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COMMENT:
#################################################################
VECTOR
#################################################################

This is a basic objecttype of SYMMETRICA. A VECTOR object consists
of two parts. A part, which is a INTEGER object, the
length of the vector, and a second part, which is an array
of objects. Let us first look at the construction of a
VECTOR object. Look at the following program

	EXAMPLE:
	#include "def.h"
	#include "macro.h"
	main()
	{
	OP a;
	anfang();
	a = callocobject();
	m_il_v(8L,a);
	println(a);
	freeall(a);
	ende();
	}

The routine m_il_v() builds an VECTOR object with eight empty objects.
The output will be

[#,#,#,#,#,#,#,#]

The complete description follows

NAME:         
	m_il_v
SYNOPSIS:    
	 INT m_il_v(INT length; OP vectorobject)
MACRO:
	 M_IL_V
DESCRIPTION:  
	builds an vector of the given length. First there is
	a check whether vectorobject is a empty object, if this
        is not the case it is freed.
	Moreover, there is the allocation of the given number of 
        objects, which are set to empty objects.
	The macro M_IL_V does the same but without any checks.
RETURN:
		      the returnvalue is OK, ERROR if some error occured, e.g.
	not enough memory for the objects.


COMMENT:
There is the routine/macro b_il_v/B_IL_V which is the same. 
There is also the routine, where you enter an INTEGER object, and you
will get a VECTOR object with such length.
.
.
.
scan(INTEGER,a);
b_l_v(a,b);
println(b);
.
.
.
Here the INTEGER object a becomes the length part of the VECTOR object b, 
so if you delete the VECTOR object using freeall(), or freeself(), you
can no longer access the INTEGER object a, because it was freed as part
of the VECTOR object b. If you want to avoid this, you must the 
make-construktor, which does a copy:
.
.
.
scan(INTEGER,a);
m_l_v(a,b);
println(b);
.
.
.
Here you can free the VECTOR object b, and you have still an INTEGER object
a. This method is easier for you, but you need more
memory for data. Now we are ready for 
the complete description of these two routines

NAME:
              b_l_v 
SYNOPSIS:     
              INT b_l_v(OP length, vectorobject)
DESCRIPTION: 
	 builds an vector of the given length. First there is
	a check whether vectorobject is a empty object, if not it is freed.
	Then there is a check whether length is an INTEGER object.
	Then there is the allocation of the given number of objects, which
	are set to empty objects. Using b_l_v length will be the
	length part of the VECTOR object. Using m_l_v a copy of the
	INTEGER object length will be the length part of the VECTOR object.
RETURN:
		      the returnvalue is OK, ERROR if some error occured, e.g.
	not enough memory for the objects.

NAME:  	
       m_l_v 
SYNOPSIS:     
	INT m_l_v(OP length, vectorobject)
DESCRIPTION: 
	 builds an vector of the given length. First there is
	a check whether vectorobject is a empty object, if not it is freed.
	Then there is a check whether length is an INTEGER object.
	Then there is the allocation of the given number of objects, which
	are set to empty objects. Using b_l_v length will be the
	length part of the VECTOR object. Using m_l_v a copy of the
	INTEGER object length will be the length part of the VECTOR object.
RETURN:
		      the returnvalue is OK, ERROR if some error occured, e.g.
	not enough memory for the objects.

COMMENT:
There are the special cases, where you have one object and you 
want to build a vector, whose single component is this object:

NAME:
              b_o_v 
SYNOPSIS:     
              INT b_o_v(OP object,vector)
DESCRIPTION:
	  builds an vector of length one, whose entry is the
        object. The object is copied in m_o_v, is not copied in
        b_o_v. The vector is first freed to an empty object.
	In the routine m_o_v the two parameters may be equal, in
	b_o_v they must be different
RETURN:
	       the returnvalue is OK, ERROR if some ERROR occured.


