Sollya User's Manual

Name:

hopitalrecursions controls the number of recursion steps when applying L'Hopital's rule.

Library names:

void sollya_lib_set_hopitalrecursions_and_print(sollya_obj_t) void sollya_lib_set_hopitalrecursions(sollya_obj_t) sollya_obj_t sollya_lib_get_hopitalrecursions()

Usage:

hopitalrecursions = n : integer -> void hopitalrecursions = n ! : integer -> void hopitalrecursions : integer

Parameters:

n represents the number of recursions

Description:

hopitalrecursions is a global variable. Its value represents the number of steps of recursion that are tried when applying L'Hopital's rule. This rule is applied by the interval evaluator present in the core of Sollya (and particularly visible in commands like infnorm).
If an expression of the form f/g has to be evaluated by interval arithmetic on an interval I and if f and g have a common zero in I, a direct evaluation leads to NaN. Sollya implements a safe heuristic to avoid this, based on L'Hopital's rule: in such a case, it can be shown that (f/g)(I) C (f'/g')(I). Since the same problem may exist for f'/g', the rule is applied recursively. The number of step in this recursion process is controlled by hopitalrecursions.
Setting hopitalrecursions to 0 makes Sollya use this rule only once; setting it to 1 makes Sollya use the rule twice, and so on. In particular: the rule is always applied at least once, if necessary.

Example 1:

   > hopitalrecursions=0;
   The number of recursions for Hopital's rule has been set to 0.
   > evaluate(log(1+x)^2/x^2,[-1/2; 1]);
   [NaN;NaN]
   > hopitalrecursions=1;
   The number of recursions for Hopital's rule has been set to 1.
   > evaluate(log(1+x)^2/x^2,[-1/2; 1]);
   [-2.5225887222397812376689284858327062723020005374411;6.7725887222397812376689284858327062723020005374412]

See also: taylorrecursions, infnorm, findzeros, evaluate

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