Summation, Products, and Index Notation

/**
 * Fintech Math Bootcamp · Lesson 006 of 120
 * Summation, Products, and Index Notation
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A ledger sum and a return product are different loops
 * Rule:     Σ cash flows; Π growth factors
 *
 * Try it:   Why does a product accumulator start at one?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson006() {
  const flows = [100, -30, 20];
  const returns = [0.10, -0.10];
  const cash = flows.reduce((a, x) => a + x, 0);
  const growth = returns.reduce((a, r) => a * (1 + r), 1);
  const result = {cash, cumulativeReturn: growth - 1};
  return result;
}

export const checkedResult = {"cash":90,"cumulativeReturn":-0.009999999999999898};

// Run this file directly: npx tsx lessons/01-mathematical-language-and-quantitative-reasoning/006-summation-products-and-index-notation.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson006(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 006 of 120
Summation, Products, and Index Notation
Module 01: Mathematical Language and Quantitative Reasoning

Scenario: A ledger sum and a return product are different loops
Rule:     Σ cash flows; Π growth factors

Try it:   Why does a product accumulator start at one?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json
import math


def lesson006() -> dict:
    flows = [100, -30, 20]
    returns = [0.10, -0.10]
    cash = sum(flows)
    growth = math.prod(1 + r for r in returns)
    result = {"cash": cash, "cumulativeReturn": growth - 1}
    return result


if __name__ == "__main__":
    print(json.dumps(lesson006(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 006 of 120
 * Summation, Products, and Index Notation
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A ledger sum and a return product are different loops
 * Rule:     Σ cash flows; Π growth factors
 *
 * Try it:   Why does a product accumulator start at one?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

import java.util.Arrays;

public class Main {
    static final class LedgerSummary {
        final double cash;
        final double cumulativeReturn;

        LedgerSummary(double cash, double cumulativeReturn) {
            this.cash = cash;
            this.cumulativeReturn = cumulativeReturn;
        }
    }

    static LedgerSummary lesson006() {
        double[] flows = {100, -30, 20};
        double[] returns = {0.10, -0.10};
        double cash = Arrays.stream(flows).reduce(0, (a, x) -> a + x);
        double growth = Arrays.stream(returns).reduce(1, (a, r) -> a * (1 + r));
        LedgerSummary result = new LedgerSummary(cash, growth - 1);
        return result;
    }

    public static void main(String[] args) {
        LedgerSummary result = lesson006();
        System.out.println(object(
            "cash", num(result.cash),
            "cumulativeReturn", num(result.cumulativeReturn)));
    }

    // Formats a double the way JSON.stringify does: whole numbers without ".0", null for NaN or infinity.
    static String num(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return String.valueOf((long) x);
        return String.valueOf(x);
    }

    static String quote(String text) {
        return "\"" + text.replace("\\", "\\\\").replace("\"", "\\\"") + "\"";
    }

    // Indents an already formatted JSON value by one level.
    static String nested(String json) {
        return json.replace("\n", "\n  ");
    }

    static String object(String... keysAndValues) {
        if (keysAndValues.length == 0) return "{}";
        StringBuilder out = new StringBuilder("{");
        for (int i = 0; i < keysAndValues.length; i += 2) {
            out.append(i == 0 ? "\n  " : ",\n  ")
               .append(quote(keysAndValues[i])).append(": ").append(nested(keysAndValues[i + 1]));
        }
        return out.append("\n}").toString();
    }
}

// Fintech Math Bootcamp · Lesson 006 of 120
// Summation, Products, and Index Notation
// Module 01: Mathematical Language and Quantitative Reasoning
//
// Scenario: A ledger sum and a return product are different loops
// Rule:     Σ cash flows; Π growth factors
//
// Try it:   Why does a product accumulator start at one?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run it: go run main.go

package main

import (
	"encoding/json"
	"fmt"
)

type LedgerSummary struct {
	Cash             float64 `json:"cash"`
	CumulativeReturn float64 `json:"cumulativeReturn"`
}

func lesson006() LedgerSummary {
	flows := []float64{100, -30, 20}
	returns := []float64{0.10, -0.10}
	cash := 0.0 // a sum starts at zero
	for _, x := range flows {
		cash += x
	}
	growth := 1.0 // a product starts at one
	for _, r := range returns {
		growth *= 1 + r
	}
	result := LedgerSummary{Cash: cash, CumulativeReturn: growth - 1}
	return result
}

func main() {
	printJSON(lesson006())
}

// printJSON prints a value as JSON indented with two spaces, like JSON.stringify(value, null, 2).
func printJSON(value any) {
	out, err := json.MarshalIndent(value, "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 006 of 120
 * Summation, Products, and Index Notation
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A ledger sum and a return product are different loops
 * Rule:     Σ cash flows; Π growth factors
 *
 * Try it:   Why does a product accumulator start at one?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: g++ -std=c++17 -o main main.cpp && ./main
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <numeric>
#include <string>
#include <utility>
#include <vector>

