bigintmat Class Reference

Matrices of numbers. More...

#include <coeffs/bigintmat.h>

Public Member Functions
	bigintmat ()
bigintmat *	transpose ()
void	inpTranspose ()
	transpose in place More...
	bigintmat (int r, int c, const coeffs n)
	constructor: the r times c zero-matrix. Beware that the creation of a large zero matrix is expensive in terms of time and memory. More...
	bigintmat (const bigintmat *m)
	copy constructor More...
number &	operator[] (int i)
	dubious: 1-dim access to 2-dim array. Entries are read row by row. More...
const number &	operator[] (int i) const
void	operator*= (int intop)
	UEberladener *=-Operator (fuer int und bigint) Frage hier: *= verwenden oder lieber = und * einzeln? problem: what about non-commuting rings. Is this from left or right? More...
void	inpMult (number bintop, const coeffs C=NULL)
	inplace version of skalar mult. CHANGES input. More...
int	length ()
int	cols () const
int	rows () const
coeffs	basecoeffs () const
	~bigintmat ()
	canonical destructor. More...
int	index (int r, int c) const
	helper function to map from 2-dim coordinates, starting by 1 to 1-dim coordinate, starting by 0 More...
number	get (int i, int j) const
	get a copy of an entry. NOTE: starts at [1,1] More...
number	view (int i, int j) const
	view an entry an entry. NOTE: starts at [1,1] More...
number	get (int i) const
	get a copy of an entry. NOTE: starts at [0] More...
number	view (int i) const
	view an entry. NOTE: starts at [0] More...
void	set (int i, int j, number n, const coeffs C=NULL)
	replace an entry with a copy (delete old + copy new!). NOTE: starts at [1,1] More...
void	set (int i, number n, const coeffs C=NULL)
	replace an entry with a copy (delete old + copy new!). NOTE: starts at [0] More...
void	rawset (int i, number n, const coeffs C=NULL)
	replace an entry with the given number n (only delete old). NOTE: starts at [0]. Should be named set_transfer More...
void	rawset (int i, int j, number n, const coeffs C=NULL)
	as above, but the 2-dim version More...
char *	String ()
	IO: String returns a singular string containing the matrix, needs freeing afterwards. More...
void	Write ()
	IO: writes the matrix into the current internal string buffer which must be started/ allocated before (e.g. StringSetS) More...
void	Print ()
	IO: simply prints the matrix to the current output (screen?) More...
char *	StringAsPrinted ()
	Returns a string as it would have been printed in the interpreter. More...
void	pprint (int maxwid)
int	compare (const bigintmat *op) const
int *	getwid (int maxwid)
void	swap (int i, int j)
	swap columns i and j More...
void	swaprow (int i, int j)
	swap rows i and j More...
int	findnonzero (int i)
	find index of 1st non-zero entry in row i More...
int	findcolnonzero (int j)
	find index of 1st non-zero entry in column j More...
void	getcol (int j, bigintmat *a)
	copies the j-th column into the matrix a - which needs to be pre-allocated with the correct size. More...
void	getColRange (int j, int no, bigintmat *a)
	copies the no-columns staring by j (so j...j+no-1) into the pre-allocated a More...
void	getrow (int i, bigintmat *a)
	Schreibt i-te Zeile in Vektor (Matrix) a. More...
void	setcol (int j, bigintmat *m)
	Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m. More...
void	setrow (int i, bigintmat *m)
	Setzt i-te Zeile gleich übergebenem Vektor (Matrix) m. More...
void	appendCol (bigintmat *a)
	horizontally join the matrices, m <- m|a More...
void	extendCols (int i)
	append i zero-columns to the matrix More...
bool	add (bigintmat *b)
	Addiert zur Matrix die Matrix b dazu. Return false => an error occurred. More...
bool	sub (bigintmat *b)
	Subtrahiert ... More...
bool	skalmult (number b, coeffs c)
	Multipliziert zur Matrix den Skalar b hinzu. More...
bool	addcol (int i, int j, number a, coeffs c)
	addiert a-faches der j-ten Spalte zur i-ten dazu More...
bool	addrow (int i, int j, number a, coeffs c)
	... Zeile ... More...
void	colskalmult (int i, number a, coeffs c)
	Multipliziert zur i-ten Spalte den Skalar a hinzu. More...
void	rowskalmult (int i, number a, coeffs c)
	... Zeile ... More...
void	coltransform (int i, int j, number a, number b, number c, number d)
	transforms cols (i,j) using the 2x2 matrix ((a,b)(c,d)) (hopefully) More...
void	concatrow (bigintmat *a, bigintmat *b)
	Fügt zwei Matrixen untereinander/nebeneinander in gegebene Matrix ein, bzw spaltet gegebenen Matrix auf. More...
void	concatcol (bigintmat *a, bigintmat *b)
void	splitrow (bigintmat *a, bigintmat *b)
	Speichert in Matrix a den oberen, in b den unteren Teil der Matrix, vorausgesetzt die Dimensionen stimmen überein. More...
void	splitcol (bigintmat *a, bigintmat *b)
	... linken ... rechten ... More...
void	splitcol (bigintmat *a, int i)
	Speichert die ersten i Spalten als Teilmatrix in a. More...
void	splitrow (bigintmat *a, int i)
	... Zeilen ... More...
bool	copy (bigintmat *b)
	Kopiert Einträge von b auf Bigintmat. More...
void	copySubmatInto (bigintmat *, int sr, int sc, int nr, int nc, int tr, int tc)
	copy the submatrix of b, staring at (a,b) having n rows, m cols into the given matrix at pos. (c,d) needs c+n, d+m <= rows, cols a+n, b+m <= b.rows(), b.cols() More...
void	one ()
	Macht Matrix (Falls quadratisch) zu Einheitsmatrix. More...
int	isOne ()
	is matrix is identity More...
void	zero ()
	Setzt alle Einträge auf 0. More...
int	isZero ()
int	colIsZero (int i)
bigintmat *	elim (int i, int j)
	Liefert Streichungsmatrix (i-te Zeile und j-te Spalte gestrichen) zurück. More...
number	pseudoinv (bigintmat *a)
	Speichert in Matrix a die Pseudoinverse, liefert den Nenner zurück. More...
number	trace ()
	the trace .... More...
number	det ()
	det (via LaPlace in general, hnf for euc. rings) More...
number	hnfdet ()
	det via HNF Primzahlen als long long int, müssen noch in number umgewandelt werden? More...
void	hnf ()
	transforms INPLACE to HNF More...
void	howell ()
	dito, but Howell form (only different for zero-divsors) More...
void	swapMatrix (bigintmat *a)
bigintmat *	modhnf (number p, coeffs c)
	computes HNF(this | p*I) More...
bigintmat *	modgauss (number p, coeffs c)
void	skaldiv (number b)
	Macht Ganzzahldivision aller Matrixeinträge mit b. More...
void	colskaldiv (int j, number b)
	Macht Ganzzahldivision aller j-ten Spalteneinträge mit b. More...
void	mod (number p)
	Reduziert komplette Matrix modulo p. More...
bigintmat *	inpmod (number p, coeffs c)
	Liefert Kopie der Matrix zurück, allerdings im Ring Z modulo p. More...
number	content ()
	the content, the gcd of all entries. Only makes sense for Euclidean rings (or possibly constructive PIR) More...
void	simplifyContentDen (number *den)
	ensures that Gcd(den, content)=1 enden hier wieder More...

Private Attributes
coeffs	m_coeffs
number *	v
int	row
int	col

Detailed Description

Matrices of numbers.

Matrices are stored as 1-dim c-arrays but interpreted 2-dim as matrices. Both modes of addressing are supported, note however, that the 1-dim adressing starts at 0, the 2-dim at 1.

Matrices are meant to represent column modules, thus the default operations are always by column.

While basic operations are supported over any ring (coeff), some more advanced ones require more special rings: eg. echelon forms, solving of linear equations is only effective over principal ideal or even Euclidean rings.

Be careful with the get/set/view/rawset functions to understand which arguments are copied/ deleted or only assigned.

@Note: no reference counting here!

Definition at line 50 of file bigintmat.h.

Constructor & Destructor Documentation

bigintmat() [1/3]

bigintmat::bigintmat ( )

inline

Definition at line 59 of file bigintmat.h.

: m_coeffs(NULL), v(NULL), row(1), col(0){}

bigintmat() [2/3]

bigintmat::bigintmat ( int  r, int  c, const coeffs  n  )

inline

constructor: the r times c zero-matrix. Beware that the creation of a large zero matrix is expensive in terms of time and memory.

Definition at line 69 of file bigintmat.h.

