AEQ.h
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1 #ifndef QPOLY
2 #define QPOLY
3 
4 #include <misc/auxiliary.h>
5 #include "si_gmp.h"
6 
7 #ifdef SINGULAR_4_1
8 
9 class Q_poly // Klasse von Q_polynomen mit Typ (Grad, Koeffizienten ganzzahlig)
10 {
11 
12 public:
13  // Charakteristika der Q_polynome (TO DO??: Dynamisches Array)
14 
15  int deg; // Grad des Q_polynoms
16  mpz_t denom; // Hauptnenner der Koeffizienten
17  mpz_t coef[100]; // Feld der Koeffizienten
18  //mpz_t coef = reinterpret_cast<mpz_t*> (omAlloc(100*sizeof(mpz_t)));
19 
20 
21  // Konstruktoren und Destruktoren
22  Q_poly();
23  Q_poly( int ,mpz_t, mpz_t*);
24  //Q_poly(int_poly,int);
25  //~Q_poly();
26 
27  //Reduktion modulo p
28  void Q_poly_reduce();
29  void Q_poly_extend(mpz_t);
30 
31  // Arithmetische Operationen
32 
33 
34  // Additionen
35 
36  void Q_poly_add(const Q_poly , const Q_poly );
37  void Q_poly_add_to(const Q_poly);
38  void Q_poly_add_mon(const Q_poly,mpz_t, int); //addiert Monome zu Q_polynom
39  void Q_poly_add_mon_to(mpz_t,int);
40  void Q_poly_add_const( Q_poly, const mpz_t);
41  void Q_poly_add_const_to(const mpz_t);
42 
43  // Subtraktion
44 
45  void Q_poly_sub(const Q_poly , const Q_poly );
46  void Q_poly_sub_to(const Q_poly);
47  void Q_poly_sub_mon(const Q_poly,mpz_t,int);
48  void Q_poly_sub_mon_to(mpz_t,int);
49  void Q_poly_sub_const( Q_poly, const mpz_t);
50  void Q_poly_sub_const_to(const mpz_t);
51 
52  //Multiplikationen
53 
55  void Q_poly_mult_n_to(const Q_poly);
56  void Q_poly_mult_ka(const Q_poly, const Q_poly);
57  void Q_poly_scalar_mult(const mpz_t ,const Q_poly);
58  void Q_poly_scalar_mult(const Q_poly, const mpz_t);
59  void Q_poly_scalar_mult_to(const mpz_t);
60  void Q_poly_neg();
61  void Q_poly_mon_mult(const Q_poly, const int);
62  void Q_poly_mon_mult_to(const int);
63 
64  //Divisionen
65  void Q_poly_div(Q_poly&, Q_poly&,const Q_poly, const Q_poly); // exakte Division
66  void Q_poly_div_to(Q_poly&, Q_poly&,const Q_poly); // To Variante exakte Division
67  void Q_poly_scalar_div(const Q_poly, const mpz_t); // Dividiert Polynom durch ganze Zahl
68  void Q_poly_scalar_div_to(const mpz_t);
69  void Q_poly_div_rem(const Q_poly, const Q_poly); //Division mit Rest
70  void Q_poly_div_rem_to(const Q_poly);
71  void Q_poly_mon_div(const Q_poly, const int); //Division durch Monom
72  void Q_poly_mon_div_rem(const Q_poly, const int);
73 
74  //Kombinationen
75 
76  void Q_poly_multadd_to(const Q_poly, const Q_poly); //a=a*b+c
77  void Q_poly_multsub_to(const Q_poly,const Q_poly); //a=a*b-c
78  //Q_poly Q_poly_addmult_to(const Q_poly, const Q_poly);
79 
80 
81 
82 
83  // Sonstige Operationen
84  void Q_poly_set(const Q_poly);
85  void Q_poly_set(const mpz_t); // Setzt Q_polynom auf Konstante aus Z
86  void Q_poly_set(const mpz_t, const mpz_t); // Setzt Q_polynom auf Konstante aus Q
87  void Q_poly_set_zero(); // Setzt Q_polynom auf 0
88  void Q_poly_horner(mpz_t, const mpz_t); // Wertet Q_polynom mittels Horner-Schema an einer Stelle aus
89  void Q_poly_horner_Q_poly(Q_poly, const Q_poly); //Setzt Q_polynom in Q_polynom mittels Horner Schema ein
90  void Q_poly_gcd(Q_poly,Q_poly); //Standard GGT
91  void Q_poly_extgcd(Q_poly &,Q_poly &,Q_poly &, Q_poly, Q_poly); //Erweiterter Standard GGT
