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Add accessors for RCF numeral internals (#7013)

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Christoph M. Wintersteiger 2023-11-23 16:54:23 +00:00 committed by GitHub
parent 9382b96a32
commit 16753e43f1
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7 changed files with 845 additions and 117 deletions
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49
examples/ml/ml_example.ml
View file

@ -19,7 +19,6 @@ open Z3.Arithmetic.Integer
open Z3.Arithmetic.Real
open Z3.BitVector
exception TestFailedException of string
(**
@ -322,11 +321,58 @@ let rcf_example ( ctx : context ) =
Printf.printf "RCFExample\n" ;
let pi = RCF.mk_pi ctx in
let e = RCF.mk_e ctx in
let inf0 = RCF.mk_infinitesimal ctx in
let inf1 = RCF.mk_infinitesimal ctx in
let r = RCF.mk_rational ctx "42.001" in
let pi_div_e = RCF.div ctx pi e in
let pi_div_r = RCF.div ctx pi r in
(Printf.printf "e: %s, pi: %s, e==pi: %b, e < pi: %b\n"
(RCF.num_to_string ctx e true false)
(RCF.num_to_string ctx pi true false)
(RCF.eq ctx e pi)
(RCF.lt ctx e pi)) ;
Printf.printf "pi_div_e: %s.\n" (RCF.num_to_string ctx pi_div_e true false);
Printf.printf "pi_div_r: %s.\n" (RCF.num_to_string ctx pi_div_r true false);
Printf.printf "inf0: %s.\n" (RCF.num_to_string ctx inf0 true false);
Printf.printf "(RCF.is_rational ctx pi): %b.\n" (RCF.is_rational ctx pi);
Printf.printf "(RCF.is_algebraic ctx pi): %b.\n" (RCF.is_algebraic ctx pi);
Printf.printf "(RCF.is_transcendental ctx pi): %b.\n" (RCF.is_transcendental ctx pi);
Printf.printf "(RCF.is_rational ctx r): %b.\n" (RCF.is_rational ctx r);
Printf.printf "(RCF.is_algebraic ctx r): %b.\n" (RCF.is_algebraic ctx r);
Printf.printf "(RCF.is_transcendental ctx r): %b.\n" (RCF.is_transcendental ctx r);
Printf.printf "(RCF.is_infinitesimal ctx inf0): %b.\n" (RCF.is_infinitesimal ctx inf0);
Printf.printf "(RCF.extension_index ctx inf0): %d.\n" (RCF.extension_index ctx inf0);
Printf.printf "(RCF.extension_index ctx inf1): %d.\n" (RCF.extension_index ctx inf1);
let poly:RCF.rcf_num list = [ e; pi; inf0 ] in
let rs:RCF.root list = RCF.roots ctx poly in
let print_root (x:RCF.root) =
begin
Printf.printf "root: %s\n%!" (RCF.num_to_string ctx x.obj true false);
if RCF.is_algebraic ctx x.obj then (
(match x.interval with
| Some ivl -> Printf.printf " interval: (%b, %b, %s, %b, %b, %s)\n"
ivl.lower_is_inf
ivl.lower_is_open
(RCF.num_to_string ctx ivl.lower true false)
ivl.upper_is_inf
ivl.upper_is_open
(RCF.num_to_string ctx ivl.upper true false);
| None -> ());
Printf.printf " polynomial coefficients:";
List.iter (fun c -> Printf.printf " %s" (RCF.num_to_string ctx c false false)) x.polynomial;
Printf.printf "\n";
Printf.printf " sign conditions:";
List.iter
(fun (poly, sign) ->
List.iter (fun p -> Printf.printf " %s" (RCF.num_to_string ctx p true false)) poly;
Printf.printf " %s" (if sign > 0 then "> 0" else if sign < 0 then "< 0" else "= 0"))
x.sign_conditions;
Printf.printf "\n")
end
in
List.iter print_root rs;
RCF.del_roots ctx rs;
RCF.del_list ctx [pi; e; inf0; inf1; r; pi_div_e; pi_div_r];
Printf.printf "Test passed.\n"
let _ =
@ -365,3 +411,4 @@ let _ =
exit 1
)
;;