                                           : m_coeffs(n), v(NULL), row(r), col(c)
    {
      assume (rows() >= 0);
      assume (cols() >= 0);
 
      const int l = r*c;
 
      if (l>0) /*(r>0) && (c>0) */
      {
        v = (number *)omAlloc(sizeof(number)*l);
 
        assume (basecoeffs() != NULL);
        for (int i = l - 1; i>=0; i--)
        {
          v[i] = n_Init(0, basecoeffs());
        }
      }
    }

bigintmat() [3/3]

bigintmat::bigintmat ( const bigintmat *  m )

inline

copy constructor

Definition at line 89 of file bigintmat.h.

                                 : m_coeffs(m->basecoeffs()), v(NULL), row(m->rows()), col(m->cols())
    {
      const int l = row*col;
 
      if (l > 0)
      {
        assume (rows() > 0);
        assume (cols() > 0);
 
        assume (m->v != NULL);
 
        v = (number *)omAlloc(sizeof(number)*row*col);
 
        assume (basecoeffs() != NULL);
 
        for (int i = l-1; i>=0; i--)
        {
          v[i] = n_Copy((*m)[i], basecoeffs());
        }
      }
    }

~bigintmat()

bigintmat::~bigintmat ( )

inline

canonical destructor.

Definition at line 149 of file bigintmat.h.

    {
      if (v!=NULL)
      {
        for (int i=row*col-1;i>=0; i--) { n_Delete(&(v[i]), basecoeffs()); }
        omFreeSize((ADDRESS)v, sizeof(number)*row*col);
        v=NULL;
      }
    }

Member Function Documentation

add()

bool bigintmat::add

(

bigintmat *

b

)

Addiert zur Matrix die Matrix b dazu. Return false => an error occurred.

Definition at line 895 of file bigintmat.cc.

{
  if ((b->rows() != row) || (b->cols() != col))
  {
    WerrorS("Error in bigintmat::add. Dimensions do not agree!");
    return false;
  }
  if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs()))
  {
    WerrorS("Error in bigintmat::add. coeffs do not agree!");
    return false;
  }
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      rawset(i, j, n_Add(b->view(i,j), view(i,j), basecoeffs()));
    }
  }
  return true;
}

addcol()

bool bigintmat::addcol	(	int	i,
		int	j,
		number	a,
		coeffs	c
	)

addiert a-faches der j-ten Spalte zur i-ten dazu

Definition at line 960 of file bigintmat.cc.

{
  if ((i>col) || (j>col) || (i<1) || (j<1))
  {
    WerrorS("Error in addcol: Index out of range!");
    return false;
  }
  if (!nCoeffs_are_equal(c, basecoeffs()))
  {
    WerrorS("Error in addcol: coeffs do not agree!");
    return false;
  }
  number t1, t2, t3;
  for (int k=1; k<=row; k++)
  {
    t1 = view(k, j);
    t2 = view(k, i);
    t3 = n_Mult(t1, a, basecoeffs());
    n_InpAdd(t3, t2, basecoeffs());
    rawset(k, i, t3);
  }
  return true;
}

addrow()

bool bigintmat::addrow	(	int	i,
		int	j,
		number	a,
		coeffs	c
	)

... Zeile ...

Definition at line 984 of file bigintmat.cc.

{
  if ((i>row) || (j>row) || (i<1) || (j<1))
  {
    WerrorS("Error in addrow: Index out of range!");
    return false;
  }
  if (!nCoeffs_are_equal(c, basecoeffs()))
  {
    WerrorS("Error in addrow: coeffs do not agree!");
    return false;
  }
  number t1, t2, t3;
  for (int k=1; k<=col; k++)
  {
    t1 = view(j, k);
    t2 = view(i, k);
    t3 = n_Mult(t1, a, basecoeffs());
    n_InpAdd(t3, t2, basecoeffs());
    rawset(i, k, t3);
  }
  return true;
}

appendCol()

void bigintmat::appendCol

(

bigintmat *

a

)

horizontally join the matrices, m <- m|a

Definition at line 1084 of file bigintmat.cc.

{
  coeffs R = basecoeffs();
  int ay = a->cols();
  int ax = a->rows();
  assume(row == ax);
 
  assume(nCoeffs_are_equal(a->basecoeffs(), R));
 
  bigintmat * tmp = new bigintmat(rows(), cols() + ay, R);
  tmp->concatcol(this, a);
  this->swapMatrix(tmp);
  delete tmp;
}

basecoeffs()

coeffs bigintmat::basecoeffs ( ) const

inline

Definition at line 146 of file bigintmat.h.

{ return m_coeffs; }

colIsZero()

int bigintmat::colIsZero

(

int

i

)

Definition at line 1578 of file bigintmat.cc.

{
  coeffs R = basecoeffs();
  for(int i=1; i<=rows(); i++)
    if (!n_IsZero(view(i, j), R)) return FALSE;
  return TRUE;
}

cols()

int bigintmat::cols ( ) const

inline

Definition at line 144 of file bigintmat.h.

{ return col; }

colskaldiv()

void bigintmat::colskaldiv	(	int	j,
		number	b
	)

Macht Ganzzahldivision aller j-ten Spalteneinträge mit b.

Definition at line 1877 of file bigintmat.cc.

{
  number tmp1, tmp2;
  for (int i=1; i<=row; i++)
  {
    tmp1 = view(i, j);
    tmp2 = n_Div(tmp1, b, basecoeffs());
    rawset(i, j, tmp2);
  }
}

colskalmult()

void bigintmat::colskalmult	(	int	i,
		number	a,
		coeffs	c
	)

Multipliziert zur i-ten Spalte den Skalar a hinzu.

Definition at line 1008 of file bigintmat.cc.

{
  if ((i>=1) && (i<=col) && (nCoeffs_are_equal(c, basecoeffs())))
  {
    number t, tmult;
    for (int j=1; j<=row; j++)
    {
      t = view(j, i);
      tmult = n_Mult(a, t, basecoeffs());
      rawset(j, i, tmult);
    }
  }
  else
    WerrorS("Error in colskalmult");
}

coltransform()

void bigintmat::coltransform	(	int	i,
		int	j,
		number	a,
		number	b,
		number	c,
		number	d
	)

transforms cols (i,j) using the 2x2 matrix ((a,b)(c,d)) (hopefully)

Definition at line 1890 of file bigintmat.cc.

{
  number tmp1, tmp2, tmp3, tmp4;
  for (int i=1; i<=row; i++)
  {
    tmp1 = get(i, j);
    tmp2 = get(i, k);
    tmp3 = n_Mult(tmp1, a, basecoeffs());
    tmp4 = n_Mult(tmp2, b, basecoeffs());
    n_InpAdd(tmp3, tmp4, basecoeffs());
    n_Delete(&tmp4, basecoeffs());
 
    n_InpMult(tmp1, c, basecoeffs());
    n_InpMult(tmp2, d, basecoeffs());
    n_InpAdd(tmp1, tmp2, basecoeffs());
    n_Delete(&tmp2, basecoeffs());
 
    set(i, j, tmp3);
    set(i, k, tmp1);
    n_Delete(&tmp1, basecoeffs());
    n_Delete(&tmp3, basecoeffs());
  }
}

compare()

int bigintmat::compare

(

const bigintmat *

op

)

const

Definition at line 362 of file bigintmat.cc.

{
  assume (basecoeffs() == op->basecoeffs() );
 
#ifndef SING_NDEBUG
  if (basecoeffs() != op->basecoeffs() )
    WerrorS("wrong bigintmat comparison: different basecoeffs!\n");
#endif
 
  if ((col!=1) ||(op->cols()!=1))
  {
    if((col!=op->cols())
       || (row!=op->rows()))
      return -2;
  }
 
  int i;
  for (i=0; i<si_min(row*col,op->rows()*op->cols()); i++)
  {
    if ( n_Greater(v[i], (*op)[i], basecoeffs()) )
      return 1;
    else if (! n_Equal(v[i], (*op)[i], basecoeffs()))
      return -1;
  }
 
  for (; i<row; i++)
  {
    if ( n_GreaterZero(v[i], basecoeffs()) )
      return 1;
    else if (! n_IsZero(v[i], basecoeffs()) )
      return -1;
  }
  for (; i<op->rows(); i++)
  {
    if ( n_GreaterZero((*op)[i], basecoeffs()) )
      return -1;
    else if (! n_IsZero((*op)[i], basecoeffs()) )
      return 1;
  }
  return 0;
}

concatcol()

void bigintmat::concatcol	(	bigintmat *	a,
		bigintmat *	b
	)

Definition at line 1099 of file bigintmat.cc.