92  int is_equal(Q_poly &); // Test auf Gleichheit
93  int is_zero() const; // Test auf Gleichheit mit 0
94  int is_one() const; // Test auf Gleichheit mit 1
95  int is_monic() const; // testet, ob das Q_polynom normiert ist
96 
97  // Ein und Ausgabe
98  void Q_poly_insert(); // Eingabe von Q_polynom
99  void Q_poly_print(); //Ausgabe von Q_polynom
100 
101 
102 };
103 
104 #endif
105 #endif
106 
107 
void Q_poly_scalar_mult(const mpz_t, const Q_poly)
Definition: AEQ.cc:312
mpz_t denom
Definition: AEQ.h:16
void Q_poly_mult_ka(const Q_poly, const Q_poly)
Definition: AEQ.cc:390
void Q_poly_mon_mult_to(const int)
Definition: AEQ.cc:288
void Q_poly_div_rem(const Q_poly, const Q_poly)
Definition: AEQ.cc:505
int is_zero() const
Definition: AEQ.cc:747
mpz_t coef[100]
Definition: AEQ.h:17
void Q_poly_scalar_div(const Q_poly, const mpz_t)
Definition: AEQ.cc:440
void Q_poly_multsub_to(const Q_poly, const Q_poly)
Definition: AEQ.cc:633
void Q_poly_add_mon(const Q_poly, mpz_t, int)
Definition: AEQ.cc:166
void Q_poly_sub_mon(const Q_poly, mpz_t, int)
Definition: AEQ.cc:256
void Q_poly_mult_n(Q_poly, Q_poly)
Definition: AEQ.cc:342
void Q_poly_gcd(Q_poly, Q_poly)
Definition: AEQ.cc:778
void Q_poly_sub(const Q_poly, const Q_poly)
Definition: AEQ.cc:212
void Q_poly_mult_n_to(const Q_poly)
Definition: AEQ.cc:384
void Q_poly_add_const_to(const mpz_t)
Definition: AEQ.cc:160
void Q_poly_sub_mon_to(mpz_t, int)
Definition: AEQ.cc:265
void Q_poly_neg()
Definition: AEQ.cc:336
void Q_poly_add_to(const Q_poly)
Definition: AEQ.cc:133
int is_one() const
Definition: AEQ.cc:758
void Q_poly_print()
Definition: AEQ.cc:900
void Q_poly_mon_div(const Q_poly, const int)
Definition: AEQ.cc:456
int is_monic() const
Definition: AEQ.cc:768
void Q_poly_scalar_mult_to(const mpz_t)
Definition: AEQ.cc:327
void Q_poly_horner_Q_poly(Q_poly, const Q_poly)
Definition: AEQ.cc:670
void Q_poly_div_to(Q_poly &, Q_poly &, const Q_poly)
Definition: AEQ.cc:617
int deg
Definition: AEQ.h:15
Definition: AEQ.h:9
void Q_poly_extend(mpz_t)
Definition: AEQ.cc:83
void Q_poly_extgcd(Q_poly &, Q_poly &, Q_poly &, Q_poly, Q_poly)
Definition: AEQ.cc:809
void Q_poly_horner(mpz_t, const mpz_t)
Definition: AEQ.cc:655
void Q_poly_add(const Q_poly, const Q_poly)
Definition: AEQ.cc:99
void Q_poly_insert()
Definition: AEQ.cc:880
All the auxiliary stuff.
void Q_poly_add_mon_to(mpz_t, int)
Definition: AEQ.cc:205
void Q_poly_multadd_to(const Q_poly, const Q_poly)
Definition: AEQ.cc:626
void Q_poly_div(Q_poly &, Q_poly &, const Q_poly, const Q_poly)
Definition: AEQ.cc:560
void Q_poly_mon_mult(const Q_poly, const int)
Definition: AEQ.cc:274
void Q_poly_scalar_div_to(const mpz_t)
Definition: AEQ.cc:450
void Q_poly_sub_const(Q_poly, const mpz_t)
Definition: AEQ.cc:229
void Q_poly_set(const Q_poly)
Definition: AEQ.cc:689
void Q_poly_div_rem_to(const Q_poly)
Definition: AEQ.cc:553
int is_equal(Q_poly &)
Definition: AEQ.cc:727
void Q_poly_reduce()
Definition: AEQ.cc:46
Q_poly()
Definition: AEQ.cc:14
void Q_poly_sub_const_to(const mpz_t)
Definition: AEQ.cc:249
void Q_poly_mon_div_rem(const Q_poly, const int)
Definition: AEQ.cc:475
void Q_poly_sub_to(const Q_poly)
Definition: AEQ.cc:223
void Q_poly_add_const(Q_poly, const mpz_t)
Definition: AEQ.cc:139
void Q_poly_set_zero()
Definition: AEQ.cc:719