Singular Manual: farey

  | ### 5.1.37 farey `Syntax:` `farey (` bigint_expression `,` bigint_expression `)` `farey (` ideal_expression `,` bigint_expression `)` `farey (` module_expression `,` bigint_expression `)` `farey (` matrix_expression `,` bigint_expression `)` `farey (` smatrix_expression `,` bigint_expression `)` `farey (` list_expression `,` bigint_expression `)` `Type:` type of the first argument (unless it is `list`) `Purpose:` lift the first argument modulo the second to the rationals. The (coefficients of the) result a/b is the best approximation under the condition 125#125`farey(list(a,b,..),B)` is equivalent to `list(farey(a,B),farey(b,B),...)`. `Note:` The current coefficient field must be the rationals. `Example:`
        ring r=0,x,dp;
        farey(2,32003);
      ==> 2
See chinrem.

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