135
src/api/api_rcf.cpp
View file

@ -302,4 +302,139 @@ extern "C" {
Z3_CATCH;
}
bool Z3_API Z3_rcf_is_rational(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_is_rational(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).is_rational(to_rcnumeral(a));
Z3_CATCH_RETURN(false);
}
bool Z3_API Z3_rcf_is_algebraic(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_is_algebraic(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).is_algebraic(to_rcnumeral(a));
Z3_CATCH_RETURN(false);
}
bool Z3_API Z3_rcf_is_infinitesimal(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_is_infinitesimal(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).is_infinitesimal(to_rcnumeral(a));
Z3_CATCH_RETURN(false);
}
bool Z3_API Z3_rcf_is_transcendental(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_is_transcendental(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).is_transcendental(to_rcnumeral(a));
Z3_CATCH_RETURN(false);
}
unsigned Z3_API Z3_rcf_extension_index(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_extension_index(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).extension_index(to_rcnumeral(a));
Z3_CATCH_RETURN(false);
}
Z3_symbol Z3_API Z3_rcf_transcendental_name(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_transcendental_name(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return of_symbol(rcfm(c).transcendental_name(to_rcnumeral(a)));
Z3_CATCH_RETURN(of_symbol(symbol::null));
}
Z3_symbol Z3_API Z3_rcf_infinitesimal_name(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_infinitesimal_name(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return of_symbol(rcfm(c).infinitesimal_name(to_rcnumeral(a)));
Z3_CATCH_RETURN(of_symbol(symbol::null));
}
unsigned Z3_API Z3_rcf_num_coefficients(Z3_context c, Z3_rcf_num a)
{
Z3_TRY;
LOG_Z3_rcf_num_coefficients(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).num_coefficients(to_rcnumeral(a));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_coefficient(Z3_context c, Z3_rcf_num a, unsigned i)
{
Z3_TRY;
LOG_Z3_rcf_coefficient(c, a, i);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return from_rcnumeral(rcfm(c).get_coefficient(to_rcnumeral(a), i));
Z3_CATCH_RETURN(nullptr);
}
int Z3_API Z3_rcf_interval(Z3_context c, Z3_rcf_num a, int * lower_is_inf, int * lower_is_open, Z3_rcf_num * lower, int * upper_is_inf, int * upper_is_open, Z3_rcf_num * upper) {
Z3_TRY;
LOG_Z3_rcf_interval(c, a, lower_is_inf, lower_is_open, lower, upper_is_inf, upper_is_open, upper);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r_lower, r_upper;
bool r = rcfm(c).get_interval(to_rcnumeral(a), *lower_is_inf, *lower_is_open, r_lower, *upper_is_inf, *upper_is_open, r_upper);
*lower = from_rcnumeral(r_lower);
*upper = from_rcnumeral(r_upper);
return r;
Z3_CATCH_RETURN(0);
}
unsigned Z3_API Z3_rcf_num_sign_conditions(Z3_context c, Z3_rcf_num a)
{
Z3_TRY;
LOG_Z3_rcf_num_sign_conditions(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).num_sign_conditions(to_rcnumeral(a));
Z3_CATCH_RETURN(0);
}
int Z3_API Z3_rcf_sign_condition_sign(Z3_context c, Z3_rcf_num a, unsigned i)
{
Z3_TRY;
LOG_Z3_rcf_sign_condition_sign(c, a, i);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).get_sign_condition_sign(to_rcnumeral(a), i);
Z3_CATCH_RETURN(0);
}
unsigned Z3_API Z3_rcf_num_sign_condition_coefficients(Z3_context c, Z3_rcf_num a, unsigned i)
{
Z3_TRY;
LOG_Z3_rcf_num_sign_condition_coefficients(c, a, i);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).num_sign_condition_coefficients(to_rcnumeral(a), i);
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_sign_condition_coefficient(Z3_context c, Z3_rcf_num a, unsigned i, unsigned j)
{
Z3_TRY;
LOG_Z3_rcf_sign_condition_coefficient(c, a, i, j);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return from_rcnumeral(rcfm(c).get_sign_condition_coefficient(to_rcnumeral(a), i, j));
Z3_CATCH_RETURN(nullptr);
}
};

