apelloni / flint-mpoly-rs

multivariate polynomial for rust with FLINT backend

flint-mpoly-rs

multivariate polynomial for rust with FLINT backend

Coefficients

• QCoeff: Coefficients that take values in $\mathbb{Q}$ (from: fmpq.h)
• ZCoeff: Coefficients that take values in $\mathbb{Z}$ (from: fmpz.h)
• ModCoeff: Coefficients that take values in $\mathbb{Z}/p\mathbb{Z}$ (from: fmpz_mod.h)

Polynomials

Multivariate

• QMPoly: Multivariate Polynomials in $\mathbb{Q}[x_1,x_2,..]$ (from: fmpq_mpoly.h)
• ZMPoly: Multivariate Polynomials in $\mathbb{Z}[x_1,x_2,..]$ (from: fmpz_mpoly.h)
• ModMPoly: Multivariate Polynomials in $\mathbb{Z}/p\mathbb{Z}[x_1,x_2,..]$ (from: fmpz_mod_mpoly.h)

Univariate

• QPoly: Univariate Polynomials in $\mathbb{Q}[x]$ (from: fmpq_poly.h)
• ZPoly: Univariate Polynomials in $\mathbb{Z}[x]$ (from: fmpz_poly.h)
• ModPoly: Univariate Polynomials in $\mathbb{Z}/p\mathbb{Z}[x]$ (from: fmpz_mod_poly.h)

Rational Polynomials

Multivariate

• QMRat: Multivariate Rational in $\mathbb{Q}(x_1,x_2,..)$
• ZMRat: Multivariate Rational in $\mathbb{Z}(x_1,x_2,..)$
• ModMRat: Multivariate Rational in $\mathbb{Z}/p\mathbb{Z}(x_1,x_2,..)$

Univariate

• QRat: Univariate Rational in $\mathbb{Q}(x)$
• ZRat: Univariate Rational in $\mathbb{Z}(x)$
• ModRat: Univariate Rational in $\mathbb{Z}/p\mathbb{Z}(x)$

---

Examples

Parse an expression

 use flint_mpoly::QMRat;

 // Define variables
 let vars : Vec<String> = ["x1","x2"].iter().map(|x| x.to_string()).collect();

 // Parse expression from string
 let f = QMRat::from_str("(1+x1+x1^2)/(1-x1^3)*x2",&vars).unwrap();

 // The parsed result is already reduced to the canonical form
 assert_eq!("(-x2)/(+x1-1)",f.to_str());

Alternatively, one can also add each coefficient individually, for example when importing it from other structures. This is defined for polynomials where one can add coefficients to an existing function.

 use flint_mpoly::{QMPoly, QCoeff};
 use std::str::FromStr;

 // Define variables
 let vars : Vec<String> = ["x1","x2"].iter().map(|x| x.to_string()).collect();

 // Create QMPoly object
 let mut f = QMPoly::new(&vars);  // currently 0

 // Feed coefficients into MPoly using different methods
 f.add_coeff_pq(&[2,0],1,2);                            // add 1/2*x1^2
 f.add_coeff_str(&[1,1],"5");                           // add 5*x1*x2
 f.add_coeff(&[1,1],&QCoeff::from_str("3/2").unwrap()); // add 3/2*x1*x2

 // The result already has all coefficients collected together
 assert_eq!("+1/2*x1^2+13/2*x1*x2",f.to_str());