# :- set\_prolog\_flag(prefer\_rationals, true). % Int/Int --\> Rational :- set\_prolog\_flag(rational\_syntax, natural). % Write as \`1/3\`

**URL:** https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013
**Category:** General
**Tags:** how-to
**Created:** [May 16, 2025, 2:14pm UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013 "2025-05-16T14:14:22Z")
**Posts on this page:** 5
**Page:** 1

<div class="post-metadata">

### Author: ![joseph-vidal-rosset](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/joseph-vidal-rosset/32/2594_2.png) [@joseph-vidal-rosset](https://swi-prolog.discourse.group/u/joseph-vidal-rosset)
#### Post date: [May 16, 2025, 2:14pm UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013/1 "2025-05-16T14:14:22Z")

</div>

How to make this code working ?

```prolog
:- set_prolog_flag(prefer_rationals, true). % Int/Int --> Rational
:- set_prolog_flag(rational_syntax, natural). % Write as `1/3`

```

I do not succeed to get rational numbers as ‘1/3’.

Thanks .

---

<div class="post-metadata">

### Author: ![ridgeworks](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/ridgeworks/32/886_2.png) [@ridgeworks](https://swi-prolog.discourse.group/u/ridgeworks)
#### Post date: [May 16, 2025, 3:56pm UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013/2 "2025-05-16T15:56:33Z")

</div>

> [@joseph-vidal-rosset](#):
>
> I do not succeed to get rational numbers as ‘1/3’.

Are you sure? On my install (9.2.9):

```prolog
?- current_prolog_flag(prefer_rationals,P).
P = true.

?- set_prolog_flag(rational_syntax, compatibility).
true.

?- X is 1/3,rational(X).
X = 1r3.

?- set_prolog_flag(rational_syntax, natural).
true.

?- X is 1/3,rational(X).
X = 1/3.

```

---

<div class="post-metadata">

### Author: ![joseph-vidal-rosset](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/joseph-vidal-rosset/32/2594_2.png) [@joseph-vidal-rosset](https://swi-prolog.discourse.group/u/joseph-vidal-rosset)
#### Post date: [May 17, 2025, 7:28am UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013/3 "2025-05-17T07:28:28Z")

</div>

This code gets around the problem:

```prolog
:- set_prolog_flag(prefer_rationals, true).
:- set_prolog_flag(rational_syntax, natural).

it_av(A, B, N) :- time(iterative_average(A, B, N)).

iterative_average(A, B, N) :-
    average(A, B, M),
    format('Step 1: Average : ~50f (', [M]),
    rational_to_string(M, S),
    write(S),
    format(')~n', []),
    iterative_average(M, B, N, 2).

iterative_average(_, _, 1, _) :- !.
iterative_average(A, B, N, I) :-
    average(A, B, M),
    format('Step ~w : Average : ~50f (', [I, M]),
    rational_to_string(M, S),
    write(S),
    format(')~n', []),
    succ(I, NewI),
    succ(N0, N),
    iterative_average(M, B, N0, NewI).

average(A, B, M) :- M is (A + B) / 2.

rational_to_string(R, S) :-
    numerator(R, N),
    denominator(R, D),
    atomic_list_concat([N, '/', D], S).

numerator(R, N) :- rational(R, N, _).
numerator(R, N) :- R = N / D, N1 is numerator(N), D1 is denominator(D), gcd(N1, D1, G), N is N1 // G.

denominator(R, D) :- rational(R, _, D).
denominator(R, D) :- R = N / D, N1 is numerator(N), D1 is denominator(D), gcd(N1, D1, G), D is D1 // G.

gcd(A, 0, A).
gcd(A, B, G) :- B > 0, R is A mod B, gcd(B, R, G).

```

output :

```prolog
?- it_av(1,2,10).
Step 1: Average : 1.50000000000000000000000000000000000000000000000000 (3/2)
Step 2 : Average : 1.75000000000000000000000000000000000000000000000000 (7/4)
Step 3 : Average : 1.87500000000000000000000000000000000000000000000000 (15/8)
Step 4 : Average : 1.93750000000000000000000000000000000000000000000000 (31/16)
Step 5 : Average : 1.96875000000000000000000000000000000000000000000000 (63/32)
Step 6 : Average : 1.98437500000000000000000000000000000000000000000000 (127/64)
Step 7 : Average : 1.99218750000000000000000000000000000000000000000000 (255/128)
Step 8 : Average : 1.99609375000000000000000000000000000000000000000000 (511/256)
Step 9 : Average : 1.99804687500000000000000000000000000000000000000000 (1023/512)
Step 10 : Average : 1.99902343750000000000000000000000000000000000000000 (2047/1024)
% 137 inferences, 0.001 CPU in 0.001 seconds (99% CPU, 232348 Lips)
true.

