ihateintegrals 0.1.2

A computer algebra library for solving integrals.
Documentation 
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use std::rc::Rc;

use crate::{
    argument::Argument,
    convenience_expressions::cot,
    expressions::{product::product_of, trig_expression::TrigFn, Expression, Fraction, TrigExp},
};

use super::DerivationRule;

/**
* sin(x)/cos(x) = tan(x)
* cos(x)/sin(x) = cot(x)
*/
pub struct TanIdentity {}

impl DerivationRule for TanIdentity {
    fn apply(&self, input: Expression) -> Vec<(Expression, Rc<Argument>)> {
        let frac = match input {
            Expression::Fraction(ref f) => f,
            _ => return vec![],
        };

        let num_factors = match frac.numerator() {
            Expression::Product(p) => p.factors().clone(),
            _ => vec![frac.numerator()],
        };

        let den_factors = match frac.denominator() {
            Expression::Product(p) => p.factors().clone(),
            _ => vec![frac.denominator()],
        };

        let trig_params =
            num_factors
                .iter()
                .chain(&den_factors)
                .filter_map(|factor| match factor {
                    Expression::Trig(t) => Some(t.exp()),
                    _ => None,
                });

        fn is(e: &Expression, trig: TrigFn, exp: &Expression) -> bool {
            match e {
                Expression::Trig(t) => t.operation == trig && t.exp() == *exp,
                _ => false,
            }
        }

        let mut results = Vec::<Expression>::new();
        for param in trig_params {
            // Check for tan
            {
                let mut found_sin = false;
                let mut found_cos = false;
                let (num, sin): (Vec<Expression>, Vec<Expression>) =
                    num_factors.iter().cloned().partition(|f| {
                        if is(f, TrigFn::Sin, &param) && !found_sin {
                            found_sin = true;
                            false
                        } else {
                            true
                        }
                    });
                let (den, cos): (Vec<Expression>, Vec<Expression>) =
                    den_factors.iter().cloned().partition(|f| {
                        if is(f, TrigFn::Cos, &param) && !found_cos {
                            found_cos = true;
                            false
                        } else {
                            true
                        }
                    });
                if !sin.is_empty() && !cos.is_empty() {
                    results.push(product_of(&[
                        Fraction::of(product_of(&num), product_of(&den)),
                        TrigExp::of(TrigFn::Tan, param.clone()),
                    ]));
                }
            }
            // Check for cot
            {
                let mut found_cos = false;
                let mut found_sin = false;
                let (num, cos): (Vec<Expression>, Vec<Expression>) =
                    num_factors.iter().cloned().partition(|f| {
                        if is(f, TrigFn::Cos, &param) && !found_cos {
                            found_cos = true;
                            false
                        } else {
                            true
                        }
                    });
                let (den, sin): (Vec<Expression>, Vec<Expression>) =
                    den_factors.iter().cloned().partition(|f| {
                        if is(f, TrigFn::Sin, &param) && !found_sin {
                            found_sin = true;
                            false
                        } else {
                            true
                        }
                    });
                if !cos.is_empty() && !sin.is_empty() {
                    results.push(product_of(&[
                        Fraction::of(product_of(&num), product_of(&den)),
                        cot(param.clone()),
                    ]));
                }
            }
        }

        results
            .into_iter()
            .map(|exp| {
                (
                    exp.clone(),
                    Argument::new(
                        String::from("Tan/Cot identitiy"),
                        vec![input.clone()],
                        self.name(),
                    ),
                )
            })
            .collect()
    }

    fn name(&self) -> String {
        String::from("TanIdentity")
    }
}

#[cfg(test)]
mod tests {
    use crate::{
        convenience_expressions::{cos, cot, sin, tan, v},
        expressions::Integer,
    };

    use super::*;

    #[test]
    fn test_1() {
        let rule = TanIdentity {};

        let start = Fraction::of(product_of(&[sin(v("x")), sin(v("y"))]), cos(v("x")));
        let result = rule.apply(start).first().unwrap().0.clone();

        assert_eq!(
            result,
            product_of(&[Fraction::of(sin(v("y")), Integer::of(1)), tan(v("x"))])
        );

        let start1 = Fraction::of(cos(v("x")), product_of(&[sin(v("x")), sin(v("y"))]));
        let result1 = rule.apply(start1).first().unwrap().0.clone();

        assert_eq!(
            result1,
            product_of(&[Fraction::of(Integer::of(1), sin(v("y"))), cot(v("x"))])
        );
    }
}