// Formats a double the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
std::string num(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    auto [end, error] = std::to_chars(buffer, buffer + sizeof buffer, x);
    (void)error;
    return std::string(buffer, end);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') out += '\\';
        out += c;
    }
    return out + "\"";
}

// Indents an already formatted JSON value by one level.
std::string nested(const std::string& json) {
    std::string out;
    for (char c : json) {
        out += c;
        if (c == '\n') out += "  ";
    }
    return out;
}

std::string object(const std::vector<std::pair<std::string, std::string>>& fields) {
    if (fields.empty()) return "{}";
    std::string out = "{";
    for (std::size_t i = 0; i < fields.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += quote(fields[i].first) + ": " + nested(fields[i].second);
    }
    return out + "\n}";
}

struct LedgerSummary {
    double cash;
    double cumulativeReturn;
};

LedgerSummary lesson006() {
    const std::vector<double> flows{100, -30, 20};
    const std::vector<double> returns{0.10, -0.10};
    const double cash = std::accumulate(flows.begin(), flows.end(), 0.0,
        [](double a, double x) { return a + x; });
    const double growth = std::accumulate(returns.begin(), returns.end(), 1.0,
        [](double a, double r) { return a * (1 + r); });
    const LedgerSummary result{cash, growth - 1};
    return result;
}

int main() {
    const LedgerSummary result = lesson006();
    std::cout << object({
        {"cash", num(result.cash)},
        {"cumulativeReturn", num(result.cumulativeReturn)}
    }) << "\n";
}

//! Fintech Math Bootcamp · Lesson 006 of 120
//! Summation, Products, and Index Notation
//! Module 01: Mathematical Language and Quantitative Reasoning
//!
//! Scenario: A ledger sum and a return product are different loops
//! Rule:     Σ cash flows; Π growth factors
//!
//! Try it:   Why does a product accumulator start at one?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct LedgerSummary {
    cash: f64,
    cumulative_return: f64,
}

fn lesson006() -> LedgerSummary {
    let flows = [100.0, -30.0, 20.0];
    let returns = [0.10, -0.10];
    let cash = flows.iter().fold(0.0_f64, |a, &x| a + x);
    let growth = returns.iter().fold(1.0_f64, |a, &r| a * (1.0 + r));
    let result = LedgerSummary { cash, cumulative_return: growth - 1.0 };
    result
}

fn main() {
    let result = lesson006();
    println!(
        "{}",
        object(&[
            ("cash", num(result.cash)),
            ("cumulativeReturn", num(result.cumulative_return)),
        ])
    );
}

/// Formats a number the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
fn num(x: f64) -> String {
    if x.is_finite() {
        format!("{}", x)
    } else {
        "null".to_string()
    }
}

fn quote(text: &str) -> String {
    format!("\"{}\"", text.replace('\\', "\\\\").replace('"', "\\\""))
}

/// Indents an already formatted JSON value by one level.
fn nested(json: &str) -> String {
    json.replace('\n', "\n  ")
}

fn object(fields: &[(&str, String)]) -> String {
    if fields.is_empty() {
        return "{}".to_string();
    }
    let lines: Vec<String> = fields
        .iter()
        .map(|(key, value)| format!("  {}: {}", quote(key), nested(value)))
        .collect();
    format!("{{\n{}\n}}", lines.join(",\n"))
}

/**
 * Fintech Math Bootcamp · Lesson 006 of 120
 * Summation, Products, and Index Notation
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A ledger sum and a return product are different loops
 * Rule:     Σ cash flows; Π growth factors
 *
 * Try it:   Why does a product accumulator start at one?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/summation-products-and-index-notation/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: dotnet run  (inside a console project that holds this Program.cs)
 */

using System.Text.Json;

var jsonOptions = new JsonSerializerOptions { WriteIndented = true, PropertyNamingPolicy = JsonNamingPolicy.CamelCase };
Console.WriteLine(JsonSerializer.Serialize(Lesson006(), jsonOptions));

static LedgerSummary Lesson006()
{
    double[] flows = { 100, -30, 20 };
    double[] returns = { 0.10, -0.10 };
    var cash = flows.Aggregate(0.0, (a, x) => a + x);
    var growth = returns.Aggregate(1.0, (a, r) => a * (1 + r));
    var result = new LedgerSummary(cash, growth - 1);
    return result;
}

record LedgerSummary(double Cash, double CumulativeReturn);