82
src/api/ml/z3.ml
View file

@ -2080,6 +2080,7 @@ struct
type rcf_num = Z3native.rcf_num
let del (ctx:context) (a:rcf_num) = Z3native.rcf_del ctx a
let del_list (ctx:context) (ns:rcf_num list) = List.iter (fun a -> Z3native.rcf_del ctx a) ns
let mk_rational (ctx:context) (v:string) = Z3native.rcf_mk_rational ctx v
let mk_small_int (ctx:context) (v:int) = Z3native.rcf_mk_small_int ctx v
@ -2087,7 +2088,9 @@ struct
let mk_e (ctx:context) = Z3native.rcf_mk_e ctx
let mk_infinitesimal (ctx:context) = Z3native.rcf_mk_infinitesimal ctx
let mk_roots (ctx:context) (n:int) (a:rcf_num list) = let n, r = Z3native.rcf_mk_roots ctx n a in r
let mk_roots (ctx:context) (a:rcf_num list) =
let n, r = Z3native.rcf_mk_roots ctx (List.length a) a in
List.init n (fun x -> List.nth r x)
let add (ctx:context) (a:rcf_num) (b:rcf_num) = Z3native.rcf_add ctx a b
let sub (ctx:context) (a:rcf_num) (b:rcf_num) = Z3native.rcf_sub ctx a b
@ -2109,6 +2112,83 @@ struct
let num_to_string (ctx:context) (a:rcf_num) (compact:bool) (html:bool) = Z3native.rcf_num_to_string ctx a compact html
let num_to_decimal_string (ctx:context) (a:rcf_num) (prec:int) = Z3native.rcf_num_to_decimal_string ctx a prec
let get_numerator_denominator (ctx:context) (a:rcf_num) = Z3native.rcf_get_numerator_denominator ctx a
let is_rational (ctx:context) (a:rcf_num) = Z3native.rcf_is_rational ctx a
let is_algebraic (ctx:context) (a:rcf_num) = Z3native.rcf_is_algebraic ctx a
let is_infinitesimal (ctx:context) (a:rcf_num) = Z3native.rcf_is_infinitesimal ctx a
let is_transcendental (ctx:context) (a:rcf_num) = Z3native.rcf_is_transcendental ctx a
let extension_index (ctx:context) (a:rcf_num) = Z3native.rcf_extension_index ctx a
let transcendental_name (ctx:context) (a:rcf_num) = Z3native.rcf_transcendental_name ctx a
let infinitesimal_name (ctx:context) (a:rcf_num) = Z3native.rcf_infinitesimal_name ctx a
let num_coefficients (ctx:context) (a:rcf_num) = Z3native.rcf_num_coefficients ctx a
let get_coefficient (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_coefficient ctx a i
let coefficients (ctx:context) (a:rcf_num) =
List.init (num_coefficients ctx a) (fun i -> Z3native.rcf_coefficient ctx a i)
type interval = {
lower_is_inf : bool;
lower_is_open : bool;
lower : rcf_num;
upper_is_inf : bool;
upper_is_open : bool;
upper : rcf_num;
}
let root_interval (ctx:context) (a:rcf_num) =
let ok, linf, lopen, l, uinf, uopen, u = Z3native.rcf_interval ctx a in
let i:interval = {
lower_is_inf = linf != 0;
lower_is_open = lopen != 0;
lower = l;
upper_is_inf = uinf != 0;
upper_is_open = uopen != 0;
upper = u } in
if ok != 0 then Some i else None
let sign_condition_sign (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_sign_condition_sign ctx a i
let sign_condition_coefficient (ctx:context) (a:rcf_num) (i:int) (j:int) = Z3native.rcf_sign_condition_coefficient ctx a i j
let num_sign_condition_coefficients (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_num_sign_condition_coefficients ctx a i
let sign_condition_coefficients (ctx:context) (a:rcf_num) (i:int) =
let n = Z3native.rcf_num_sign_condition_coefficients ctx a i in
List.init n (fun j -> Z3native.rcf_sign_condition_coefficient ctx a i j)
let sign_conditions (ctx:context) (a:rcf_num) =
let n = Z3native.rcf_num_sign_conditions ctx a in
List.init n (fun i ->
(let nc = Z3native.rcf_num_sign_condition_coefficients ctx a i in
List.init nc (fun j -> Z3native.rcf_sign_condition_coefficient ctx a i j)),
Z3native.rcf_sign_condition_sign ctx a i)
type root = {
obj : rcf_num;
polynomial : rcf_num list;
interval : interval option;
sign_conditions : (rcf_num list * int) list;
}
let roots (ctx:context) (a:rcf_num list) =
let rs = mk_roots ctx a in
List.map
(fun r -> {
obj = r;
polynomial = coefficients ctx r;
interval = root_interval ctx r;
sign_conditions = sign_conditions ctx r})
rs
let del_root (ctx:context) (r:root) =
del ctx r.obj;
List.iter (fun n -> del ctx n) r.polynomial;
List.iter (fun (ns, _) -> del_list ctx ns) r.sign_conditions
let del_roots (ctx:context) (rs:root list) =
List.iter (fun r -> del_root ctx r) rs
end