                                                     {
  int ay = a->cols();
  int ax = a->rows();
  int by = b->cols();
  int bx = b->rows();
  number tmp;
 
  assume(row==ax && row == bx && ay+by ==col);
 
  assume(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs()));
 
  for (int i=1; i<=ax; i++)
  {
    for (int j=1; j<=ay; j++)
    {
      tmp = a->view(i,j);
      set(i, j, tmp);
    }
  }
  for (int i=1; i<=bx; i++)
  {
    for (int j=1; j<=by; j++)
    {
      tmp = b->view(i,j);
      set(i, j+ay, tmp);
    }
  }
}

concatrow()

void bigintmat::concatrow	(	bigintmat *	a,
		bigintmat *	b
	)

Fügt zwei Matrixen untereinander/nebeneinander in gegebene Matrix ein, bzw spaltet gegebenen Matrix auf.

Definition at line 1040 of file bigintmat.cc.

{
  int ay = a->cols();
  int ax = a->rows();
  int by = b->cols();
  int bx = b->rows();
  number tmp;
  if (!((col == ay) && (col == by) && (ax+bx == row)))
  {
    WerrorS("Error in concatrow. Dimensions must agree!");
    return;
  }
  if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs())))
  {
    WerrorS("Error in concatrow. coeffs do not agree!");
    return;
  }
  for (int i=1; i<=ax; i++)
  {
    for (int j=1; j<=ay; j++)
    {
      tmp = a->get(i,j);
      set(i, j, tmp);
      n_Delete(&tmp, basecoeffs());
    }
  }
  for (int i=1; i<=bx; i++)
  {
    for (int j=1; j<=by; j++)
    {
      tmp = b->get(i,j);
      set(i+ax, j, tmp);
      n_Delete(&tmp, basecoeffs());
    }
  }
}

content()

number bigintmat::content

(

)

the content, the gcd of all entries. Only makes sense for Euclidean rings (or possibly constructive PIR)

Definition at line 2676 of file bigintmat.cc.

{
  coeffs r = basecoeffs();
  number g = get(1,1), h;
  int n=rows()*cols();
  for(int i=1; i<n && !n_IsOne(g, r); i++)
  {
    h = n_Gcd(g, view(i), r);
    n_Delete(&g, r);
    g=h;
  }
  return g;
}

copy()

bool bigintmat::copy

(

bigintmat *

b

)

Kopiert Einträge von b auf Bigintmat.

Definition at line 1260 of file bigintmat.cc.

{
  if ((b->rows() != row) || (b->cols() != col))
  {
    WerrorS("Error in bigintmat::copy. Dimensions do not agree!");
    return false;
  }
  if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs()))
  {
    WerrorS("Error in bigintmat::copy. coeffs do not agree!");
    return false;
  }
  number t1;
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      t1 = b->view(i, j);
      set(i, j, t1);
    }
  }
  return true;
}

copySubmatInto()

void bigintmat::copySubmatInto	(	bigintmat *	B,
		int	sr,
		int	sc,
		int	nr,
		int	nc,
		int	tr,
		int	tc
	)

copy the submatrix of b, staring at (a,b) having n rows, m cols into the given matrix at pos. (c,d) needs c+n, d+m <= rows, cols a+n, b+m <= b.rows(), b.cols()

Definition at line 1288 of file bigintmat.cc.

{
  number t1;
  for (int i=1; i<=n; i++)
  {
    for (int j=1; j<=m; j++)
    {
      t1 = B->view(a+i-1, b+j-1);
      set(c+i-1, d+j-1, t1);
    }
  }
}

det()

number bigintmat::det

(

)

det (via LaPlace in general, hnf for euc. rings)

Definition at line 1513 of file bigintmat.cc.

{
  assume (row==col);
 
  if (col == 1)
    return get(1, 1);
  // should work as well in Z/pZ of type n_Zp?
  // relies on XExtGcd and the other euc. functinos.
  if ( getCoeffType(basecoeffs())== n_Z || getCoeffType(basecoeffs() )== n_Zn) {
    return hnfdet();
  }
  number sum = n_Init(0, basecoeffs());
  number t1, t2, t3, t4;
  bigintmat *b;
  for (int i=1; i<=row; i++) {
    b = elim(i, 1);
    t1 = get(i, 1);
    t2 = b->det();
    t3 = n_Mult(t1, t2, basecoeffs());
    t4 = n_Copy(sum, basecoeffs());
    n_Delete(&sum, basecoeffs());
    if ((i+1)>>1<<1==(i+1))
      sum = n_Add(t4, t3, basecoeffs());
    else
      sum = n_Sub(t4, t3, basecoeffs());
    n_Delete(&t1, basecoeffs());
    n_Delete(&t2, basecoeffs());
    n_Delete(&t3, basecoeffs());
    n_Delete(&t4, basecoeffs());
  }
  return sum;
}

elim()

bigintmat * bigintmat::elim	(	int	i,
		int	j
	)

Liefert Streichungsmatrix (i-te Zeile und j-te Spalte gestrichen) zurück.

Definition at line 1382 of file bigintmat.cc.

{
  if ((i<=0) || (i>row) || (j<=0) || (j>col))
    return NULL;
  int cx, cy;
  cx=1;
  cy=1;
  number t;
  bigintmat *b = new bigintmat(row-1, col-1, basecoeffs());
  for (int k=1; k<=row; k++) {
    if (k!=i)
    {
      cy=1;
      for (int l=1; l<=col; l++)
      {
        if (l!=j)
        {
          t = get(k, l);
          b->set(cx, cy, t);
          n_Delete(&t, basecoeffs());
          cy++;
        }
      }
      cx++;
    }
  }
  return b;
}

extendCols()

void bigintmat::extendCols

(

int

i

)

append i zero-columns to the matrix

Definition at line 1077 of file bigintmat.cc.

{
  bigintmat * tmp = new bigintmat(rows(), i, basecoeffs());
  appendCol(tmp);
  delete tmp;
}

findcolnonzero()

int bigintmat::findcolnonzero

(

int

j

)

find index of 1st non-zero entry in column j

Definition at line 736 of file bigintmat.cc.

{
  for (int i=row; i>=1; i--)
  {
    if (!n_IsZero(view(i,j), basecoeffs()))
    {
      return i;
    }
  }
  return 0;
}

findnonzero()

int bigintmat::findnonzero

(

int

i

)

find index of 1st non-zero entry in row i

Definition at line 724 of file bigintmat.cc.

{
  for (int j=1; j<=col; j++)
  {
    if (!n_IsZero(view(i,j), basecoeffs()))
    {
      return j;
    }
  }
  return 0;
}

get() [1/2]

number bigintmat::get

(

int

i

)

const

get a copy of an entry. NOTE: starts at [0]

Definition at line 103 of file bigintmat.cc.

{
  assume (i >= 0);
  assume (i<rows()*cols());
 
  return n_Copy(v[i], basecoeffs());
}

get() [2/2]

number bigintmat::get	(	int	i,
		int	j
	)		const

get a copy of an entry. NOTE: starts at [1,1]

Definition at line 119 of file bigintmat.cc.

{
  assume (i > 0 && j > 0);
  assume (i <= rows() && j <= cols());
 
  return get(index(i, j));
}

getcol()

void bigintmat::getcol	(	int	j,
		bigintmat *	a
	)

copies the j-th column into the matrix a - which needs to be pre-allocated with the correct size.

Definition at line 748 of file bigintmat.cc.

{
  assume((j<=col) && (j>=1));
  if (((a->rows() != row) || (a->cols() != 1)) && ((a->rows() != 1) || (a->cols() != row)))
  {
    assume(0);
    WerrorS("Error in getcol. Dimensions must agree!");
    return;
  }
  if (!nCoeffs_are_equal(basecoeffs(), a->basecoeffs()))
  {
    nMapFunc f = n_SetMap(basecoeffs(), a->basecoeffs());
    number t1, t2;
    for (int i=1; i<=row;i++)
    {
      t1 = get(i,j);
      t2 = f(t1, basecoeffs(), a->basecoeffs());
      a->set(i-1,t1);
      n_Delete(&t1, basecoeffs());
      n_Delete(&t2, a->basecoeffs());
    }
    return;
  }
  number t1;
  for (int i=1; i<=row;i++)
  {
    t1 = view(i,j);
    a->set(i-1,t1);
  }
}

getColRange()

void bigintmat::getColRange	(	int	j,
		int	no,
		bigintmat *	a
	)

copies the no-columns staring by j (so j...j+no-1) into the pre-allocated a

Definition at line 779 of file bigintmat.cc.

