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Add accessors for RCF numeral internals (#7013)
This commit is contained in:
Christoph M. Wintersteiger
GitHub
parent
9382b96a32
commit
16753e43f1
7 changed files with 845 additions and 117 deletions
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@ -2080,6 +2080,7 @@ struct
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type rcf_num = Z3native.rcf_num
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let del (ctx:context) (a:rcf_num) = Z3native.rcf_del ctx a
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let del_list (ctx:context) (ns:rcf_num list) = List.iter (fun a -> Z3native.rcf_del ctx a) ns
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let mk_rational (ctx:context) (v:string) = Z3native.rcf_mk_rational ctx v
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let mk_small_int (ctx:context) (v:int) = Z3native.rcf_mk_small_int ctx v
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@ -2087,7 +2088,9 @@ struct
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let mk_e (ctx:context) = Z3native.rcf_mk_e ctx
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let mk_infinitesimal (ctx:context) = Z3native.rcf_mk_infinitesimal ctx
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let mk_roots (ctx:context) (n:int) (a:rcf_num list) = let n, r = Z3native.rcf_mk_roots ctx n a in r
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let mk_roots (ctx:context) (a:rcf_num list) =
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let n, r = Z3native.rcf_mk_roots ctx (List.length a) a in
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List.init n (fun x -> List.nth r x)
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let add (ctx:context) (a:rcf_num) (b:rcf_num) = Z3native.rcf_add ctx a b
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let sub (ctx:context) (a:rcf_num) (b:rcf_num) = Z3native.rcf_sub ctx a b
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@ -2109,6 +2112,83 @@ struct
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let num_to_string (ctx:context) (a:rcf_num) (compact:bool) (html:bool) = Z3native.rcf_num_to_string ctx a compact html
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let num_to_decimal_string (ctx:context) (a:rcf_num) (prec:int) = Z3native.rcf_num_to_decimal_string ctx a prec
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let get_numerator_denominator (ctx:context) (a:rcf_num) = Z3native.rcf_get_numerator_denominator ctx a
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let is_rational (ctx:context) (a:rcf_num) = Z3native.rcf_is_rational ctx a
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let is_algebraic (ctx:context) (a:rcf_num) = Z3native.rcf_is_algebraic ctx a
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let is_infinitesimal (ctx:context) (a:rcf_num) = Z3native.rcf_is_infinitesimal ctx a
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let is_transcendental (ctx:context) (a:rcf_num) = Z3native.rcf_is_transcendental ctx a
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let extension_index (ctx:context) (a:rcf_num) = Z3native.rcf_extension_index ctx a
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let transcendental_name (ctx:context) (a:rcf_num) = Z3native.rcf_transcendental_name ctx a
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let infinitesimal_name (ctx:context) (a:rcf_num) = Z3native.rcf_infinitesimal_name ctx a
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let num_coefficients (ctx:context) (a:rcf_num) = Z3native.rcf_num_coefficients ctx a
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let get_coefficient (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_coefficient ctx a i
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let coefficients (ctx:context) (a:rcf_num) =
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List.init (num_coefficients ctx a) (fun i -> Z3native.rcf_coefficient ctx a i)
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type interval = {
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lower_is_inf : bool;
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lower_is_open : bool;
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lower : rcf_num;
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upper_is_inf : bool;
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upper_is_open : bool;
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upper : rcf_num;
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}
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let root_interval (ctx:context) (a:rcf_num) =
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let ok, linf, lopen, l, uinf, uopen, u = Z3native.rcf_interval ctx a in
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let i:interval = {
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lower_is_inf = linf != 0;
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lower_is_open = lopen != 0;
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lower = l;
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upper_is_inf = uinf != 0;
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upper_is_open = uopen != 0;
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upper = u } in
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if ok != 0 then Some i else None
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let sign_condition_sign (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_sign_condition_sign ctx a i
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let sign_condition_coefficient (ctx:context) (a:rcf_num) (i:int) (j:int) = Z3native.rcf_sign_condition_coefficient ctx a i j
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let num_sign_condition_coefficients (ctx:context) (a:rcf_num) (i:int) = Z3native.rcf_num_sign_condition_coefficients ctx a i
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let sign_condition_coefficients (ctx:context) (a:rcf_num) (i:int) =
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let n = Z3native.rcf_num_sign_condition_coefficients ctx a i in
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List.init n (fun j -> Z3native.rcf_sign_condition_coefficient ctx a i j)
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let sign_conditions (ctx:context) (a:rcf_num) =
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let n = Z3native.rcf_num_sign_conditions ctx a in
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List.init n (fun i ->
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(let nc = Z3native.rcf_num_sign_condition_coefficients ctx a i in
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List.init nc (fun j -> Z3native.rcf_sign_condition_coefficient ctx a i j)),
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Z3native.rcf_sign_condition_sign ctx a i)
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type root = {
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obj : rcf_num;
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polynomial : rcf_num list;
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interval : interval option;
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sign_conditions : (rcf_num list * int) list;
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}
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let roots (ctx:context) (a:rcf_num list) =
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let rs = mk_roots ctx a in
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List.map
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(fun r -> {
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obj = r;
