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use std::hash::Hash;
use std::{collections::HashSet, rc::Rc};
use crate::convenience_expressions::sum_of_iter;
use crate::expressions::product::{product_of, product_of_iter};
use crate::expressions::Negation;
use crate::{argument::Argument, expressions::Expression};
use super::DerivationRule;
/**
* a + 2a = (1 + 2)a
* a + -(2a) = (1 - 2)a
* a + ba = (1+b)a
*/
pub struct SumCoefficientsOfTerms {}
// Excludes the empty set
fn power_set<T>(set: Vec<T>) -> Vec<Vec<T>>
where
T: PartialEq + Eq + Hash + Clone,
{
let mut power_set = Vec::<Vec<T>>::new();
let base: u32 = 2;
for i in 1..base.pow(set.len() as u32) {
let mut subset = Vec::<T>::new();
(0..set.len()).for_each(|j| {
if i & (1 << j) != 0 {
subset.push(set[j].clone());
}
});
power_set.push(subset);
}
power_set
}
impl DerivationRule for SumCoefficientsOfTerms {
fn apply(&self, input: Expression) -> Vec<(Expression, Rc<Argument>)> {
let terms = match input {
Expression::Sum(ref s) => s.terms(),
_ => return vec![],
};
let expanded_terms = terms
.iter()
.map(|term| match term {
Expression::Negation(n) => (true, n.exp()),
_ => (false, term.clone()),
})
.map(|term| match term.1 {
Expression::Product(p) => (term.0, p.factors().clone()),
_ => (term.0, vec![term.1.clone()]),
})
.collect::<Vec<(bool, Vec<Expression>)>>();
let factors = expanded_terms
.iter()
.flat_map(|term| term.1.clone())
.collect::<HashSet<Expression>>()
.into_iter()
.collect();
let mut equivalents = Vec::<Expression>::new();
for subset in power_set(factors) {
// Figure out which terms are affected
// The term is included if it contains all elements of subset
let mut relevant = Vec::<(bool, Vec<Expression>)>::new();
let mut others = Vec::<Expression>::new();
for term in &expanded_terms {
let mut overlaps_subset = false;
for factor in &subset {
//TODO: Check tonains all temrs
if term.1.contains(factor) {
overlaps_subset = true;
}
}
if overlaps_subset {
relevant.push(term.clone());
} else {
others.push(product_of(&term.1));
}
}
if relevant.is_empty() {
continue;
}
fn remove_factors(exp: &[Expression], exclude: &[Expression]) -> Expression {
product_of_iter(&mut exp.iter().filter(|f| !exclude.contains(*f)).cloned())
}
// Remove the pulled out factors
let mut filtered_terms = relevant
.into_iter()
.map(|exp| (exp.0, remove_factors(&exp.1, &subset)))
.map(|exp| if exp.0 { Negation::of(exp.1) } else { exp.1 });
let sum = sum_of_iter(&mut filtered_terms);
let product = product_of(&[sum, product_of(&subset)]);
let result = sum_of_iter(&mut [product].into_iter().chain(others.into_iter()));
equivalents.push(result);
}
equivalents
.into_iter()
.map(|exp| {
(
exp,
Argument::new(
String::from("Sum coefficients of terms"),
vec![input.clone()],
self.name(),
),
)
})
.collect()
}
fn name(&self) -> String {
String::from("SumCoefficientsOfTerms")
}
}
#[cfg(test)]
mod tests {
// use super::*;
// use crate::{
// convenience_expressions::{i, v},
// derivation_rules::DerivationRule,
// expressions::sum::sum_of,
// };
#[test]
fn test_1() {
// let rule = SumCoefficientsOfTerms {};
// // ab + ac + 1
// let start = sum_of(&[
// product_of(&[v("a"), v("b")]),
// product_of(&[v("a"), v("c")]),
// i(1),
// ]);
//
// let result = rule.apply(start).first().unwrap().0.clone();
// // (b + c)a + 1
// assert_eq!(
// result,
// sum_of(&[product_of(&[sum_of(&[v("b"), v("c")]), v("a")]), i(1)])
// );
}
}