{
  number t1;
  for(int ii=0; ii< no; ii++)
  {
    for (int i=1; i<=row;i++)
    {
      t1 = view(i, ii+j);
      a->set(i, ii+1, t1);
    }
  }
}

getrow()

void bigintmat::getrow	(	int	i,
		bigintmat *	a
	)

Schreibt i-te Zeile in Vektor (Matrix) a.

Definition at line 792 of file bigintmat.cc.

{
  if ((i>row) || (i<1))
  {
    WerrorS("Error in getrow: Index out of range!");
    return;
  }
  if (((a->rows() != 1) || (a->cols() != col)) && ((a->rows() != col) || (a->cols() != 1)))
  {
    WerrorS("Error in getrow. Dimensions must agree!");
    return;
  }
  if (!nCoeffs_are_equal(basecoeffs(), a->basecoeffs()))
  {
    nMapFunc f = n_SetMap(basecoeffs(), a->basecoeffs());
    number t1, t2;
    for (int j=1; j<=col;j++)
    {
      t1 = get(i,j);
      t2 = f(t1, basecoeffs(), a->basecoeffs());
      a->set(j-1,t2);
      n_Delete(&t1, basecoeffs());
      n_Delete(&t2, a->basecoeffs());
    }
    return;
  }
  number t1;
  for (int j=1; j<=col;j++)
  {
    t1 = get(i,j);
    a->set(j-1,t1);
    n_Delete(&t1, basecoeffs());
  }
}

getwid()

int * bigintmat::getwid

(

int

maxwid

)

Definition at line 580 of file bigintmat.cc.

{
  int const c = /*2**/(col-1)+1;
  int * wv = (int*)omAlloc(sizeof(int)*col*row);
  int * cwv = (int*)omAlloc(sizeof(int)*col);
  for (int j=0; j<col; j++)
  {
    cwv[j] = 0;
    for (int i=0; i<row; i++)
    {
      StringSetS("");
      n_Write(v[col*i+j], basecoeffs());
      char * tmp = StringEndS();
      const int _nl = strlen(tmp);
      wv[col*i+j] = _nl;
      if (_nl > cwv[j])
        cwv[j]=_nl;
        omFree(tmp);
    }
  }
 
  // Groesse verkleinern, bis < maxwid
  if (intArrSum(cwv, col)+c > maxwid)
  {
    int j = findLongest(cwv, col);
    cwv[j] = getShorter(wv, cwv[j], j, col, row);
  }
  omFree(wv);
  return cwv;
}

hnf()

void bigintmat::hnf

(

)

transforms INPLACE to HNF

Definition at line 1661 of file bigintmat.cc.

{
  // Laufen von unten nach oben und von links nach rechts
  // CF: TODO: for n_Z: write a recursive version. This one will
  //     have exponential blow-up. Look at Michianchio
  //     Alternatively, do p-adic det and modular method
 
#if 0
    char * s;
    ::PrintS("mat over Z is \n");
    ::Print("%s\n", s = nCoeffString(basecoeffs()));
    omFree(s);
    Print();
    ::Print("\n(%d x %d)\n", rows(), cols());
#endif
 
  int i = rows();
  int j = cols();
  number q = n_Init(0, basecoeffs());
  number one = n_Init(1, basecoeffs());
  number minusone = n_Init(-1, basecoeffs());
  number tmp1 = n_Init(0, basecoeffs());
  number tmp2 = n_Init(0, basecoeffs());
  number co1, co2, co3, co4;
  number ggt = n_Init(0, basecoeffs());
 
  while ((i>0) && (j>0))
  {
    // Falls erstes Nicht-Null-Element in Zeile i nicht existiert, oder hinter Spalte j vorkommt, gehe in nächste Zeile
    if ((findnonzero(i)==0) || (findnonzero(i)>j))
    {
      i--;
    }
    else
    {
      // Laufe von links nach rechts durch die Zeile:
      for (int l=1; l<=j-1; l++)
      {
        n_Delete(&tmp1, basecoeffs());
        tmp1 = get(i, l);
        // Falls Eintrag (im folgenden x genannt) gleich 0, gehe eine Spalte weiter. Ansonsten...
        if (!n_IsZero(tmp1, basecoeffs()))
        {
          n_Delete(&tmp2, basecoeffs());
          tmp2 = get(i, l+1);
          // Falls Eintrag (i.f. y g.) rechts daneben gleich 0, tausche beide Spalten, sonst...
          if (!n_IsZero(tmp2, basecoeffs()))
          {
            n_Delete(&ggt, basecoeffs());
            ggt = n_XExtGcd(tmp1, tmp2, &co1, &co2, &co3, &co4, basecoeffs());
            // Falls x=ggT(x, y), tausche die beiden Spalten und ziehe die (neue) rechte Spalte so häufig von der linken ab, dass an der ehemaligen Stelle von x nun eine 0 steht. Dazu:
            if (n_Equal(tmp1, ggt, basecoeffs()))
            {
              swap(l, l+1);
              n_Delete(&q, basecoeffs());
              q = n_Div(tmp2, ggt, basecoeffs());
              q = n_InpNeg(q, basecoeffs());
              // Dann addiere das -q-fache der (neuen) rechten Spalte zur linken dazu. Damit erhalten wir die gewünschte 0
 
              addcol(l, l+1, q, basecoeffs());
              n_Delete(&q, basecoeffs());
            }
            else if (n_Equal(tmp1, minusone, basecoeffs()))
            {
              // Falls x=-1, so ist x=-ggt(x, y). Dann gehe wie oben vor, multipliziere aber zuerst die neue rechte Spalte (die mit x) mit -1
              // Die Berechnung von q (=y/ggt) entfällt, da ggt=1
              swap(l, l+1);
              colskalmult(l+1, minusone, basecoeffs());
              tmp2 = n_InpNeg(tmp2, basecoeffs());
              addcol(l, l+1, tmp2, basecoeffs());
            }
            else
            {
              // CF: use the 2x2 matrix (co1, co2)(co3, co4) to
              // get the gcd in position and the 0 in the other:
#ifdef CF_DEB
              ::PrintS("applying trafo\n");
              StringSetS("");
              n_Write(co1, basecoeffs()); StringAppendS("\t");
              n_Write(co2, basecoeffs()); StringAppendS("\t");
              n_Write(co3, basecoeffs()); StringAppendS("\t");
              n_Write(co4, basecoeffs()); StringAppendS("\t");
              ::Print("%s\nfor l=%d\n", StringEndS(), l);
              {char * s = String();
              ::Print("to %s\n", s);omFree(s);};
#endif
              coltransform(l, l+1, co3, co4, co1, co2);
#ifdef CF_DEB
              {char * s = String();
              ::Print("gives %s\n", s);}
#endif
            }
            n_Delete(&co1, basecoeffs());
            n_Delete(&co2, basecoeffs());
            n_Delete(&co3, basecoeffs());
            n_Delete(&co4, basecoeffs());
          }
          else
          {
            swap(l, l+1);
          }
          // Dann betrachte die vormals rechte Spalte als neue linke, und die rechts daneben als neue rechte.
        }
      }
 
      #ifdef HAVE_RINGS
      // normalize by units:
      if (!n_IsZero(view(i, j), basecoeffs()))
      {
        number u = n_GetUnit(view(i, j), basecoeffs());
        if (!n_IsOne(u, basecoeffs()))
        {
          colskaldiv(j, u);
        }
        n_Delete(&u, basecoeffs());
      }
      #endif
      // Zum Schluss mache alle Einträge rechts vom Diagonalelement betragsmäßig kleiner als dieses
      for (int l=j+1; l<=col; l++)
      {
        n_Delete(&q, basecoeffs());
        q = n_QuotRem(view(i, l), view(i, j), NULL, basecoeffs());
        q = n_InpNeg(q, basecoeffs());
        addcol(l, j, q, basecoeffs());
      }
      i--;
      j--;
      // Dann betrachte die Zeile darüber und gehe dort wie vorher vor
    }
  }
  n_Delete(&q, basecoeffs());
  n_Delete(&tmp1, basecoeffs());
  n_Delete(&tmp2, basecoeffs());
  n_Delete(&ggt, basecoeffs());
  n_Delete(&one, basecoeffs());
  n_Delete(&minusone, basecoeffs());
 
#if 0
    ::PrintS("hnf over Z is \n");
    Print();
    ::Print("\n(%d x %d)\n", rows(), cols());
#endif
}

hnfdet()

number bigintmat::hnfdet

(

)

det via HNF Primzahlen als long long int, müssen noch in number umgewandelt werden?