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polynomial = coefficients ctx r;
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interval = root_interval ctx r;
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sign_conditions = sign_conditions ctx r})
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rs
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let del_root (ctx:context) (r:root) =
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del ctx r.obj;
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List.iter (fun n -> del ctx n) r.polynomial;
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List.iter (fun (ns, _) -> del_list ctx ns) r.sign_conditions
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let del_roots (ctx:context) (rs:root list) =
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List.iter (fun r -> del_root ctx r) rs
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end
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@ -3553,77 +3553,147 @@ end
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(** Real closed field *)
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module RCF :
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sig
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type rcf_num
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type rcf_num
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(** Delete a RCF numeral created using the RCF API. *)
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val del : context -> rcf_num -> unit
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(** Delete a RCF numeral created using the RCF API. *)
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val del : context -> rcf_num -> unit
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(** Return a RCF rational using the given string. *)
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val mk_rational : context -> string -> rcf_num
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(** Delete RCF numerals created using the RCF API. *)
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val del_list : context -> rcf_num list -> unit
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(** Return a RCF small integer. *)
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val mk_small_int : context -> int -> rcf_num
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(** Return a RCF rational using the given string. *)
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val mk_rational : context -> string -> rcf_num
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(** Return Pi *)
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val mk_pi : context -> rcf_num
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(** Return a RCF small integer. *)
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val mk_small_int : context -> int -> rcf_num
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(** Return e (Euler's constant) *)
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val mk_e : context -> rcf_num
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(** Return Pi *)
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val mk_pi : context -> rcf_num
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(** Return a new infinitesimal that is smaller than all elements in the Z3 field. *)
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val mk_infinitesimal : context -> rcf_num
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(** Return e (Euler's constant) *)
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val mk_e : context -> rcf_num
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(** Extract the roots of a polynomial. Precondition: The input polynomial is not the zero polynomial. *)
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val mk_roots : context -> int -> rcf_num list -> rcf_num list
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(** Return a new infinitesimal that is smaller than all elements in the Z3 field. *)
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val mk_infinitesimal : context -> rcf_num
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(** Addition *)
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val add : context -> rcf_num -> rcf_num -> rcf_num
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(** Extract the roots of a polynomial. Precondition: The input polynomial is not the zero polynomial. *)
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val mk_roots : context -> rcf_num list -> rcf_num list
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(** Subtraction *)
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val sub : context -> rcf_num -> rcf_num -> rcf_num
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(** Addition *)
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val add : context -> rcf_num -> rcf_num -> rcf_num
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(** Multiplication *)
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val mul : context -> rcf_num -> rcf_num -> rcf_num
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(** Subtraction *)
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val sub : context -> rcf_num -> rcf_num -> rcf_num
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(** Division *)
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val div : context -> rcf_num -> rcf_num -> rcf_num
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(** Multiplication *)
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val mul : context -> rcf_num -> rcf_num -> rcf_num
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(** Negation *)
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val neg : context -> rcf_num -> rcf_num
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(** Division *)
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val div : context -> rcf_num -> rcf_num -> rcf_num
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(** Multiplicative Inverse *)
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val inv : context -> rcf_num -> rcf_num
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(** Negation *)
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val neg : context -> rcf_num -> rcf_num
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(** Power *)
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val power : context -> rcf_num -> int -> rcf_num
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(** Multiplicative Inverse *)
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val inv : context -> rcf_num -> rcf_num
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(** less-than *)
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val lt : context -> rcf_num -> rcf_num -> bool
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(** Power *)
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val power : context -> rcf_num -> int -> rcf_num
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(** greater-than *)
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val gt : context -> rcf_num -> rcf_num -> bool
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(** less-than *)
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val lt : context -> rcf_num -> rcf_num -> bool
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(** less-than or equal *)
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val le : context -> rcf_num -> rcf_num -> bool
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(** greater-than *)
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val gt : context -> rcf_num -> rcf_num -> bool
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(** greater-than or equal *)
