59 size_t s=((size_t)r)*((size_t)c)*
sizeof(
poly);
78 for (i=m*n-1; i>=0; i--)
101 for (i=m*n-1; i>=0; i--)
123 int i=
si_min(r,c), n = c*(i-1)+i-1, inc = c+1;
148 for (k=
m*n-1; k>0; k--)
160 for (k=
m*n-1; k>0; k--)
177 for (k=
m*n-1; k>0; k--)
198 for (k=
m*n-1; k>=0; k--)
215 for (k=
m*n-1; k>=0; k--)
251 if ( (*cij)==
NULL) (*cij)=
s;
252 else (*cij) =
p_Add_q((*cij) ,s, R);
329 for (i=
IDELEMS(I)-1; i>=0; i--)
342 for (i=
IDELEMS(I)-1; i>=0; i--)
358 MATELEM(co,(c-1)*(m+1)+l+1,i+1)
496 for (i=1; i<=
rVar(R); i++)
627 if (p2==
NULL)
return p1;
633 c =
p_Cmp(a1, a2, R);
687 for (i=1; i<=
rVar(R); i++)
718 for (i=lr-1;i>=0;i--)
721 for (j=lc-1;j>=0;j--)
if(q1[j])
p_Delete(&q1[j], R);
749 for (i=0; i<=ii; i++)
751 for (j=0; j<=jj; j++)
754 Print(
"%-*.*s",spaces,spaces,
" ");
755 if (dim == 2)
Print(
"%s[%u,%u]=",n,i+1,j+1);
756 else if (dim == 1)
Print(
"%s[%u]=",n,j+1);
757 else if (dim == 0)
Print(
"%s=",n);
758 if ((i<ii)||(j<jj))
p_Write(*pp++, r);
785 s[strlen(s)- (dim > 1 ? 2 : 1)]=
'\0';
837 int a_m, a_n, s_m, s_n,
sign, piv_s;
843 {
return &(Xarray[a_n*qrow[
r]]); }
845 {
return &(Xarray[qcol[c]]); }
846 void mpRowWeight(
float *);
847 void mpColWeight(
float *);
848 void mpRowSwap(
int,
int);
849 void mpColSwap(
int,
int);
860 void mpSetSearch(
int s);
862 poly mpGetElem(
int,
int);
863 void mpSetElem(
poly,
int,
int);
864 void mpDelElem(
int,
int);
865 void mpElimBareiss(
poly);
868 void mpToIntvec(
intvec *);
892 for (i=
a_m-1; i>=0; i--)
896 for (j=
a_n-1; j>=0; j--)
917 for (k=
a_m*
a_n-1; k>=0; k--)
932 for (j=
s_n; j>=0; j--)
936 for(i=
s_m; i>=0; i--)
951 for (i=
s_m; i>=0; i--)
955 for(j=
s_n; j>=0; j--)
972 for (j=
a_n-1; j>= 0; j--)
987 for (i=0; i<
k; i+=
a_n)
1003 for (k=
a_m-1; k>=0; k--)
qrow[k] = k;
1004 for (k=
a_n-1; k>=0; k--)
qcol[k] = k;
1015 for (j=
a_n-1; j>=
k; j--)
1022 while (
qcol[j2] != j) j2++;
1036 for (i=
a_m-1; i>=
k; i--)
1043 while (
qrow[i2] != i) i2++;
1071 int i,
j, iopt, jopt;
1072 float sum, f1, f2, fo,
r, ro, lp;
1073 float *dr = C->
wrow, *dc = C->
wcol;
1085 for(i=
s_m; i>=0; i--)
1109 for(i=
s_m; i>=0; i--)
1111 for(i=
s_m; i>=0; i--)
1115 for(j=
s_n; j>=0; j--)
1122 f1 = ro * (dc[
j]-lp);
1125 f2 = lp * (sum - ro - dc[
j]);
1155 poly piv, elim, q1, q2, *ap, *
a;
1160 for(i=
s_m-1; i>=0; i--)
1163 elim = a[qcol[
s_n]];
1167 for (j=
s_n-1; j>=0; j--)
1181 else if (a[jj] !=
NULL)
1185 if ((q2!=
NULL) && div)
1193 for (j=
s_n-1; j>=0; j--)
1219 for (i=r->N;i>0;i--)
1251 for (i=lr-1;i>=0;i--)
1253 q1 = &(a->
m)[i*a->
ncols];
1255 for (j=lc-1;j>=0;j--)
1260 if ((f2!=0.0) && (f2<f1))
1277 a2 = &a2[a->
ncols*(lr-1)];
1278 for (j=lc-1; j>=0; j--)
1311 q1 = &(a->
m)[(lr-1)*a->
ncols];
1312 for (j=lc-1;j>=0;j--)
1333 poly* a1 = &a2[pos-1];
1362 poly piv, elim, q1, *ap, *
a, *q;
1365 ap = &b[r*a0->
ncols];
1367 for(j=c-1; j>=0; j--)
1369 for(i=r-1; i>=0; i--)
1371 a = &b[i*a0->
ncols];
1376 for (j=c-1; j>=0; j--)
1388 else if (ap[j] !=
NULL)
1400 for (j=c-1; j>=0; j--)
1417 ideal
R,
const ring)
1425 for (i=r-1;i>=0;i--)
1427 q1 = &(a->
m)[i*a->
ncols];
1434 for (i=r-1;i>=0;i--)
1436 q1 = &(a->