72
src/api/ml/z3.mli
View file

@ -3558,6 +3558,9 @@ sig
(** Delete a RCF numeral created using the RCF API. *)
val del : context -> rcf_num -> unit
(** Delete RCF numerals created using the RCF API. *)
val del_list : context -> rcf_num list -> unit
(** Return a RCF rational using the given string. *)
val mk_rational : context -> string -> rcf_num
@ -3574,7 +3577,7 @@ sig
val mk_infinitesimal : context -> rcf_num
(** Extract the roots of a polynomial. Precondition: The input polynomial is not the zero polynomial. *)
val mk_roots : context -> int -> rcf_num list -> rcf_num list
val mk_roots : context -> rcf_num list -> rcf_num list
(** Addition *)
val add : context -> rcf_num -> rcf_num -> rcf_num
@ -3624,6 +3627,73 @@ sig
(** Extract the "numerator" and "denominator" of the given RCF numeral.
We have that \ccode{a = n/d}, moreover \c n and \c d are not represented using rational functions. *)
val get_numerator_denominator : context -> rcf_num -> (rcf_num * rcf_num)
(** Return \c true if \c a represents a rational number. *)
val is_rational : context -> rcf_num -> bool
(** Return \c true if \c a represents an algebraic number. *)
val is_algebraic : context -> rcf_num -> bool
(** Return \c true if \c a represents an infinitesimal. *)
val is_infinitesimal : context -> rcf_num -> bool
(** Return \c true if \c a represents a transcendental number. *)
val is_transcendental : context -> rcf_num -> bool
(** Return the index of a field extension. *)
val extension_index : context -> rcf_num -> int
(** Return the name of a transcendental. *)
val transcendental_name : context -> rcf_num -> Symbol.symbol
(** Return the name of an infinitesimal. *)
val infinitesimal_name : context -> rcf_num -> Symbol.symbol
(** Return the number of coefficients in an algebraic number. *)
val num_coefficients : context -> rcf_num -> int
(** Extract a coefficient from an algebraic number. *)
val get_coefficient : context -> rcf_num -> int -> rcf_num
(** Extract the coefficients from an algebraic number. *)
val coefficients : context -> rcf_num -> rcf_num list
(** Extract the sign of a sign condition from an algebraic number. *)
val sign_condition_sign : context -> rcf_num -> int -> int
(** Return the size of a sign condition polynomial. *)
val num_sign_condition_coefficients : context -> rcf_num -> int -> int
(** Extract a sign condition polynomial coefficient from an algebraic number. *)
val sign_condition_coefficient : context -> rcf_num -> int -> int -> rcf_num
(** Extract sign conditions from an algebraic number. *)
val sign_conditions : context -> rcf_num -> (rcf_num list * int) list
(** Extract the interval from an algebraic number. *)
type interval = {
lower_is_inf : bool;
lower_is_open : bool;
lower : rcf_num;
upper_is_inf : bool;
upper_is_open : bool;
upper : rcf_num;
}
val root_interval : context -> rcf_num -> interval option
type root = {
obj : rcf_num;
polynomial : rcf_num list;
interval : interval option;
sign_conditions : (rcf_num list * int) list;
}
val roots : context -> rcf_num list -> root list
val del_root : context -> root -> unit
val del_roots : context -> root list -> unit
end
(** Set a global (or module) parameter, which is shared by all Z3 contexts.