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val ge : context -> rcf_num -> rcf_num -> bool
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(** less-than or equal *)
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val le : context -> rcf_num -> rcf_num -> bool
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(** equality *)
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val eq : context -> rcf_num -> rcf_num -> bool
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(** greater-than or equal *)
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val ge : context -> rcf_num -> rcf_num -> bool
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(** not equal *)
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val neq : context -> rcf_num -> rcf_num -> bool
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(** equality *)
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val eq : context -> rcf_num -> rcf_num -> bool
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(** Convert the RCF numeral into a string. *)
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val num_to_string : context -> rcf_num -> bool -> bool -> string
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(** not equal *)
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val neq : context -> rcf_num -> rcf_num -> bool
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(** Convert the RCF numeral into a string in decimal notation. *)
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val num_to_decimal_string : context -> rcf_num -> int -> string
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(** Convert the RCF numeral into a string. *)
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val num_to_string : context -> rcf_num -> bool -> bool -> string
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(** Extract the "numerator" and "denominator" of the given RCF numeral.
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We have that \ccode{a = n/d}, moreover \c n and \c d are not represented using rational functions. *)
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val get_numerator_denominator : context -> rcf_num -> (rcf_num * rcf_num)
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(** Convert the RCF numeral into a string in decimal notation. *)
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val num_to_decimal_string : context -> rcf_num -> int -> string
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(** Extract the "numerator" and "denominator" of the given RCF numeral.
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We have that \ccode{a = n/d}, moreover \c n and \c d are not represented using rational functions. *)
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val get_numerator_denominator : context -> rcf_num -> (rcf_num * rcf_num)
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(** Return \c true if \c a represents a rational number. *)
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val is_rational : context -> rcf_num -> bool
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(** Return \c true if \c a represents an algebraic number. *)
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val is_algebraic : context -> rcf_num -> bool
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(** Return \c true if \c a represents an infinitesimal. *)
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val is_infinitesimal : context -> rcf_num -> bool
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(** Return \c true if \c a represents a transcendental number. *)
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val is_transcendental : context -> rcf_num -> bool
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(** Return the index of a field extension. *)
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val extension_index : context -> rcf_num -> int
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(** Return the name of a transcendental. *)
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val transcendental_name : context -> rcf_num -> Symbol.symbol
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(** Return the name of an infinitesimal. *)
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val infinitesimal_name : context -> rcf_num -> Symbol.symbol
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(** Return the number of coefficients in an algebraic number. *)
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val num_coefficients : context -> rcf_num -> int
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(** Extract a coefficient from an algebraic number. *)
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val get_coefficient : context -> rcf_num -> int -> rcf_num
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(** Extract the coefficients from an algebraic number. *)
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val coefficients : context -> rcf_num -> rcf_num list
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(** Extract the sign of a sign condition from an algebraic number. *)
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val sign_condition_sign : context -> rcf_num -> int -> int
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(** Return the size of a sign condition polynomial. *)
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val num_sign_condition_coefficients : context -> rcf_num -> int -> int
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(** Extract a sign condition polynomial coefficient from an algebraic number. *)
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val sign_condition_coefficient : context -> rcf_num -> int -> int -> rcf_num
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(** Extract sign conditions from an algebraic number. *)
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val sign_conditions : context -> rcf_num -> (rcf_num list * int) list
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(** Extract the interval from an algebraic number. *)
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type interval = {
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lower_is_inf : bool;
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lower_is_open : bool;
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lower : rcf_num;
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upper_is_inf : bool;
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upper_is_open : bool;
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upper : rcf_num;
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}
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val root_interval : context -> rcf_num -> interval option
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type root = {
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obj : rcf_num;
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polynomial : rcf_num list;
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interval : interval option;
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sign_conditions : (rcf_num list * int) list;
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}
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val roots : context -> rcf_num list -> root list
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val del_root : context -> root -> unit
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val del_roots : context -> root list -> unit
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end
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(** Set a global (or module) parameter, which is shared by all Z3 contexts.
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