NAME:
         m_o_v  
SYNOPSIS:     
	INT m_o_v(OP object,vector)
DESCRIPTION:
	  builds an vector of length one, whose entry is the
        object. The object is copied in m_o_v, is not copied in
        b_o_v. The vector is first freed to an empty object.
	In the routine m_o_v the two parameters may be equal, in
	b_o_v they must be different
RETURN:
	       the returnvalue is OK, ERROR if some ERROR occured.

COMMENT:
These are the routines for the construction of VECTOR objects, now we
come to routines for the selection of parts. The following program
uses these routines

	EXAMPLE:
	#include "def.h"
	#include "macro.h"
	main()
	{
	OP a;
	anfang();
	a = callocobject();
	m_il_v(8L,a);
	m_i_i(5L,s_v_i(a,3L));
	println(s_v_i(a,2L));
	println(s_v_l(a));
	printf("%ld\n",s_v_li(a)+3L);
	freeall(a);
	ende();
	}

The routine s_v_i(), selects the i_th object of the vector, the routine
s_v_l() selects the length of a VECTOR object, and as you know that this
an INTEGER object you can access the INTvalue of the length with s_v_li().
So the output of the above programm, will be the following three lines

#
8
11

There are also routines, which allow you to access the pointer to the array
of objects, this is the routine s_v_s(), and if you know that the entries
of the VECTOR object are INTEGER objects you can access their INTvalues using
s_v_ii(). Here is the complete description:

NAME:         
	s_v_l           select_vectorobject_length
  s_v_li          select_vectorobject_lengthinteger
SYNOPSIS:
	     OP s_v_l(OP vectorobject)
       INT s_v_li(OP vectorobject)
MACRO:
	S_V_L
	S_V_LI
DESCRIPTION:
	  selects the length of an VECTOR object. There is first a 
	check whether it is really an VECTOR object. There is also a 
	check whether the length is a not negative number.
	The macro versions do the same but without checks.
RETURN:
		      s_v_l gives the length part of the VECTOR object, this is
	an INTEGER object, it is not a copy of the length part.
	s_v_li gives the INTvalue of the length part. It is equivalent
	to s_i_i(s_v_l()). If an error occured s_v_l returns NULL
	and s_v_li() returns ERROR.

COMMENT:
To access the parts of the VECTOR object, there is the routine s_v_i(),
and the routine s_v_ii(), which gives you the INTvalue, of the
i-th object of the VECTOR object, which must be an INTEGER object.

NAME:
         s_v_i
SYNOPSIS: 
    OP s_v_i(OP vectorobject; INT index)
MACRO:
	S_V_I
DESCRIPTION:
  selects the ith entry of an VECTOR object. There is first a 
	check whether it is really an VECTOR object. Then there is a check
	whether index is a value inside the length.
	As the VECTOR object is indexed by INT-numbers there is a 
	(theoretical) limit on the size of a VECTOR object, namely
	there a maximal 2^31 elements.
	The macro version does the same but without checks.
RETURN:
	s_v_i gives the ith  entry of the VECTOR object. In the case
	of an error it returns NULL. 

NAME:
    s_v_ii
SYNOPSIS: 
    INT s_v_ii(OP vectorobject; INT index)
MACRO:
	S_V_II
DESCRIPTION:
  selects the INT value of the
	ith entry of an VECTOR object. There is first a 
	check whether it is really an VECTOR object. Then there is a check
	whether index is a value inside the length. And a last check
	wether the ith- is a INTEGER object.
	As the VECTOR object is indexed by INT-numbers there is a 
	(theoretical) limit on the size of a VECTOR object, namely
	there a maximal 2^31 elements.
	The macro version does the same but without checks.
RETURN:	      
	s_v_ii gives the INT value of the
	ith  entry of the VECTOR object. 


NAME:
         init_vector
SYNOPSIS:   
  INT init_vector(OP a)
DESCRIPTION:
	this is the subroutine  of the global routine init, which is called
	if
  you can call the general routine init()
        described in rest.doc with the OBJECTKIND VECTOR as
        first parameter, after that the object a will be an 
        VECTOR object with length 0 and the self part is equal 
        to NULL.

COMMENT:
Very often it happens, that you want to initialize the VECTOR
object with zeros.