Definition at line 1546 of file bigintmat.cc.

{
  assume (col == row);
 
  if (col == 1)
    return get(1, 1);
  bigintmat *m = new bigintmat(this);
  m->hnf();
  number prod = n_Init(1, basecoeffs());
  number temp, temp2;
  for (int i=1; i<=col; i++) {
    temp = m->get(i, i);
    temp2 = n_Mult(temp, prod, basecoeffs());
    n_Delete(&prod, basecoeffs());
    prod = temp2;
    n_Delete(&temp, basecoeffs());
  }
  delete m;
  return prod;
}

howell()

void bigintmat::howell

(

)

dito, but Howell form (only different for zero-divsors)

Definition at line 1586 of file bigintmat.cc.

{
  coeffs R = basecoeffs();
  hnf(); // as a starting point...
  if (getCoeffType(R)== n_Z) return; //wrong, need to prune!
 
  int n = cols(), m = rows(), i, j, k;
 
  //make sure, the matrix has enough space. We need no rows+1 columns.
  //The resulting Howell form will be pruned to be at most square.
  bigintmat * t = new bigintmat(m, m+1, R);
  t->copySubmatInto(this, 1, n>m ? n-m+1 : 1, m, n>m ? m : n, 1, n>m ? 2 : m+2-n  );
  swapMatrix(t);
  delete t;
  for(i=1; i<= cols(); i++) {
    if (!colIsZero(i)) break;
  }
  assume (i>1);
  if (i>cols()) {
    t = new bigintmat(rows(), 0, R);
    swapMatrix(t);
    delete t;
    return; // zero matrix found, clearly normal.
  }
 
  int last_zero_col = i-1;
  for (int c = cols(); c>0; c--) {
    for(i=rows(); i>0; i--) {
      if (!n_IsZero(view(i, c), R)) break;
    }
    if (i==0) break; // matrix SHOULD be zero from here on
    number a = n_Ann(view(i, c), R);
    addcol(last_zero_col, c, a, R);
    n_Delete(&a, R);
    for(j = c-1; j>last_zero_col; j--) {
      for(k=rows(); k>0; k--) {
        if (!n_IsZero(view(k, j), R)) break;
        if (!n_IsZero(view(k, last_zero_col), R)) break;
      }
      if (k==0) break;
      if (!n_IsZero(view(k, last_zero_col), R)) {
        number gcd, co1, co2, co3, co4;
        gcd = n_XExtGcd(view(k, last_zero_col), view(k, j), &co1, &co2, &co3, &co4, R);
        if (n_Equal(gcd, view(k, j), R)) {
          number q = n_Div(view(k, last_zero_col), gcd, R);
          q = n_InpNeg(q, R);
          addcol(last_zero_col, j, q, R);
          n_Delete(&q, R);
        } else if (n_Equal(gcd, view(k, last_zero_col), R)) {
          swap(last_zero_col, k);
          number q = n_Div(view(k, last_zero_col), gcd, R);
          q = n_InpNeg(q, R);
          addcol(last_zero_col, j, q, R);
          n_Delete(&q, R);
        } else {
          coltransform(last_zero_col, j, co3, co4, co1, co2);
        }
        n_Delete(&gcd, R);
        n_Delete(&co1, R);
        n_Delete(&co2, R);
        n_Delete(&co3, R);
        n_Delete(&co4, R);
      }
    }
    for(k=rows(); k>0; k--) {
      if (!n_IsZero(view(k, last_zero_col), R)) break;
    }
    if (k) last_zero_col--;
  }
  t = new bigintmat(rows(), cols()-last_zero_col, R);
  t->copySubmatInto(this, 1, last_zero_col+1, rows(), cols()-last_zero_col, 1, 1);
  swapMatrix(t);
  delete t;
}

index()

int bigintmat::index ( int  r, int  c  ) const

inline

helper function to map from 2-dim coordinates, starting by 1 to 1-dim coordinate, starting by 0

Definition at line 161 of file bigintmat.h.

    {
      assume (rows() >= 0 && cols() >= 0);
 
      assume (r > 0 && c > 0);
      assume (r <= rows() && c <= cols());
 
      const int index = ((r-1)*cols() + (c-1));
 
      assume (index >= 0 && index < rows() * cols());
      return index;
    }

inpmod()

bigintmat * bigintmat::inpmod	(	number	p,
		coeffs	c
	)

Liefert Kopie der Matrix zurück, allerdings im Ring Z modulo p.

inpMult()

void bigintmat::inpMult	(	number	bintop,
		const coeffs	C = NULL
	)

inplace version of skalar mult. CHANGES input.

Definition at line 145 of file bigintmat.cc.

{
  assume (C == NULL || C == basecoeffs());
 
  const int l = rows() * cols();
 
  for (int i=0; i < l; i++)
    n_InpMult(v[i], bintop, basecoeffs());
}

inpTranspose()

void bigintmat::inpTranspose

(

)

transpose in place

Definition at line 50 of file bigintmat.cc.

{
  int n = row,
      m = col,
      nm = n<m?n : m; // the min, describing the square part of the matrix
  //CF: this is not optimal, but so far, it seems to work
 
#define swap(_i, _j)        \
  int __i = (_i), __j=(_j); \
  number c = v[__i];        \
  v[__i] = v[__j];          \
  v[__j] = c                \
 
  for (int i=0; i< nm; i++)
    for (int j=i+1; j< nm; j++)
    {
      swap(i*m+j, j*n+i);
    }
  if (n<m)
    for (int i=nm; i<m; i++)
      for(int j=0; j<n; j++)
      {
        swap(j*n+i, i*m+j);
      }
  if (n>m)
    for (int i=nm; i<n; i++)
      for(int j=0; j<m; j++)
      {
        swap(i*m+j, j*n+i);
      }
#undef swap
  row = m;
  col = n;
}

isOne()

int bigintmat::isOne

(

)

is matrix is identity

Definition at line 1301 of file bigintmat.cc.

{
  coeffs r = basecoeffs();
  if (row==col)
  {
    for (int i=1; i<=row; i++)
    {
      for (int j=1; j<=col; j++)
      {
        if (i==j)
        {
          if (!n_IsOne(view(i, j), r))
            return 0;
        }
        else
        {
          if (!n_IsZero(view(i,j), r))
            return 0;
        }
      }
    }
  }
  return 1;
}

isZero()

int bigintmat::isZero

(

)

Definition at line 1364 of file bigintmat.cc.

{
  for (int i=1; i<=row; i++) {
    for (int j=1; j<=col; j++) {
      if (!n_IsZero(view(i,j), basecoeffs()))
        return FALSE;
    }
  }
  return TRUE;
}

length()

int bigintmat::length ( )

inline

Definition at line 143 of file bigintmat.h.

{ return col*row; }

mod()

void bigintmat::mod

(

number

p

)

Reduziert komplette Matrix modulo p.

Definition at line 1917 of file bigintmat.cc.

{
  // produce the matrix in Z/pZ
  number tmp1, tmp2;
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      tmp1 = get(i, j);
      tmp2 = n_IntMod(tmp1, p, basecoeffs());
      n_Delete(&tmp1, basecoeffs());
      set(i, j, tmp2);
    }
  }
}

modgauss()

bigintmat * bigintmat::modgauss	(	number	p,
		coeffs	c
	)

modhnf()

bigintmat * bigintmat::modhnf	(	number	p,
		coeffs	c
	)

computes HNF(this | p*I)

Definition at line 1833 of file bigintmat.cc.

{
  coeffs Rp = numbercoeffs(p, R); // R/pR
  bigintmat *m = bimChangeCoeff(this, Rp);
  m->howell();
  bigintmat *a = bimChangeCoeff(m, R);
  delete m;
  bigintmat *C = new bigintmat(rows(), rows(), R);
  int piv = rows(), i = a->cols();
  while (piv)
  {
    if (!i || n_IsZero(a->view(piv, i), R))
    {
      C->set(piv, piv, p, R);
    }
    else
    {
      C->copySubmatInto(a, 1, i, rows(), 1, 1, piv);
      i--;
    }
    piv--;
  }
  delete a;
  return C;
}

one()

void bigintmat::one

(

)

Macht Matrix (Falls quadratisch) zu Einheitsmatrix.

Definition at line 1326 of file bigintmat.cc.

