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https://github.com/dcasella/multivariate-polynomials
Multivariate polynomials manipulation libraries for Lisp and Prolog
https://github.com/dcasella/multivariate-polynomials
common-lisp multivariate-polynomials prolog
Last synced: about 2 months ago
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Multivariate polynomials manipulation libraries for Lisp and Prolog
- Host: GitHub
- URL: https://github.com/dcasella/multivariate-polynomials
- Owner: dcasella
- License: gpl-3.0
- Created: 2016-11-15T09:05:28.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2017-02-14T13:58:59.000Z (almost 8 years ago)
- Last Synced: 2024-12-07T09:44:13.333Z (about 2 months ago)
- Topics: common-lisp, multivariate-polynomials, prolog
- Language: Common Lisp
- Homepage:
- Size: 20.5 KB
- Stars: 0
- Watchers: 4
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Multivariate Polynomials
> Translated and adapted from MV-201701 PDF written by Marco Antoniotti and Gabriella Pasi.
One of the first and most important computer applications was the _symbolic_ manipulation of mathematical operations. In particular, known systems like _Computer Algebra Systems_ preoccupy to offer _multivariate polynomials_ manipulation functionalities.
The Project consists in Common Lisp and Prolog libraries implementing multivariate polynomials manipulation.
## List of contents
- [Representation](#representation)
- [Interface](#interface)
- [Examples](#examples)
## Representation
### Common Lisp
Expression:
```
Variable X → 'x
Monomial XY^3 → '(* x (expt y 3))
Monomial 5XW → '(* 5 x w)
Polynomial XY^3 + 5XW → '(+ (* x (expt y 3)) (* 5 x w))
```
VarPower: (__V__ _Power_ _Variable_)
```lisp
; X^5
(V 5 X)
```
Monomial: (__M__ _Coefficient_ _TotalDegree_ _VarPowers_)
```lisp
; 2*X^4*Y
(M 2 5 ((V 4 X) (V 1 Y)))
```
Polynomial: (__P__ _Monomials_)
```lisp
; 4*X*Y + 2*Y*Z
(P ((M 4 2 ((V 1 X) (V 1 Y))) (M 2 2 ((V 1 Y) (V 1 Z)))))
```
### Prolog
Expression:
```
Variable X → x
Monomial XY^3 → x * y^3
Monomial 5XW → 5 * x * w
Polynomial XY^3 + 5XW → x * y^3 + 5 * x * w
```
VarPower: __v__(_Power_, _Variable_)
```prolog
% X^5
v(5, x)
```
Monomial: __m__(_Coefficient_, _TotalDegree_, _VarPowers_)
```prolog
% 2*X^4*Y
m(2, 5, [v(4, x), v(1, y)])
```
Polynomial: __poly__(_Monomials_)
```prolog
% 4*X*Y + 2*Y*Z
poly(m(4, 2, [v(1, x), v(1, y)]), m(2, 2, [v(1, y), v(1, z)]))
```
## Interface
### Common Lisp
(__coefficients__ _Poly_) → _Coefficients_
(__variables__ _Poly_) → _Variables_
(__monomials__ _Poly_) → _Monomials_
(__maxdegree__ _Poly_) → _Degree_
(__mindegree__ _Poly_) → _Degree_
(__polyplus__ _Poly1_ _Poly2_) → _Result_
(__polyminus__ _Poly1_ _Poly2_) → _Result_
(__polytimes__ _Poly1_ _Poly2_) → _Result_
(__as_monomial__ _Expression_) → _Monomial_
(__as_polynomial__ _Expression_) → _Monomial_
(__polyval__ _Polynomial_ _VariableValues_) → _Value_
(__pprint_polynomial__ _Polynomial_) → _NIL_
### Prolog
__coefficients__(_+Poly_, _-Coefficients_)
__variables__(_+Poly_, _-Variables_)
__monomials__(_+Poly_, _-Monomials_)
__maxdegree__(_+Poly_, _-Degree_)
__mindegree__(_+Poly_, _-Degree_)
__polyplus__(_+Poly1_, _+Poly2_, _-Result_)
__polyminus__(_+Poly1_, _+Poly2_, _-Result_)
__polytimes__(_+Poly1_, _+Poly2_, _-Result_)
__as_monomial__(_+Expression_, _-Monomial_)
__as_polynomial__(_+Expression_, _-Monomial_)
__polyval__(_+Polynomial_, _+VariableValues_, _-Value_)
__pprint_polynomial__(_+Polynomial_)
## Examples
### Common Lisp
```lisp
CL-USER> (as-monomial '(* 3 y w (expt u 3)))
(M 3 5 ((V 3 U) (V 1 W) (V 1 Y)))
CL-USER> (setf qd (as-monomial 42))
(M 42 0 NIL)
CL-USER> (setf m1 (as-monomial '(* y (expt s 3) (expt u 3))))
(M 1 7 ((V 3 S) (V 3 U) (V 1 Y)))
CL-USER> (setf p1 (as-polynomial '(+ (* -1 x) (* x y))))
(P ((M -1 1 ((V 1 X))) (M 1 2 ((V 1 X) (V 1 Y)))))
CL-USER> (setf p2 (as-polynomial '(+ (* y (expt s 3) (expt u 3)) -4 (* x y))))
(P ((M -4 0 NIL)
(M 1 2 ((V 1 X) (V 1 Y)))
(M 1 7 ((V 3 S) (V 3 U) (V 1 Y)))))
CL-USER> (polytimes m1 p1)
(P ((M -1 8 ((V 3 S) (V 3 U) (V 1 X) (V 1 Y)))
(M 1 9 ((V 3 S) (V 3 U) (V 1 X) (V 2 Y)))))
CL-USER> (pprint-polynomial *)
-1 * S^3 * U^3 * X * Y + S^3 * U^3 * X * Y^2
NIL
```
### Prolog
```prolog
?- as_monomial(3 * y * w * u^3, M).
M = m(3, 5, [v(3, u), v(1, w), v(1, y)]).
?- as_monomial(42, QD).
QD = m(42, 0, []).
?- as_polynomial(-1 * x + x * y, P1), variables(P1, Vs).
P1 = poly([m(-1, 1, [v(1, x)]), m(1, 2, [v(1, x), v(1, y)])]),
Vs = [x, y].
?- as_monomial(y * s^3 * u^3, M1),
| as_polynomial(-1 * x + x * y, P1),
| polytimes(M1, P1, R),
| pprint_polynomial(R).
-1 * S^3 * U^3 * X * Y + S^3 * U^3 * X * Y^2
M1 = m(1, 7, [v(3, s), v(3, u), v(1, y)]),
P1 = poly([m(-1, 1, [v(1, x)]), m(1, 2, [v(1, x), v(1, y)])]),
R = poly([m(-1, 8, [v(3, s), v(3, u), v(1, x), v(1, y)]),
m(1, 9, [v(3, s), v(3, u), v(1, x), v(2, y)])]).
```