116
src/api/z3_rcf.h
View file

@ -196,6 +196,122 @@ extern "C" {
*/
void Z3_API Z3_rcf_get_numerator_denominator(Z3_context c, Z3_rcf_num a, Z3_rcf_num * n, Z3_rcf_num * d);
/**
\brief Return \c true if \c a represents a rational number.
def_API('Z3_rcf_is_rational', BOOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
bool Z3_API Z3_rcf_is_rational(Z3_context c, Z3_rcf_num a);
/**
\brief Return \c true if \c a represents an algebraic number.
def_API('Z3_rcf_is_algebraic', BOOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
bool Z3_API Z3_rcf_is_algebraic(Z3_context c, Z3_rcf_num a);
/**
\brief Return \c true if \c a represents an infinitesimal.
def_API('Z3_rcf_is_infinitesimal', BOOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
bool Z3_API Z3_rcf_is_infinitesimal(Z3_context c, Z3_rcf_num a);
/**
\brief Return \c true if \c a represents a transcendental number.
def_API('Z3_rcf_is_transcendental', BOOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
bool Z3_API Z3_rcf_is_transcendental(Z3_context c, Z3_rcf_num a);
/**
\brief Return the index of a field extension.
def_API('Z3_rcf_extension_index', UINT, (_in(CONTEXT), _in(RCF_NUM)))
*/
unsigned Z3_API Z3_rcf_extension_index(Z3_context c, Z3_rcf_num a);
/**
\brief Return the name of a transcendental.
\pre Z3_rcf_is_transcendtal(ctx, a);
def_API('Z3_rcf_transcendental_name', SYMBOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
Z3_symbol Z3_API Z3_rcf_transcendental_name(Z3_context c, Z3_rcf_num a);
/**
\brief Return the name of an infinitesimal.
\pre Z3_rcf_is_infinitesimal(ctx, a);
def_API('Z3_rcf_infinitesimal_name', SYMBOL, (_in(CONTEXT), _in(RCF_NUM)))
*/
Z3_symbol Z3_API Z3_rcf_infinitesimal_name(Z3_context c, Z3_rcf_num a);
/**
\brief Return the number of coefficients in an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_num_coefficients', UINT, (_in(CONTEXT), _in(RCF_NUM)))
*/
unsigned Z3_API Z3_rcf_num_coefficients(Z3_context c, Z3_rcf_num a);
/**
\brief Extract a coefficient from an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_coefficient', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(UINT)))
*/
Z3_rcf_num Z3_API Z3_rcf_coefficient(Z3_context c, Z3_rcf_num a, unsigned i);
/**
\brief Extract an interval from an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_interval', INT, (_in(CONTEXT), _in(RCF_NUM), _out(INT), _out(INT), _out(RCF_NUM), _out(INT), _out(INT), _out(RCF_NUM)))
*/
int Z3_API Z3_rcf_interval(Z3_context c, Z3_rcf_num a, int * lower_is_inf, int * lower_is_open, Z3_rcf_num * lower, int * upper_is_inf, int * upper_is_open, Z3_rcf_num * upper);
/**
\brief Return the number of sign conditions of an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_num_sign_conditions', UINT, (_in(CONTEXT), _in(RCF_NUM)))
*/
unsigned Z3_API Z3_rcf_num_sign_conditions(Z3_context c, Z3_rcf_num a);
/**
\brief Extract the sign of a sign condition from an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_sign_condition_sign', INT, (_in(CONTEXT), _in(RCF_NUM), _in(UINT)))
*/
int Z3_API Z3_rcf_sign_condition_sign(Z3_context c, Z3_rcf_num a, unsigned i);
/**
\brief Return the number of sign condition polynomial coefficients of an algebraic number.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_num_sign_condition_coefficients', UINT, (_in(CONTEXT), _in(RCF_NUM), _in(UINT)))
*/
unsigned Z3_API Z3_rcf_num_sign_condition_coefficients(Z3_context c, Z3_rcf_num a, unsigned i);
/**
\brief Extract the j-th polynomial coefficient of the i-th sign condition.
\pre Z3_rcf_is_algebraic(ctx, a);
def_API('Z3_rcf_sign_condition_coefficient', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(UINT), _in(UINT)))
*/
Z3_rcf_num Z3_API Z3_rcf_sign_condition_coefficient(Z3_context c, Z3_rcf_num a, unsigned i, unsigned j);
/**@}*/
/**@}*/