{
  if (row==col)
  {
    number one = n_Init(1, basecoeffs()),
           zero = n_Init(0, basecoeffs());
    for (int i=1; i<=row; i++)
    {
      for (int j=1; j<=col; j++)
      {
        if (i==j)
        {
          set(i, j, one);
        }
        else
        {
          set(i, j, zero);
        }
      }
    }
    n_Delete(&one, basecoeffs());
    n_Delete(&zero, basecoeffs());
  }
}

operator*=()

void bigintmat::operator*=

(

int

intop

)

UEberladener *=-Operator (fuer int und bigint) Frage hier: *= verwenden oder lieber = und * einzeln? problem: what about non-commuting rings. Is this from left or right?

Definition at line 136 of file bigintmat.cc.

{
  number iop = n_Init(intop, basecoeffs());
 
  inpMult(iop, basecoeffs());
 
  n_Delete(&iop, basecoeffs());
}

operator[]() [1/2]

number & bigintmat::operator[] ( int  i )

inline

dubious: 1-dim access to 2-dim array. Entries are read row by row.

Definition at line 111 of file bigintmat.h.

    {
#ifndef SING_NDEBUG
      if((i<0)||(i>=row*col))
      {
        Werror("wrong bigintmat index:%d\n",i);
      }
      assume ( !((i<0)||(i>=row*col)) );
#endif
      return v[i];  // Hier sollte imho kein nlCopy rein...
    }

operator[]() [2/2]

const number & bigintmat::operator[] ( int  i ) const

inline

Definition at line 122 of file bigintmat.h.

    {
#ifndef SING_NDEBUG
      if((i<0)||(i>=row*col))
      {
        Werror("wrong bigintmat index:%d\n",i);
      }
      assume ( !((i<0)||(i>=row*col)) );
#endif
      return v[i];
    }

pprint()

void bigintmat::pprint

(

int

maxwid

)

Definition at line 611 of file bigintmat.cc.

{
  if ((col==0) || (row==0))
    PrintS("");
  else
  {
    int * colwid = getwid(maxwid);
    char * ps;
    int slength = 0;
    for (int j=0; j<col; j++)
      slength += colwid[j]*row;
    slength += col*row+row;
    ps = (char*) omAlloc0(sizeof(char)*(slength));
    int pos = 0;
    for (int i=0; i<col*row; i++)
    {
      StringSetS("");
      n_Write(v[i], basecoeffs());
      char * ts = StringEndS();
      const int _nl = strlen(ts);
      int cj = i%col;
      if (_nl > colwid[cj])
      {
        StringSetS("");
        int ci = i/col;
        StringAppend("[%d,%d]", ci+1, cj+1);
        char * ph = StringEndS();
        int phl = strlen(ph);
        if (phl > colwid[cj])
        {
          for (int j=0; j<colwid[cj]-1; j++)
            ps[pos+j] = ' ';
          ps[pos+colwid[cj]-1] = '*';
        }
        else
        {
          for (int j=0; j<colwid[cj]-phl; j++)
            ps[pos+j] = ' ';
          for (int j=0; j<phl; j++)
            ps[pos+colwid[cj]-phl+j] = ph[j];
        }
          omFree(ph);
      }
      else  // Mit Leerzeichen auffüllen und zahl reinschreiben
      {
        for (int j=0; j<colwid[cj]-_nl; j++)
          ps[pos+j] = ' ';
        for (int j=0; j<_nl; j++)
          ps[pos+colwid[cj]-_nl+j] = ts[j];
      }
      // ", " und (evtl) "\n" einfügen
      if ((i+1)%col == 0)
      {
        if (i != col*row-1)
        {
          ps[pos+colwid[cj]] = ',';
          ps[pos+colwid[cj]+1] = '\n';
          pos += colwid[cj]+2;
        }
      }
      else
      {
        ps[pos+colwid[cj]] = ',';
        pos += colwid[cj]+1;
      }
 
      omFree(ts);  // Hier ts zerstören
    }
    PrintS(ps);
    omFree(ps);
  }
}

Print()

void bigintmat::Print

(

)

IO: simply prints the matrix to the current output (screen?)

Definition at line 443 of file bigintmat.cc.

{
  char * s = String();
  PrintS(s);
  omFree(s);
}

pseudoinv()

number bigintmat::pseudoinv

(

bigintmat *

a

)

Speichert in Matrix a die Pseudoinverse, liefert den Nenner zurück.

Definition at line 1416 of file bigintmat.cc.

                                        {
 
  // Falls Matrix über reellen Zahlen nicht invertierbar, breche ab
 assume((a->rows() == row) && (a->rows() == a->cols()) && (row == col));
 
 number det = this->det(); //computes the HNF, so should e reused.
 if ((n_IsZero(det, basecoeffs())))
    return det;
 
 // Hänge Einheitsmatrix über Matrix und wendet HNF an. An Stelle der Einheitsmatrix steht im Ergebnis die Transformationsmatrix dazu
  a->one();
  bigintmat *m = new bigintmat(2*row, col, basecoeffs());
  m->concatrow(a,this);
  m->hnf();
  // Arbeite weiterhin mit der zusammengehängten Matrix
  // Laufe durch die Diagonalelemente, und multipliziere jede Spalte rechts davon damit, speichere aber den alten Eintrag der Spalte, temp, der in der Zeile des Diagonalelements liegt, zwischen. Dann addiere das -temp-Fache der Diagonalspalte zur entsprechenenden Spalte rechts davon. Dadurch entsteht überall rechts der Diagonalen eine 0
  number diag;
  number temp, ttemp;
  for (int i=1; i<=col; i++) {
    diag = m->get(row+i, i);
    for (int j=i+1; j<=col; j++) {
      temp = m->get(row+i, j);
      m->colskalmult(j, diag, basecoeffs());
      temp = n_InpNeg(temp, basecoeffs());
      m->addcol(j, i, temp, basecoeffs());
      n_Delete(&temp, basecoeffs());
    }
    n_Delete(&diag, basecoeffs());
  }
  // Falls wir nicht modulo n arbeiten, können wir die Spalten durch den ggT teilen, um die Einträge kleiner zu bekommen
  // Bei Z/n sparen wir uns das, da es hier sinnlos ist
  number g;
  number gcd;
  for (int j=1; j<=col; j++) {
    g = n_Init(0, basecoeffs());
    for (int i=1; i<=2*row; i++) {
      temp = m->get(i,j);
      gcd = n_Gcd(g, temp, basecoeffs());
      n_Delete(&g, basecoeffs());
      n_Delete(&temp, basecoeffs());
      g = n_Copy(gcd, basecoeffs());
      n_Delete(&gcd, basecoeffs());
    }
    if (!(n_IsOne(g, basecoeffs())))
      m->colskaldiv(j, g);
    n_Delete(&g, basecoeffs());
  }
 
  // Nun müssen die Diagonalelemente durch Spaltenmultiplikation gleich gesett werden. Bei Z können wir mit dem kgV arbeiten, bei Z/n bringen wir jedes Diagonalelement auf 1 (wir arbeiten immer mit n = Primzahl. Für n != Primzahl muss noch an anderen Stellen etwas geändert werden)
 
  g = n_Init(0, basecoeffs());
  number prod = n_Init(1, basecoeffs());
  for (int i=1; i<=col; i++) {
    gcd = n_Gcd(g, m->get(row+i, i), basecoeffs());
    n_Delete(&g, basecoeffs());
    g = n_Copy(gcd, basecoeffs());
    n_Delete(&gcd, basecoeffs());
    ttemp = n_Copy(prod, basecoeffs());
    temp = m->get(row+i, i);
    n_Delete(&prod, basecoeffs());
    prod = n_Mult(ttemp, temp, basecoeffs());
    n_Delete(&ttemp, basecoeffs());
    n_Delete(&temp, basecoeffs());
  }
  number lcm;
  lcm = n_Div(prod, g, basecoeffs());
  for (int j=1; j<=col; j++) {
    ttemp = m->get(row+j,j);
    temp = n_QuotRem(lcm, ttemp, NULL, basecoeffs());
    m->colskalmult(j, temp, basecoeffs());
    n_Delete(&ttemp, basecoeffs());
    n_Delete(&temp, basecoeffs());
  }
  n_Delete(&lcm, basecoeffs());
  n_Delete(&prod, basecoeffs());
 
  number divisor = m->get(row+1, 1);
  m->splitrow(a, 1);
  delete m;
  n_Delete(&det, basecoeffs());
  return divisor;
}

rawset() [1/2]

void bigintmat::rawset ( int  i, int  j, number  n, const coeffs  C = NULL  )

inline

as above, but the 2-dim version

Definition at line 216 of file bigintmat.h.

    {
      rawset( index(i,j), n, C);
    }

rawset() [2/2]

void bigintmat::rawset ( int  i, number  n, const coeffs  C = NULL  )

inline

replace an entry with the given number n (only delete old). NOTE: starts at [0]. Should be named set_transfer

Definition at line 196 of file bigintmat.h.

