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</pre><div class="example-wrap"><pre class="rust ">
<span class="kw">use</span> <span class="ident">approx</span>::<span class="ident">RelativeEq</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"decimal"</span>)]</span>
<span class="kw">use</span> <span class="ident">decimal</span>::<span class="ident">d128</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">Num</span>;
<span class="kw">use</span> <span class="ident">num_complex</span>::<span class="ident">Complex</span>;
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">general</span>::<span class="ident">wrapper</span>::<span class="ident">Wrapper</span> <span class="kw">as</span> <span class="ident">W</span>;
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">general</span>::{
<span class="ident">AbstractGroupAbelian</span>, <span class="ident">AbstractMonoid</span>, <span class="ident">Additive</span>, <span class="ident">ClosedNeg</span>, <span class="ident">Multiplicative</span>, <span class="ident">Operator</span>,
};
<span class="doccomment">/// A **ring** is the combination of an Abelian group and a multiplicative monoid structure.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// A ring is equipped with:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// * An abstract operator (usually the addition, "+") that fulfills the constraints of an Abelian group.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// *An Abelian group is a set with a closed commutative and associative addition with the divisibility property and an identity element.*</span>
<span class="doccomment">/// * A second abstract operator (usually the multiplication, "×") that fulfills the constraints of a monoid.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// *A set equipped with a closed associative multiplication with the divisibility property and an identity element.*</span>
<span class="doccomment">///</span>
<span class="doccomment">/// The multiplication is distributive over the addition:</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Distributivity</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ~~~notrust</span>
<span class="doccomment">/// a, b, c ∈ Self, a × (b + c) = a × b + a × c.</span>
<span class="doccomment">/// ~~~</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">AbstractRing</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Additive</span>, <span class="ident">M</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Multiplicative</span><span class="op">></span>:
<span class="ident">AbstractGroupAbelian</span><span class="op"><</span><span class="ident">A</span><span class="op">></span> <span class="op">+</span> <span class="ident">AbstractMonoid</span><span class="op"><</span><span class="ident">M</span><span class="op">></span>
{
<span class="doccomment">/// Returns `true` if the multiplication and addition operators are distributive for</span>
<span class="doccomment">/// the given argument tuple. Approximate equality is used for verifications.</span>
<span class="kw">fn</span> <span class="ident">prop_mul_and_add_are_distributive_approx</span>(<span class="ident">args</span>: (<span class="self">Self</span>, <span class="self">Self</span>, <span class="self">Self</span>)) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">RelativeEq</span>,
{
<span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">c</span>) <span class="op">=</span> <span class="ident">args</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">a</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">b</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">c</span>.<span class="ident">clone</span>());
<span class="comment">// Left distributivity</span>
<span class="macro">relative_eq</span><span class="macro">!</span>(<span class="ident">a</span>() <span class="op">*</span> (<span class="ident">b</span>() <span class="op">+</span> <span class="ident">c</span>()), <span class="ident">a</span>() <span class="op">*</span> <span class="ident">b</span>() <span class="op">+</span> <span class="ident">a</span>() <span class="op">*</span> <span class="ident">c</span>()) <span class="kw-2">&</span><span class="op">&</span>
<span class="comment">// Right distributivity</span>
<span class="macro">relative_eq</span><span class="macro">!</span>((<span class="ident">b</span>() <span class="op">+</span> <span class="ident">c</span>()) <span class="op">*</span> <span class="ident">a</span>(), <span class="ident">b</span>() <span class="op">*</span> <span class="ident">a</span>() <span class="op">+</span> <span class="ident">c</span>() <span class="op">*</span> <span class="ident">a</span>())
}
<span class="doccomment">/// Returns `true` if the multiplication and addition operators are distributive for</span>
<span class="doccomment">/// the given argument tuple.</span>
<span class="kw">fn</span> <span class="ident">prop_mul_and_add_are_distributive</span>(<span class="ident">args</span>: (<span class="self">Self</span>, <span class="self">Self</span>, <span class="self">Self</span>)) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Eq</span>,
{
<span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">c</span>) <span class="op">=</span> <span class="ident">args</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">a</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">b</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">c</span>.<span class="ident">clone</span>());
<span class="comment">// Left distributivity</span>
<span class="ident">a</span>() <span class="op">*</span> (<span class="ident">b</span>() <span class="op">+</span> <span class="ident">c</span>()) <span class="op">=</span><span class="op">=</span> (<span class="ident">a</span>() <span class="op">*</span> <span class="ident">b</span>()) <span class="op">+</span> (<span class="ident">a</span>() <span class="op">*</span> <span class="ident">c</span>()) <span class="kw-2">&</span><span class="op">&</span>
<span class="comment">// Right distributivity</span>
(<span class="ident">b</span>() <span class="op">+</span> <span class="ident">c</span>()) <span class="op">*</span> <span class="ident">a</span>() <span class="op">=</span><span class="op">=</span> (<span class="ident">b</span>() <span class="op">*</span> <span class="ident">a</span>()) <span class="op">+</span> (<span class="ident">c</span>() <span class="op">*</span> <span class="ident">a</span>())
}
}
<span class="doccomment">/// Implements the ring trait for types provided.</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// # #[macro_use]</span>
<span class="doccomment">/// # extern crate alga;</span>