m)[i*a->
ncols];
1437 for (j=c-1;j>=0;j--)
1447 result->m[elems] = q1[
j];
1513 poly barDiv, ideal
R,
const ring
r)
1516 int kr=lr-1,kc=lc-1;
1663 int *rowchoise,*colchoise;
1672 rowchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1673 colchoise=(
int *)
omAlloc(ar*
sizeof(
int));
1674 result =
mpNew(i,j);
1684 for (i=1; i<=ar; i++)
1686 for (j=1; j<=ar; j++)
1692 if ((k+l) & 1) p=
p_Neg(p, R);
1702 for (i=1; i<=ar; i++)
1722 for(
int i=0;
i<
l;
i++)
1734 for(
int j=0;
j<q;
j++)
1752 res->m[col+
i]=
p_Add_q(res->m[col+
i],sm->m[
i],r);
1766 for(
int i=0;
i<n;
i++)
1768 memset(a,0,m*
sizeof(
poly));
1770 for(
int j=0;
j<
m;
j++)
BOOLEAN rHasLocalOrMixedOrdering(const ring r)
int status int void size_t count
matrix mp_CoeffProc(poly f, poly vars, const ring R)
const CanonicalForm int s
void sm_SpecialPolyDiv(poly a, poly b, const ring R)
poly prCopyR_NoSort(poly p, ring src_r, ring dest_r)
static int p_Cmp(poly p1, poly p2, ring r)
static poly mp_Select(poly fro, poly what, const ring)
static int si_min(const int a, const int b)
matrix mp_InitP(int r, int c, poly p, const ring R)
make it a p * unit matrix
static int mp_PivBar(matrix a, int lr, int lc, const ring r)
matrix mp_Coeffs(ideal I, int var, const ring R)
corresponds to Maple's coeffs: var has to be the number of a variable
static ideal mp_MultAndShift(poly f, ideal B, int s, const ring r)
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
poly mp_Trace(matrix a, const ring R)
void mp_RecMin(int ar, ideal result, int &elems, matrix a, int lr, int lc, poly barDiv, ideal R, const ring r)
produces recursively the ideal of all arxar-minors of a
static void mp_ElimBar(matrix a0, matrix re, poly div, int lr, int lc, const ring R)
#define omFreeSize(addr, size)
static BOOLEAN p_IsUnit(const poly p, const ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
#define omfreeSize(addr, size)
void mpColWeight(float *)
static void mpFinalClean(matrix a)
static poly mp_Exdiv(poly m, poly d, poly vars, const ring)
static int mp_PrepareRow(matrix a, int lr, int lc, const ring R)
void mpRowWeight(float *)
static void mp_PartClean(matrix a, int lr, int lc, const ring R)
void mp_MinorToResult(ideal result, int &elems, matrix a, int r, int c, ideal R, const ring)
entries of a are minors and go to result (only if not in R)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
int mpPivotBareiss(row_col_weight *)
static void p_DecomposeComp(poly p, poly *a, int l, const ring r)
ideal mp_Tensor(ideal A, ideal B, const ring r)
poly p_Sub(poly p1, poly p2, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
void iiWriteMatrix(matrix im, const char *n, int dim, const ring r, int spaces)
set spaces to zero by default
static void mpSwapCol(matrix a, int pos, int lr, int lc)
static void mpReplace(int j, int n, int &sign, int *perm)
matrix mp_Transp(matrix a, const ring R)
static poly p_Head(poly p, const ring r)
static int mp_PreparePiv(matrix a, int lr, int lc, const ring r)
matrix mp_Wedge(matrix a, int ar, const ring R)
for(int i=0;i< R->ExpL_Size;i++) Print("%09lx "