    {
      assume (C == NULL || C == basecoeffs());
      assume (i >= 0);
      const int l = rows() * cols();
      assume (i<l);
 
      if (i < l)
      {
        n_Delete(&(v[i]), basecoeffs()); v[i] = n;
      }
#ifndef SING_NDEBUG
      else
      {
        Werror("wrong bigintmat index:%d\n",i);
      }
#endif
    }

rows()

int bigintmat::rows ( ) const

inline

Definition at line 145 of file bigintmat.h.

{ return row; }

rowskalmult()

void bigintmat::rowskalmult	(	int	i,
		number	a,
		coeffs	c
	)

... Zeile ...

Definition at line 1024 of file bigintmat.cc.

{
  if ((i>=1) && (i<=row) && (nCoeffs_are_equal(c, basecoeffs())))
  {
    number t, tmult;
    for (int j=1; j<=col; j++)
    {
      t = view(i, j);
      tmult = n_Mult(a, t, basecoeffs());
      rawset(i, j, tmult);
    }
  }
  else
    WerrorS("Error in rowskalmult");
}

set() [1/2]

void bigintmat::set	(	int	i,
		int	j,
		number	n,
		const coeffs	C = NULL
	)

replace an entry with a copy (delete old + copy new!). NOTE: starts at [1,1]

Definition at line 95 of file bigintmat.cc.

{
  assume (C == NULL || C == basecoeffs());
  assume (i > 0 && j > 0);
  assume (i <= rows() && j <= cols());
  set(index(i, j), n, C);
}

set() [2/2]

void bigintmat::set	(	int	i,
		number	n,
		const coeffs	C = NULL
	)

replace an entry with a copy (delete old + copy new!). NOTE: starts at [0]

Definition at line 87 of file bigintmat.cc.

{
  assume (C == NULL || C == basecoeffs());
 
  rawset(i, n_Copy(n, basecoeffs()), basecoeffs());
}

setcol()

void bigintmat::setcol	(	int	j,
		bigintmat *	m
	)

Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m.

Definition at line 827 of file bigintmat.cc.

{
   if ((j>col) || (j<1))
   {
    WerrorS("Error in setcol: Index out of range!");
    return;
  }
  if (((m->rows() != row) || (m->cols() != 1)) && ((m->rows() != 1) || (m->cols() != row)))
  {
    WerrorS("Error in setcol. Dimensions must agree!");
    return;
  }
  if (!nCoeffs_are_equal(basecoeffs(), m->basecoeffs()))
  {
    nMapFunc f = n_SetMap(m->basecoeffs(), basecoeffs());
    number t1,t2;
    for (int i=1; i<=row; i++)
    {
      t1 = m->get(i-1);
      t2 = f(t1, m->basecoeffs(),basecoeffs());
      set(i, j, t2);
      n_Delete(&t2, basecoeffs());
      n_Delete(&t1, m->basecoeffs());
    }
    return;
  }
  number t1;
  for (int i=1; i<=row; i++)
  {
    t1 = m->view(i-1);
    set(i, j, t1);
  }
}

setrow()

void bigintmat::setrow	(	int	i,
		bigintmat *	m
	)

Setzt i-te Zeile gleich übergebenem Vektor (Matrix) m.

Definition at line 861 of file bigintmat.cc.

{
  if ((j>row) || (j<1))
  {
    WerrorS("Error in setrow: Index out of range!");
    return;
  }
  if (((m->rows() != 1) || (m->cols() != col)) && ((m->rows() != col) || (m->cols() != 1)))
  {
    WerrorS("Error in setrow. Dimensions must agree!");
    return;
  }
  if (!nCoeffs_are_equal(basecoeffs(), m->basecoeffs()))
  {
    nMapFunc f = n_SetMap(m->basecoeffs(), basecoeffs());
    number tmp1,tmp2;
    for (int i=1; i<=col; i++)
    {
      tmp1 = m->get(i-1);
      tmp2 = f(tmp1, m->basecoeffs(),basecoeffs());
      set(j, i, tmp2);
      n_Delete(&tmp2, basecoeffs());
      n_Delete(&tmp1, m->basecoeffs());
    }
    return;
  }
  number tmp;
  for (int i=1; i<=col; i++)
  {
    tmp = m->view(i-1);
    set(j, i, tmp);
  }
}

simplifyContentDen()

void bigintmat::simplifyContentDen

(

number *

den

)

ensures that Gcd(den, content)=1 enden hier wieder

Definition at line 2689 of file bigintmat.cc.

{
  coeffs r = basecoeffs();
  number g = n_Copy(*d, r), h;
  int n=rows()*cols();
  for(int i=0; i<n && !n_IsOne(g, r); i++)
  {
    h = n_Gcd(g, view(i), r);
    n_Delete(&g, r);
    g=h;
  }
  *d = n_Div(*d, g, r);
  if (!n_IsOne(g, r))
  skaldiv(g);
}

skaldiv()

void bigintmat::skaldiv

(

number

b

)

Macht Ganzzahldivision aller Matrixeinträge mit b.

Definition at line 1862 of file bigintmat.cc.

{
  number tmp1, tmp2;
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      tmp1 = view(i, j);
      tmp2 = n_Div(tmp1, b, basecoeffs());
      rawset(i, j, tmp2);
    }
  }
}

skalmult()

bool bigintmat::skalmult	(	number	b,
		coeffs	c
	)

Multipliziert zur Matrix den Skalar b hinzu.

Definition at line 939 of file bigintmat.cc.

{
  if (!nCoeffs_are_equal(c, basecoeffs()))
  {
    WerrorS("Wrong coeffs\n");
    return false;
  }
  number t1, t2;
  if ( n_IsOne(b,c)) return true;
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      t1 = view(i, j);
      t2 = n_Mult(t1, b, basecoeffs());
      rawset(i, j, t2);
    }
  }
  return true;
}

splitcol() [1/2]

void bigintmat::splitcol	(	bigintmat *	a,
		bigintmat *	b
	)

... linken ... rechten ...

Definition at line 1170 of file bigintmat.cc.

{
  int ay = a->cols();
  int ax = a->rows();
  int by = b->cols();
  int bx = b->rows();
  number tmp;
  if (!((row == ax) && (row == bx)))
  {
    WerrorS("Error in splitcol. Dimensions must agree!");
  }
  else if (!(ay+by == col))
  {
    WerrorS("Error in splitcol. Dimensions must agree!");
  }
  else if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs())))
  {
    WerrorS("Error in splitcol. coeffs do not agree!");
  }
  else
  {
    for (int i=1; i<=ax; i++)
    {
      for (int j=1; j<=ay; j++)
      {
        tmp = view(i,j);
        a->set(i,j,tmp);
      }
    }
    for (int i=1; i<=bx; i++)
    {
      for (int j=1; j<=by; j++)
      {
        tmp = view(i,j+ay);
        b->set(i,j,tmp);
      }
    }
  }
}

splitcol() [2/2]

void bigintmat::splitcol	(	bigintmat *	a,
		int	i
	)

Speichert die ersten i Spalten als Teilmatrix in a.

Definition at line 1210 of file bigintmat.cc.

{
  number tmp;
  if ((a->rows() != row) || (a->cols()+i-1 > col) || (i<1))
  {
    WerrorS("Error in splitcol. Dimensions must agree!");
    return;
  }
  if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs())))
  {
    WerrorS("Error in splitcol. coeffs do not agree!");
    return;
  }
  int width = a->cols();
  for (int j=1; j<=width; j++)
  {
    for (int k=1; k<=row; k++)
    {
      tmp = get(k, j+i-1);
      a->set(k, j, tmp);
      n_Delete(&tmp, basecoeffs());
    }
  }
}

splitrow() [1/2]

void bigintmat::splitrow	(	bigintmat *	a,
		bigintmat *	b
	)

Speichert in Matrix a den oberen, in b den unteren Teil der Matrix, vorausgesetzt die Dimensionen stimmen überein.

Definition at line 1128 of file bigintmat.cc.