```

More elegant solutions for this program are welcome.

---

<div class="post-metadata">

### Author: ![jan](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/jan/32/4_2.png) [@jan](https://swi-prolog.discourse.group/u/jan)
#### Post date: [May 17, 2025, 9:04am UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013/4 "2025-05-17T09:04:21Z")

</div>

> [@joseph-vidal-rosset](#):
>
> More elegant solutions for this program are welcome.

There seems to be a but in write/1. Using write\_term/2, all works as expected, so we get

```prolog
:- set_prolog_flag(prefer_rationals, true).
:- set_prolog_flag(rational_syntax, natural).

it_av(A, B, N) :-
    time(iterative_average(A, B, N)).

iterative_average(A, B, N) :-
    average(A, B, M),
    format('Step~t1~7|: Average: ~50f (~W)~n', [M, M, []]),
    iterative_average(M, B, N, 2).

iterative_average(_, _, 1, _) :- !.
iterative_average(A, B, N, I) :-
    average(A, B, M),
    format('Step~t~w~7|: Average: ~50f (~W)~n', [I, M, M, []]),
    succ(I, NewI),
    succ(N0, N),
    iterative_average(M, B, N0, NewI).

average(A, B, M) :- M is (A + B) / 2.

```

```prolog
?- it_av(1,2,10).
Step 1: Average: 1.50000000000000000000000000000000000000000000000000 (3/2)
Step 2: Average: 1.75000000000000000000000000000000000000000000000000 (7/4)
Step 3: Average: 1.87500000000000000000000000000000000000000000000000 (15/8)
Step 4: Average: 1.93750000000000000000000000000000000000000000000000 (31/16)
Step 5: Average: 1.96875000000000000000000000000000000000000000000000 (63/32)
Step 6: Average: 1.98437500000000000000000000000000000000000000000000 (127/64)
Step 7: Average: 1.99218750000000000000000000000000000000000000000000 (255/128)
Step 8: Average: 1.99609375000000000000000000000000000000000000000000 (511/256)
Step 9: Average: 1.99804687500000000000000000000000000000000000000000 (1023/512)
Step 10: Average: 1.99902343750000000000000000000000000000000000000000 (2047/1024)
% 57 inferences, 0.000 CPU in 0.000 seconds (97% CPU, 745556 Lips)
true.

```

**edit** fixed with 457b6270d94c662b9af3d57b7537e7576b060ddf

---

<div class="post-metadata">

### Author: ![joseph-vidal-rosset](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/joseph-vidal-rosset/32/2594_2.png) [@joseph-vidal-rosset](https://swi-prolog.discourse.group/u/joseph-vidal-rosset)
#### Post date: [May 17, 2025, 9:24am UTC](https://swi-prolog.discourse.group/t/set-prolog-flag-prefer-rationals-true-int-int-rational-set-prolog-flag-rational-syntax-natural-write-as-1-3/9013/5 "2025-05-17T09:24:59Z")

</div>

> [@jan](#):
>
> ```prolog
> :- set_prolog_flag(prefer_rationals, true).
> :- set_prolog_flag(rational_syntax, natural).
> 
> it_av(A, B, N) :-
> time(iterative_average(A, B, N)).
> 
> iterative_average(A, B, N) :-
> average(A, B, M),
> format('Step~t1~7|: Average: ~50f (~W)~n', [M, M, []]),
> iterative_average(M, B, N, 2).
> 
> iterative_average(_, _, 1, _) :- !.
> iterative_average(A, B, N, I) :-
> average(A, B, M),
> format('Step~t~w~7|: Average: ~50f (~W)~n', [I, M, M, []]),
> succ(I, NewI),
> succ(N0, N),
> iterative_average(M, B, N0, NewI).
> 
> average(A, B, M) :- M is (A + B) / 2.
> 
> ```

Many thanks Jan !