<span class="doccomment">/// # use alga::general::{AbstractMagma, AbstractRing, Additive, Multiplicative, TwoSidedInverse, Identity};</span>
<span class="doccomment">/// # fn main() {}</span>
<span class="doccomment">/// #[derive(PartialEq, Clone)]</span>
<span class="doccomment">/// struct Wrapper<T>(T);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Additive>> AbstractMagma<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: TwoSidedInverse<Additive>> TwoSidedInverse<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn two_sided_inverse(&self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.two_sided_inverse())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Additive>> Identity<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Multiplicative>> AbstractMagma<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Multiplicative>> Identity<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl_ring!(<Additive, Multiplicative> for Wrapper<T> where T: AbstractRing);</span>
<span class="doccomment">/// ```</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">impl_ring</span>(
(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span>:<span class="ident">ty</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">tt</span>)<span class="op">+</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">impl_abelian</span><span class="macro">!</span>(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_monoid</span><span class="macro">!</span>(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractRing</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
}
);
<span class="doccomment">/// A ring with a commutative multiplication.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// *A **commutative ring** is a set with two binary operations: a closed commutative and associative with the divisibility property and an identity element,</span>
<span class="doccomment">/// and another closed associative and **commutative** with the divisibility property and an identity element.*</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Commutativity</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```notrust</span>
<span class="doccomment">/// ∀ a, b ∈ Self, a × b = b × a</span>
<span class="doccomment">/// ```</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">AbstractRingCommutative</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Additive</span>, <span class="ident">M</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Multiplicative</span><span class="op">></span>:
<span class="ident">AbstractRing</span><span class="op"><</span><span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>
{
<span class="doccomment">/// Returns `true` if the multiplication operator is commutative for the given argument tuple.</span>
<span class="doccomment">/// Approximate equality is used for verifications.</span>
<span class="kw">fn</span> <span class="ident">prop_mul_is_commutative_approx</span>(<span class="ident">args</span>: (<span class="self">Self</span>, <span class="self">Self</span>)) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">RelativeEq</span>,
{
<span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>) <span class="op">=</span> <span class="ident">args</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">a</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">b</span>.<span class="ident">clone</span>());
<span class="macro">relative_eq</span><span class="macro">!</span>(<span class="ident">a</span>() <span class="op">*</span> <span class="ident">b</span>(), <span class="ident">b</span>() <span class="op">*</span> <span class="ident">a</span>())
}
<span class="doccomment">/// Returns `true` if the multiplication operator is commutative for the given argument tuple.</span>
<span class="kw">fn</span> <span class="ident">prop_mul_is_commutative</span>(<span class="ident">args</span>: (<span class="self">Self</span>, <span class="self">Self</span>)) <span class="op">-</span><span class="op">></span> <span class="ident">bool</span>
<span class="kw">where</span>
<span class="self">Self</span>: <span class="ident">Eq</span>,
{
<span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>) <span class="op">=</span> <span class="ident">args</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">a</span>.<span class="ident">clone</span>());
<span class="kw">let</span> <span class="ident">b</span> <span class="op">=</span> <span class="op">|</span><span class="op">|</span> <span class="ident">W</span>::<span class="op"><</span><span class="kw">_</span>, <span class="ident">A</span>, <span class="ident">M</span><span class="op">></span>::<span class="ident">new</span>(<span class="ident">b</span>.<span class="ident">clone</span>());
<span class="ident">a</span>() <span class="op">*</span> <span class="ident">b</span>() <span class="op">=</span><span class="op">=</span> <span class="ident">b</span>() <span class="op">*</span> <span class="ident">a</span>()
}
}
<span class="doccomment">/// Implements the commutative ring trait for types provided.</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// # #[macro_use]</span>
<span class="doccomment">/// # extern crate alga;</span>
<span class="doccomment">/// # use alga::general::{AbstractMagma, AbstractRingCommutative, Additive, Multiplicative, TwoSidedInverse, Identity};</span>
<span class="doccomment">/// # fn main() {}</span>
<span class="doccomment">/// #[derive(PartialEq, Clone)]</span>
<span class="doccomment">/// struct Wrapper<T>(T);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Additive>> AbstractMagma<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: TwoSidedInverse<Additive>> TwoSidedInverse<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn two_sided_inverse(&self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.two_sided_inverse())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Additive>> Identity<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Multiplicative>> AbstractMagma<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Multiplicative>> Identity<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl_ring!(<Additive, Multiplicative> for Wrapper<T> where T: AbstractRingCommutative);</span>
<span class="doccomment">/// ```</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">impl_ring_commutative</span>(
(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span>:<span class="ident">ty</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">tt</span>)<span class="op">+</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">impl_ring</span><span class="macro">!</span>(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractRingCommutative</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
}
);