{
  int ay = a->cols();
  int ax = a->rows();
  int by = b->cols();
  int bx = b->rows();
  number tmp;
  if (!(ax + bx == row))
  {
    WerrorS("Error in splitrow. Dimensions must agree!");
  }
  else if (!((col == ay) && (col == by)))
  {
    WerrorS("Error in splitrow. Dimensions must agree!");
  }
  else if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs())))
  {
    WerrorS("Error in splitrow. coeffs do not agree!");
  }
  else
  {
    for(int i = 1; i<=ax; i++)
    {
      for(int j = 1; j<=ay;j++)
      {
        tmp = get(i,j);
        a->set(i,j,tmp);
        n_Delete(&tmp, basecoeffs());
      }
    }
    for (int i =1; i<=bx; i++)
    {
      for (int j=1;j<=col;j++)
      {
        tmp = get(i+ax, j);
        b->set(i,j,tmp);
        n_Delete(&tmp, basecoeffs());
      }
    }
  }
}

splitrow() [2/2]

void bigintmat::splitrow	(	bigintmat *	a,
		int	i
	)

... Zeilen ...

Definition at line 1235 of file bigintmat.cc.

{
  number tmp;
  if ((a->cols() != col) || (a->rows()+i-1 > row) || (i<1))
  {
    WerrorS("Error in Marco-splitrow");
    return;
  }
 
  if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs())))
  {
    WerrorS("Error in splitrow. coeffs do not agree!");
    return;
  }
  int height = a->rows();
  for (int j=1; j<=height; j++)
  {
    for (int k=1; k<=col; k++)
    {
      tmp = view(j+i-1, k);
      a->set(j, k, tmp);
    }
  }
}

String()

char * bigintmat::String

(

)

IO: String returns a singular string containing the matrix, needs freeing afterwards.

Definition at line 436 of file bigintmat.cc.

{
  StringSetS("");
  Write();
  return StringEndS();
}

StringAsPrinted()

char * bigintmat::StringAsPrinted

(

)

Returns a string as it would have been printed in the interpreter.

Used e.g. in print functions of various blackbox types.

Definition at line 451 of file bigintmat.cc.

{
  if ((col==0) || (row==0))
    return NULL;
  else
  {
    int * colwid = getwid(80);
    if (colwid == NULL)
    {
      WerrorS("not enough space to print bigintmat");
      WerrorS("try string(...) for a unformatted output");
      return NULL;
    }
    char * ps;
    int slength = 0;
    for (int j=0; j<col; j++)
      slength += colwid[j]*row;
    slength += col*row+row;
    ps = (char*) omAlloc0(sizeof(char)*(slength));
    int pos = 0;
    for (int i=0; i<col*row; i++)
    {
      StringSetS("");
      n_Write(v[i], basecoeffs());
      char * ts = StringEndS();
      const int _nl = strlen(ts);
      int cj = i%col;
      if (_nl > colwid[cj])
      {
        StringSetS("");
        int ci = i/col;
        StringAppend("[%d,%d]", ci+1, cj+1);
        char * ph = StringEndS();
        int phl = strlen(ph);
        if (phl > colwid[cj])
        {
          for (int j=0; j<colwid[cj]-1; j++)
            ps[pos+j] = ' ';
          ps[pos+colwid[cj]-1] = '*';
        }
        else
        {
          for (int j=0; j<colwid[cj]-phl; j++)
            ps[pos+j] = ' ';
          for (int j=0; j<phl; j++)
            ps[pos+colwid[cj]-phl+j] = ph[j];
        }
        omFree(ph);
    }
    else  // Mit Leerzeichen auffüllen und zahl reinschreiben
    {
      for (int j=0; j<(colwid[cj]-_nl); j++)
        ps[pos+j] = ' ';
      for (int j=0; j<_nl; j++)
        ps[pos+colwid[cj]-_nl+j] = ts[j];
    }
    // ", " und (evtl) "\n" einfügen
    if ((i+1)%col == 0)
    {
      if (i != col*row-1)
      {
        ps[pos+colwid[cj]] = ',';
        ps[pos+colwid[cj]+1] = '\n';
        pos += colwid[cj]+2;
      }
    }
    else
    {
      ps[pos+colwid[cj]] = ',';
      pos += colwid[cj]+1;
    }
    omFree(ts);  // Hier ts zerstören
  }
  return(ps);
  // omFree(ps);
}
}

sub()

bool bigintmat::sub

(

bigintmat *

b

)

Subtrahiert ...

Definition at line 917 of file bigintmat.cc.

{
 if ((b->rows() != row) || (b->cols() != col))
 {
   WerrorS("Error in bigintmat::sub. Dimensions do not agree!");
   return false;
  }
  if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs()))
  {
    WerrorS("Error in bigintmat::sub. coeffs do not agree!");
    return false;
  }
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      rawset(i, j, n_Sub(view(i,j), b->view(i,j), basecoeffs()));
    }
  }
  return true;
}

swap()

void bigintmat::swap	(	int	i,
		int	j
	)

swap columns i and j

Definition at line 686 of file bigintmat.cc.

{
  if ((i <= col) && (j <= col) && (i>0) && (j>0))
  {
    number tmp;
    number t;
    for (int k=1; k<=row; k++)
    {
      tmp = get(k, i);
      t = view(k, j);
      set(k, i, t);
      set(k, j, tmp);
      n_Delete(&tmp, basecoeffs());
    }
  }
  else
    WerrorS("Error in swap");
}

swapMatrix()

void bigintmat::swapMatrix

(

bigintmat *

a

)

Definition at line 1567 of file bigintmat.cc.

{
  int n = rows(), m = cols();
  row = a->rows();
  col = a->cols();
  number * V = v;
  v = a->v;
  a->v = V;
  a->row = n;
  a->col = m;
}

swaprow()

void bigintmat::swaprow	(	int	i,
		int	j
	)

swap rows i and j

Definition at line 705 of file bigintmat.cc.

{
  if ((i <= row) && (j <= row) && (i>0) && (j>0))
  {
    number tmp;
    number t;
    for (int k=1; k<=col; k++)
    {
      tmp = get(i, k);
      t = view(j, k);
      set(i, k, t);
      set(j, k, tmp);
      n_Delete(&tmp, basecoeffs());
    }
  }
  else
    WerrorS("Error in swaprow");
}

trace()

number bigintmat::trace

(

)

the trace ....

Definition at line 1499 of file bigintmat.cc.

{
  assume (col == row);
  number t = get(1,1),
         h;
  coeffs r = basecoeffs();
  for(int i=2; i<= col; i++) {
    h = n_Add(t, view(i,i), r);
    n_Delete(&t, r);
    t = h;
  }
  return t;
}

transpose()

bigintmat * bigintmat::transpose

(

)

Definition at line 37 of file bigintmat.cc.

{
  bigintmat * t = new bigintmat(col, row, basecoeffs());
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      t->set(j, i, BIMATELEM(*this,i,j));
    }
  }
  return t;
}

view() [1/2]

number bigintmat::view

(

int

i

)

const

view an entry. NOTE: starts at [0]

Definition at line 111 of file bigintmat.cc.

{
  assume (i >= 0);
  assume (i<rows()*cols());
 
  return v[i];
}

view() [2/2]

number bigintmat::view	(	int	i,
		int	j
	)		const

view an entry an entry. NOTE: starts at [1,1]

Definition at line 127 of file bigintmat.cc.

{
  assume (i >= 0 && j >= 0);
  assume (i <= rows() && j <= cols());
 
  return view(index(i, j));
}

Write()

void bigintmat::Write

(

)

IO: writes the matrix into the current internal string buffer which must be started/ allocated before (e.g. StringSetS)

Definition at line 413 of file bigintmat.cc.

{
  int n = cols(), m=rows();
 
  StringAppendS("[ ");
  for(int i=1; i<= m; i++)
  {
    StringAppendS("[ ");
    for(int j=1; j< n; j++)
    {
      n_Write(v[(i-1)*n+j-1], basecoeffs());
      StringAppendS(", ");
    }
    if (n) n_Write(v[i*n-1], basecoeffs());
    StringAppendS(" ]");
    if (i<m)
    {
      StringAppendS(", ");
    }
  }
  StringAppendS(" ] ");
}

zero()

void bigintmat::zero

(

)

Setzt alle Einträge auf 0.

Definition at line 1351 of file bigintmat.cc.

{
  number tmp = n_Init(0, basecoeffs());
  for (int i=1; i<=row; i++)
  {
    for (int j=1; j<=col; j++)
    {
      set(i, j, tmp);
    }
  }
  n_Delete(&tmp,basecoeffs());
}

Field Documentation

col

int bigintmat::col

private

Definition at line 56 of file bigintmat.h.

m_coeffs

coeffs bigintmat::m_coeffs

private

Definition at line 53 of file bigintmat.h.

row

int bigintmat::row

private

Definition at line 55 of file bigintmat.h.

v

number* bigintmat::v

private

Definition at line 54 of file bigintmat.h.

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The documentation for this class was generated from the following files:

• libpolys/coeffs/bigintmat.h
• libpolys/coeffs/bigintmat.cc