NAME: 
	        m_il_nv
SYNOPSIS:     
	INT m_il_nv(INT il, OP v)
DESCRIPTION:  
	like the routines m_il_v but the elements
        in the VECTOR object v are INTEGER objects with value 0.

EXAMPLE:
	.
	.
	a = callocobject();
	m_il_nv(2L,a);
	if (nullp(S_V_I(a,1L)))
		printf("the second entry is zero\n");
	freeall(a);
        .
	.
	will produce the line
			the second entry is zero
	on the terminal.


NAME: 
              m_l_nv 
SYNOPSIS:     
              INT m_l_nv(OP l, OP v)
DESCRIPTION:  
	like the routine  m_l_v  but the elements
        in the VECTOR object v are INTEGER objects with value 0.

NAME: 
              b_l_nv 
SYNOPSIS:     
              INT b_l_nv(OP l, OP v)
DESCRIPTION:
	like the routine  b_l_v  but the elements
        in the VECTOR object v are INTEGER objects with value 0.

NAME:
	comp_numeric_vector
SYNOPSIS:	
	INT comp_numeric_vector(OP a,b)
DESCRIPTION:	
	a special routine for the comparision of two VECTOR
	objects with INTEGER entries. If the length of the VECTOR
	objects a and b differs, the smaller is filled temporarily
	with zero entries and the routine does a lexicographic
	comparision.
RETURN:		
	0 if equal, -1 if a is smaller, 1 if a is bigger

NAME:		
	comp_colex_vector
SYNOPSIS:	
	INT comp_colex_vector(OP a,b)
DESCRIPTION:	
	comparison by reading the VECTOR objects from the end



NAME:         
	add_apply_vector
SYNOPSIS:     
	INT add_apply_vector(OP a,b)
DESCRIPTION:  
	a,b should be two VECTOR objects, and the routine
        computes b = b+a, where the addition of the two vectors is
        componentwise. This also works, if the VECTOR objects have
        different length. a,b must be different objects.
	This is a subroutine of the general routine add_apply
RETURN:
       OK, or ERROR if some error occures.
BUG:
          there is no check on typs, because this is a special 
        routine, normally you should use add_apply instead.


NAME:         
	add_vector
SYNOPSIS:
	     INT add_vector(OP a,b,c)
DESCRIPTION:
	  a,b should be VECTOR objects, c should be a empty object.
        The routine computes c = a+b. The addition is componentwise,
        and it also works if the vectors have different length.
	a,b,c must all be different
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use add instead.



NAME:  
	       addinvers_apply_vector
SYNOPSIS:
	     INT addinvers_apply_vector(OP a)
DESCRIPTION:
	  a should be a VECTOR object. The routine computes
        a = -a. This is also meant componentwise.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use addinvers_apply instead.



NAME:  
	       addinvers_vector
SYNOPSIS:
	     INT addinvers_vector(OP a,b)
DESCRIPTION:
	  a should be a VECTOR object. b should be a empty
        object. The routine computes b = -a. This is meant componentwise.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use addinvers instead.


NAME:  
	       addtoallvectorelements
SYNOPSIS:
	     INT addtoallvectorelements(OP a,b,c)
DESCRIPTION:
	  b should be a vector, the routine adds a to all the 
        elements of b, the result will become c.
RETURN:
	OK or ERROR
BUG:   
	       it only works for different a,b,c


NAME:	     
	 einsp_vector
SYNOPSIS:
	     INT einsp_vector(OP a)
DESCRIPTION:
	  return TRUE if all entries of the VECTOR object are
	unity. Else the return value is FALSE
BUG:
		      this is a special routine, you should better use the
	general routine einsp.

NAME:  
	       mult_scalar_vector
SYNOPSIS:
	     INT mult_scalar_vector(OP a,b,c)
DESCRIPTION:
	  b should be a VECTOR object, c should be an empty object.
        The routine multiplies each element of b by a, and the result
        is c.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use mult instead.



