Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Equal authenticity rule be printed and published in both those Languages [i.e. both English and French]." The rule requires courts to treat "both [the English and French] versions of statutes [as] equally valid and authoritative interpretations of the law," The rule holds that both versions are equally authoritative even if the statute in question was clearly drafted in one language and translated into the other, and even if the two versions of the law are incompatible. An early version of the principle may be found a statute of the Parliament of the Province of Canada, enacted in 1857. The "Act respecting the Codification