<span class="doccomment">/// A field is a commutative ring, and an Abelian group under both operators.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// *A **field** is a set with two binary operations, an addition and a multiplication, which are both closed, commutative, associative</span>
<span class="doccomment">/// possess the divisibility property and an identity element, noted 0 and 1 respectively. Furthermore the multiplication is distributive</span>
<span class="doccomment">/// over the addition.*</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">AbstractField</span><span class="op"><</span><span class="ident">A</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Additive</span>, <span class="ident">M</span>: <span class="ident">Operator</span> <span class="op">=</span> <span class="ident">Multiplicative</span><span class="op">></span>:
<span class="ident">AbstractRingCommutative</span><span class="op"><</span><span class="ident">A</span>, <span class="ident">M</span><span class="op">></span> <span class="op">+</span> <span class="ident">AbstractGroupAbelian</span><span class="op"><</span><span class="ident">M</span><span class="op">></span>
{
}
<span class="doccomment">/// Implements the field trait for types provided.</span>
<span class="doccomment">/// # Examples</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// # #[macro_use]</span>
<span class="doccomment">/// # extern crate alga;</span>
<span class="doccomment">/// # use alga::general::{AbstractMagma, AbstractField, Additive, Multiplicative, TwoSidedInverse, Identity};</span>
<span class="doccomment">/// # fn main() {}</span>
<span class="doccomment">/// #[derive(PartialEq, Clone)]</span>
<span class="doccomment">/// struct Wrapper<T>(T);</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Additive>> AbstractMagma<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: TwoSidedInverse<Additive>> TwoSidedInverse<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn two_sided_inverse(&self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.two_sided_inverse())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Additive>> Identity<Additive> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: AbstractMagma<Multiplicative>> AbstractMagma<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn operate(&self, right: &Self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.operate(&right.0))</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// impl<T: TwoSidedInverse<Multiplicative>> TwoSidedInverse<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn two_sided_inverse(&self) -> Self {</span>
<span class="doccomment">/// Wrapper(self.0.two_sided_inverse())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl<T: Identity<Multiplicative>> Identity<Multiplicative> for Wrapper<T> {</span>
<span class="doccomment">/// fn identity() -> Self {</span>
<span class="doccomment">/// Wrapper(T::identity())</span>
<span class="doccomment">/// }</span>
<span class="doccomment">/// }</span>
<span class="doccomment">///</span>
<span class="doccomment">/// impl_field!(<Additive, Multiplicative> for Wrapper<T> where T: AbstractField);</span>
<span class="doccomment">/// ```</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">impl_field</span>(
(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>:<span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span>:<span class="ident">ty</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>:<span class="ident">tt</span>)<span class="op">+</span>) <span class="op">=</span><span class="op">></span> {
<span class="macro">impl_ring_commutative</span><span class="macro">!</span>(<span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span> <span class="kw">for</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractQuasigroup</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractLoop</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractGroup</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractGroupAbelian</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
<span class="macro">impl_marker</span><span class="macro">!</span>(<span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">general</span>::<span class="ident">AbstractField</span><span class="op"><</span><span class="macro-nonterminal">$</span><span class="macro-nonterminal">A</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">M</span><span class="op">></span>; $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">T</span>)<span class="op">+</span>);
}
);
<span class="comment">/*
*
* Implementations.
*
*/</span>
<span class="macro">impl_ring_commutative</span><span class="macro">!</span>(<span class="op"><</span><span class="ident">Additive</span>, <span class="ident">Multiplicative</span><span class="op">></span> <span class="kw">for</span> <span class="ident">i8</span>; <span class="ident">i16</span>; <span class="ident">i32</span>; <span class="ident">i64</span>; <span class="ident">isize</span>);
<span class="macro">impl_field</span><span class="macro">!</span>(<span class="op"><</span><span class="ident">Additive</span>, <span class="ident">Multiplicative</span><span class="op">></span> <span class="kw">for</span> <span class="ident">f32</span>; <span class="ident">f64</span>);
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"decimal"</span>)]</span>
<span class="macro">impl_field</span><span class="macro">!</span>(<span class="op"><</span><span class="ident">Additive</span>, <span class="ident">Multiplicative</span><span class="op">></span> <span class="kw">for</span> <span class="ident">d128</span>);
<span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">ClosedNeg</span> <span class="op">+</span> <span class="ident">AbstractRing</span><span class="op">></span> <span class="ident">AbstractRing</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> {}
<span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">ClosedNeg</span> <span class="op">+</span> <span class="ident">AbstractRingCommutative</span><span class="op">></span> <span class="ident">AbstractRingCommutative</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> {}
<span class="kw">impl</span><span class="op"><</span><span class="ident">N</span>: <span class="ident">Num</span> <span class="op">+</span> <span class="ident">Clone</span> <span class="op">+</span> <span class="ident">ClosedNeg</span> <span class="op">+</span> <span class="ident">AbstractField</span><span class="op">></span> <span class="ident">AbstractField</span> <span class="kw">for</span> <span class="ident">Complex</span><span class="op"><</span><span class="ident">N</span><span class="op">></span> {}
</pre></div>
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