NAME:  
	       mult_apply_vector_vector
SYNOPSIS:
	     INT mult_apply_vector_vector(OP a,b)
DESCRIPTION:
	  a,b should be VECTOR objects,
        The routine multiplies componentwise, and the result
        is b. The vectors must be of the same length.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use mult_apply instead.


NAME:  
	       mult_vector_matrix
SYNOPSIS:
	     INT mult_vector_matrix(OP a,b,c)
DESCRIPTION:
	  a should be a VECTOR object, b should be a 
	MATRIX object, c should be an empty object.
        The routine multiplies according to the rules for the
	mutiplication of matrices, and the result becomes
        a VECTOR object. The length of the VECTOR object a must be 
	equal to the height of the MATRIX object b.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use mult instead.

NAME:  
	       mult_vector_vector
SYNOPSIS:
	     INT mult_vector_vector(OP a,b,c)
DESCRIPTION:
	  a,b should be VECTOR objects, c should be an empty object.
        The routine multiplies componentwise, and the result
        is c. The vectors must be of the same length.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use mult instead.


NAME:
		      nullp_vector
SYNOPSIS:
	     INT nullp_vector(OP a)
DESCRIPTION:
	  return TRUE if all entries of the VECTOR object are
	zero. Else the return value is FALSE
BUG:
		      this is a special routine, you should better use the
	general routine nullp.

NAME:  
	       scalarproduct_vector
SYNOPSIS:
	     INT scalarproduct_vector(OP a,b,c)
DESCRIPTION:
	  a,b should be VECTOR objects, c should be the empty
        object. a and b must have the same length. c becomes the
        euclidian scalarproduct of a and b.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use scalarproduct instead.


NAME:  
	       sum_vector
SYNOPSIS:
	     INT sum_vector(OP a,b)
DESCRIPTION:
	  a should be a VECTOR object, b should be the empty
        object. b becomes the sum over the vector a.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use sum instead.





NAME:
	         append_vector
SYNOPSIS:
	     INT append_vector(OP a,b,c)
DESCRIPTION:
	  a,b should be VECTOR objects, c the empty object.
        The routine bulids an new VECTOR object c, where the
        first part is a copy of a and the second part a copy of
        b. All three parameter must be different.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use append instead.

NAME:  
	       comp_vector
SYNOPSIS:
	     INT comp_vector(OP a,b)
DESCRIPTION:
	  a,b should be VECTOR objects, the routine does
        lexikographic comparision.
RETURN:
	       0 = equal <0  if a <b  >0 if a>b
BUG:   
	       there is no check on typs, because this is a special 
        routine, normally you should use comp instead.

NAME:  
	       copy_vector
SYNOPSIS:
	     INT copy_vector(OP a,b)
DESCRIPTION:
	  a should be a VECTOR object, b the empty object.
        b becomes a copy of a. a and b must be different. This
	routine is called by other copy routines,
	which copy objects with VECTOR type components.
RETURN:
	       OK, or ERROR
BUG:   
	       there is no check on typs, and there is no check
	whether a nd b are different. Because this is a special 
        routine, normaly you should use copy instead.

NAME:
			find_vector
SYNOPSIS:
		OP find_vector(OP a,b)
DESCRIPTION:
	none
RETURN:
	returns NULL if there is no object in the VECTOR object b,
	which is equal to the object a. If such a object exists,
	the result is the object in the vector, not a copy of
	it, so you should not remove the result of this routine.

NAME:
			index_vector
SYNOPSIS:
		INT index_vector(OP a,b)
DESCRIPTION:
	none
RETURN:
	returns -1L if there is no object in the VECTOR object b,
	which is equal to the object a. If such a object exists,
	the result is the index in the vector. So the result is
	always smaller then the length of the VECTOR object b.





COMMENT:

	INTEGERVECTOR
	 
	this is a special type of VECTOR object, where we now for
	sure, that all the parts are INTEGER objects, so all the
	routines for VECTOR objects can be applied, but the general 
	routines like add etc., can call special functions which may be
	faster.

	BITVECTOR

	this is a type which is simliar to VECTOR objects, but not
	compatibel.