptic curve by an integer.

Compute the order of a point on an elliptic curve.

Compute the discrete logarithm of a point on an elliptic curve.

Compute the trace of Frobenius for an elliptic curve at prime p.

Compute the torsion subgroup of an elliptic curve.

Compute the global reduction type of an elliptic curve.

Compute the local reduction type at prime p.

Compute the canonical height of a point on an elliptic curve.

Compute the j-invariant of an elliptic curve.

Compute the eta-quotients for an elliptic curve.

Compute the Weierstrass p-function.

Compute the Weierstrass zeta function.

Create an n x n identity matrix.

Create a zero matrix.

Compute the determinant of a matrix.

Compute the inverse of a matrix.

Compute the rank of a matrix.

Compute the kernel of a matrix.

Compute the image of a matrix.

Compute the eigenvalues of a matrix.

Compute the characteristic polynomial of a matrix.

Compute the Hessenberg form of a matrix.

Create an empty list or convert to a list.

Convert to a row vector.

Convert to a column vector.

Convert to a matrix.

Convert to a set.

Convert to a polynomial.

Convert to a polynomial (reverse order).

Convert to a power series.

Get the value of pi.

Get Euler's constant.

Get Catalan's constant.

Create a complex number.

Get the imaginary unit.

Returns: The imaginary unit I = sqrt(-1).

Example: >>> I() I

Get the integer 1.

Returns: Integer 1.

Example: >>> one() 1

Get the integer 0.

Returns: Integer 0.

Example: >>> zero() 0

Compute absolute value.

Compute square root.

Compute exponential.

Compute natural logarithm.

Compute sine.

Compute cosine.

Compute tangent.