240
src/math/realclosure/realclosure.cpp
View file

@ -2498,6 +2498,35 @@ namespace realclosure {
}
}
/**
\brief Return true if a is an algebraic number.
*/
bool is_algebraic(numeral const & a) {
return is_rational_function(a) && to_rational_function(a)->ext()->is_algebraic();
}
/**
\brief Return true if a represents an infinitesimal.
*/
bool is_infinitesimal(numeral const & a) {
return is_rational_function(a) && to_rational_function(a)->ext()->is_infinitesimal();
}
/**
\brief Return true if a is a transcendental.
*/
bool is_transcendental(numeral const & a) {
return is_rational_function(a) && to_rational_function(a)->ext()->is_transcendental();
}
/**
\brief Return true if a is a rational.
*/
bool is_rational(numeral const & a) {
return a.m_value->is_rational();
}
/**
\brief Return true if a depends on infinitesimal extensions.
*/
@ -3330,6 +3359,151 @@ namespace realclosure {
set(q, _q);
}
unsigned extension_index(numeral const & a) {
if (!is_rational_function(a))
return -1;
return to_rational_function(a)->ext()->idx();
}
symbol transcendental_name(numeral const & a) {
if (!is_transcendental(a))
return symbol();
return to_transcendental(to_rational_function(a)->ext())->m_name;
}
symbol infinitesimal_name(numeral const & a) {
if (!is_infinitesimal(a))
return symbol();
return to_infinitesimal(to_rational_function(a)->ext())->m_name;
}
unsigned num_coefficients(numeral const & a) {
if (!is_algebraic(a))
return 0;
return to_algebraic(to_rational_function(a)->ext())->p().size();
}
numeral get_coefficient(numeral const & a, unsigned i)
{
if (!is_algebraic(a))
return numeral();
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
if (i >= ext->p().size())
return numeral();
value_ref v(*this);
v = ext->p()[i];
numeral r;
set(r, v);
return r;
}
unsigned num_sign_conditions(numeral const & a) {
unsigned r = 0;
if (is_algebraic(a)) {
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
const sign_det * sdt = ext->sdt();
if (sdt) {
sign_condition * sc = sdt->sc(ext->sc_idx());
while (sc) {
r++;
sc = sc->prev();
}
}
}
return r;
}
int get_sign_condition_sign(numeral const & a, unsigned i)
{
if (!is_algebraic(a))
return 0;
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
const sign_det * sdt = ext->sdt();
if (!sdt)
return 0;
else {
sign_condition * sc = sdt->sc(ext->sc_idx());
while (i) {
if (sc) sc = sc->prev();
i--;
}
return sc ? sc->sign() : 0;
}
}
bool get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper)
{
if (!is_algebraic(a))
return false;
lower = numeral();
upper = numeral();
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
mpbqi &ivl = ext->iso_interval();
lower_is_inf = ivl.lower_is_inf();
lower_is_open = ivl.lower_is_open();
if (!m_bqm.is_zero(ivl.lower()))
set(lower, mk_rational(ivl.lower()));
upper_is_inf = ivl.upper_is_inf();
upper_is_open = ivl.upper_is_open();
if (!m_bqm.is_zero(ivl.upper()))
set(upper, mk_rational(ivl.upper()));
return true;
}
unsigned get_sign_condition_size(numeral const &a, unsigned i) {
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
const sign_det * sdt = ext->sdt();
if (!sdt)
return 0;
sign_condition * sc = sdt->sc(ext->sc_idx());
while (i) {
if (sc) sc = sc->prev();
i--;
}
return ext->sdt()->qs()[sc->qidx()].size();
}
int num_sign_condition_coefficients(numeral const &a, unsigned i)
{
if (!is_algebraic(a))
return 0;
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
const sign_det * sdt = ext->sdt();
if (!sdt)
return 0;
sign_condition * sc = sdt->sc(ext->sc_idx());
while (i) {
if (sc) sc = sc->prev();
i--;
}
const polynomial & q = ext->sdt()->qs()[sc->qidx()];
return q.size();
}
numeral get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j)
{
if (!is_algebraic(a))
return numeral();
algebraic * ext = to_algebraic(to_rational_function(a)->ext());
const sign_det * sdt = ext->sdt();
if (!sdt)
return numeral();
sign_condition * sc = sdt->sc(ext->sc_idx());
while (i) {
if (sc) sc = sc->prev();
i--;
}
const polynomial & q = ext->sdt()->qs()[sc->qidx()];
if (j >= q.size())
return numeral();
value_ref v(*this);
v = q[j];
numeral r;
set(r, v);
return r;
}
// ---------------------------------
//
// GCD of integer coefficients
@ -6103,6 +6277,22 @@ namespace realclosure {
return m_imp->is_int(a);
}
bool manager::is_rational(numeral const & a) {
return m_imp->is_rational(a);
}
bool manager::is_algebraic(numeral const & a) {
return m_imp->is_algebraic(a);
}
bool manager::is_infinitesimal(numeral const & a) {
return m_imp->is_infinitesimal(a);
}
bool manager::is_transcendental(numeral const & a) {
return m_imp->is_transcendental(a);
}
bool manager::depends_on_infinitesimals(numeral const & a) {
return m_imp->depends_on_infinitesimals(a);
}
@ -6251,6 +6441,56 @@ namespace realclosure {
save_interval_ctx ctx(this);
m_imp->clean_denominators(a, p, q);
}
unsigned manager::extension_index(numeral const & a)
{
return m_imp->extension_index(a);
}
symbol manager::transcendental_name(numeral const &a)
{
return m_imp->transcendental_name(a);
}
symbol manager::infinitesimal_name(numeral const &a)
{
return m_imp->infinitesimal_name(a);
}
unsigned manager::num_coefficients(numeral const &a)
{
return m_imp->num_coefficients(a);
}
manager::numeral manager::get_coefficient(numeral const &a, unsigned i)
{
return m_imp->get_coefficient(a, i);
}
unsigned manager::num_sign_conditions(numeral const &a)
{
return m_imp->num_sign_conditions(a);
}
int manager::get_sign_condition_sign(numeral const &a, unsigned i)
{
return m_imp->get_sign_condition_sign(a, i);
}
bool manager::get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper)
{
return m_imp->get_interval(a, lower_is_inf, lower_is_open, lower, upper_is_inf, upper_is_open, upper);
}
unsigned manager::num_sign_condition_coefficients(numeral const &a, unsigned i)
{
return m_imp->num_sign_condition_coefficients(a, i);
}
manager::numeral manager::get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j)
{
return m_imp->get_sign_condition_coefficient(a, i, j);
}
};
void pp(realclosure::manager::imp * imp, realclosure::polynomial const & p, realclosure::extension * ext) {

