Template talk:Sqr
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- {{subst:#if:1|{{subst:sqr|5}}}} gives 2.2360679775 in one edit.
Maximum value of argument:
- {{subst:#if:1|{{subst:sqr|1999999999997}}}} gives 1414213.56237.
- {{subst:#if:1|{{subst:sqr|1999999999998}}}} gives "Expression error: Unrecognised word "e"".
Minimum value of argument:
- {{subst:#if:1|{{subst:sqr|.00000001000000000000001}}}} gives 0.000100000000001.
- {{subst:#if:1|{{subst:sqr|.000000010000000000000001}}}} gives "Expression error: Unrecognised word "e"".
Golden ratio: {{subst:#expr:({{subst:#if:1|{{subst:sqr|5}}}}+1)/2}} gives 1.61803398875.
The template content on substitution is of the form
{{subst:#ifexpr:boolean_for_"not_finished"|{{subst:sqr|argument_of_square_root|new_approximation}}|old_approximation}}</nowiki>
{{subst:sqr|5}} gives the wikitext
- {{subst:#ifexpr:1|{{subst:sqr|5|1}}|{{{2}}}}}
{{subst:sqr|5|2}} gives:
- {{subst:#ifexpr:1|{{subst:sqr|5|2.25}}|2}}
{{subst:sqr|5|2.2360679775}} gives:
- {{subst:#ifexpr:0|{{subst:sqr|5|2.2360679775}}|2.2360679775}}
Thus the edit history records the number for which the square root is computed and the starting value, if any, with the next approximation (otherwise it gives {{{2}}} as starting value and 1 as the next approximation); in all cases the next edit/save gives 2.2360679775.
[edit] Square root templates
- template:square root ( talk edit history links ) - one step at each save
- template:square root A ( talk edit history links ) - with absolute error stop criterion, one or two saves produce all approximations and the differences between consecutive ones
- template:square root B ( talk edit history links ) - with absolute error stop criterion, one or two saves produce the final approximation and the differences between consecutive ones
- template:sqr ( talk edit history links ) - one or two saves produce the final approximation, with fixed stop criterion of relative error <1e-11 (based on use of a server with 12-digit results); gives a single value, a call can be put in an expression
- template:sqri ( talk edit history links ) - one or two saves produce all intermediate results and the final approximation at the top (so backward), with fixed stop criterion of relative error <1e-11 (based on use of a server with 12-digit results)
- template:sqrif ( talk edit history links ) - ditto, forward
- template:square root with defaults ( talk edit history links )
- template:square root with defaults A ( talk edit history links )
See also:
