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use std::{collections::HashSet, rc::Rc, sync::Arc};
use crate::{
argument::Argument,
convenience_expressions::sum_of_iter,
expressions::{trig_expression::TrigFn, Exponent, Expression, Integer, TrigExp},
};
use super::DerivationRule;
/**
* sin^2(x) + cos^2(x) = 1
* 1 + cot^2(x) = csc^2(x)
* 1 + tan^2(x) = sec^2(x)
*/
pub struct Pythagoras {}
fn unwrap_squared_trig(exp: &Expression) -> Option<Arc<TrigExp>> {
match exp {
Expression::Exponent(ref e) => {
if e.power() == Integer::of(2) {
match e.base() {
Expression::Trig(t) => Some(t),
_ => None,
}
} else {
None
}
}
_ => None,
}
}
fn is_one(exp: &&Expression) -> bool {
match exp {
Expression::Integer(i) => i.value() == 1,
_ => false,
}
}
impl DerivationRule for Pythagoras {
fn apply(&self, input: Expression) -> Vec<(Expression, Rc<Argument>)> {
let sum = match input {
Expression::Sum(ref s) => s,
_ => return vec![],
};
let squared_trig_terms = sum
.terms()
.iter()
.filter_map(unwrap_squared_trig)
.collect::<HashSet<_>>();
// List of expressions acted on by trig expressions
let trig_params = squared_trig_terms
.iter()
.map(|x| x.exp())
.collect::<HashSet<_>>();
let ones = sum.terms().iter().filter(is_one).count();
let has_term = |op: TrigFn, exp: &Expression| {
squared_trig_terms
.iter()
.any(|t| t.operation == op && &t.exp() == exp)
};
// Check for each known combination
let mut results = Vec::<Expression>::new();
for exp in &trig_params {
if has_term(TrigFn::Sin, exp) && has_term(TrigFn::Cos, exp) {
let mut found_sin = false;
let mut found_cos = false;
results.push(sum_of_iter(
&mut sum
.terms()
.iter()
.filter(|term| {
let trig = match unwrap_squared_trig(term) {
Some(t) => t,
None => return true,
};
if trig.exp() == *exp {
if trig.operation == TrigFn::Sin && !found_sin {
found_sin = true;
false
} else if trig.operation == TrigFn::Cos && !found_cos {
found_cos = true;
false
} else {
true
}
} else {
true
}
})
.chain(&[Integer::of(1)])
.cloned(),
))
}
if has_term(TrigFn::Cot, exp) && ones > 0 {
let mut found_cot = false;
let mut found_one = false;
results.push(sum_of_iter(
&mut sum
.terms()
.iter()
.filter(|term| {
let trig = match unwrap_squared_trig(term) {
Some(t) => t,
None => {
if **term == Integer::of(1) && !found_one {
found_one = true;
return false;
}
return true;
}
};
if trig.exp() == *exp {
if trig.operation == TrigFn::Cot && !found_cot {
found_cot = true;
false
} else {
true
}
} else {
true
}
})
.chain(&[Exponent::of(
TrigExp::of(TrigFn::Csc, exp.clone()),
Integer::of(2),
)])
.cloned(),
))
}
if has_term(TrigFn::Tan, exp) && ones > 0 {
let mut found_tan = false;
let mut found_one = false;
results.push(sum_of_iter(
&mut sum
.terms()
.iter()
.filter(|term| {
let trig = match unwrap_squared_trig(term) {
Some(t) => t,
None => {
if **term == Integer::of(1) && !found_one {
found_one = true;
return false;
}
return true;
}
};
if trig.exp() == *exp {
if trig.operation == TrigFn::Tan && !found_tan {
found_tan = true;
false
} else {
true
}
} else {
true
}
})
.chain(&[Exponent::of(
TrigExp::of(TrigFn::Sec, exp.clone()),
Integer::of(2),
)])
.cloned(),
))
}
}
results
.into_iter()
.map(|equiv| {
(
equiv,
Argument::new(
String::from("Pythagorean identity"),
vec![input.clone()],
self.name(),
),
)
})
.collect()
}
fn name(&self) -> String {
String::from("PythagoreanIdentities")
}
}
#[cfg(test)]
mod tests {
use crate::{
convenience_expressions::v,
expressions::{sum::sum_of, Exponent},
};
use super::*;
#[test]
fn test_1() {
let rule = Pythagoras {};
let start = sum_of(&[
Exponent::of(TrigExp::of(TrigFn::Sin, v("x")), Integer::of(2)),
Exponent::of(TrigExp::of(TrigFn::Cos, v("x")), Integer::of(2)),
]);
let result = rule.apply(start).first().unwrap().0.clone();
assert_eq!(result, Integer::of(1));
let start2 = sum_of(&[
Exponent::of(TrigExp::of(TrigFn::Sin, v("x")), Integer::of(2)),
Exponent::of(TrigExp::of(TrigFn::Cos, v("x")), Integer::of(2)),
Exponent::of(TrigExp::of(TrigFn::Sin, v("x")), Integer::of(2)),
]);
let result2 = rule.apply(start2).first().unwrap().0.clone();
assert_eq!(
result2,
sum_of(&[
Exponent::of(TrigExp::of(TrigFn::Sin, v("x")), Integer::of(2)),
Integer::of(1)
])
);
let start3 = sum_of(&[
Exponent::of(TrigExp::of(TrigFn::Cot, v("x")), Integer::of(2)),
Integer::of(1),
]);
let result3 = rule.apply(start3).first().unwrap().0.clone();
assert_eq!(
result3,
Exponent::of(TrigExp::of(TrigFn::Csc, v("x")), Integer::of(2))
);
}
}