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
static BOOLEAN p_IsConstant(const poly p, const ring r)
void StringSetS(const char *st)
static poly pp_Mult_qq(poly p, poly q, const ring r)
void StringAppendS(const char *st)
matrix mp_MultI(matrix a, int f, const ring R)
c = f*a
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
matrix pMultMp(poly p, matrix a, const ring R)
static int si_max(const int a, const int b)
int p_Compare(const poly a, const poly b, const ring R)
static unsigned pLength(poly a)
void mp_Delete(matrix *a, const ring r)
static poly pReverse(poly p)
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
matrix mpNew(int r, int c)
create a r x c zero-matrix
void p_Normalize(poly p, const ring r)
void p_Write0(poly p, ring lmRing, ring tailRing)
static void p_Delete(poly *p, const ring r)
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
ideal idInit(int idsize, int rank)
initialise an ideal / module
const Variable & v
< [in] a sqrfree bivariate poly
matrix mp_Mult(matrix a, matrix b, const ring R)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
static void mpSwapRow(matrix a, int pos, int lr, int lc)
void mp_Coef2(poly v, poly mon, matrix *c, matrix *m, const ring R)
corresponds to Macauley's coef: the exponent vector of vars has to contain the variables, eg 'xy'; then the poly f is searched for monomials in x and y, these monimials are written to the first row of the matrix co. the second row of co contains the respective factors in f. Thus f = sum co[1,i]*co[2,i], i = 1..cols, rows equals 2.
matrix mp_InitI(int r, int c, int v, const ring R)
make it a v * unit matrix
void mp_Monomials(matrix c, int r, int var, matrix m, const ring R)
matrix mp_Add(matrix a, matrix b, const ring R)
void pEnlargeSet(poly **p, int l, int increment)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
BOOLEAN mp_IsDiagUnit(matrix U, const ring R)
static void p_Setm(poly p, const ring r)
poly sm_MultDiv(poly a, poly b, const poly c, const ring R)
BOOLEAN mp_Equal(matrix a, matrix b, const ring R)
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
static void mp_AddSubMat(ideal res, ideal sm, int col, const ring r)
static poly p_Neg(poly p, const ring r)
static void p_LmDelete(poly p, const ring r)
int mp_Compare(matrix a, matrix b, const ring R)
void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
poly TraceOfProd(matrix a, matrix b, int n, const ring R)
void p_Write(poly p, ring lmRing, ring tailRing)
matrix mp_Sub(matrix a, matrix b, const ring R)
static poly p_Add_q(poly p, poly q, const ring r)
#define omFreeBin(addr, bin)
char * iiStringMatrix(matrix im, int dim, const ring r, char ch)
static float mp_PolyWeight(poly p, const ring r)
static FORCE_INLINE int n_Size(number n, const coeffs r)
return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used fo...
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
static poly p_Mult_q(poly p, poly q, const ring r)
static poly p_Insert(poly p1, poly p2, const ring R)
void Werror(const char *fmt,...)
#define MATELEM(mat, i, j)
static int mp_PivRow(matrix a, int lr, int lc, const ring r)