40
src/math/realclosure/realclosure.h
View file

@ -130,6 +130,26 @@ namespace realclosure {
*/
bool is_int(numeral const & a);
/**
\brief Return true if a is a rational.
*/
bool is_rational(numeral const & a);
/**
\brief Return true if a is an algebraic number.
*/
bool is_algebraic(numeral const & a);
/**
\brief Return true if a represents an infinitesimal.
*/
bool is_infinitesimal(numeral const & a);
/**
\brief Return true if a is a transcendental.
*/
bool is_transcendental(numeral const & a);
/**
\brief Return true if the representation of \c a depends on
infinitesimal extensions.
@ -263,6 +283,26 @@ namespace realclosure {
void display_interval(std::ostream & out, numeral const & a) const;
void clean_denominators(numeral const & a, numeral & p, numeral & q);
unsigned extension_index(numeral const & a);
symbol transcendental_name(numeral const &a);
symbol infinitesimal_name(numeral const &a);
unsigned num_coefficients(numeral const &a);
numeral get_coefficient(numeral const &a, unsigned i);
unsigned num_sign_conditions(numeral const &a);
int get_sign_condition_sign(numeral const &a, unsigned i);
bool get_interval(numeral const & a, int & lower_is_inf, int & lower_is_open, numeral & lower, int & upper_is_inf, int & upper_is_open, numeral & upper);
unsigned num_sign_condition_coefficients(numeral const &a, unsigned i);
numeral get_sign_condition_coefficient(numeral const &a, unsigned i, unsigned j);
};
struct value;