plan.md

my math package

1. Fraction: A class that represents a fraction and provides methods for adding, subtracting, multiplying, and dividing fractions, as well as methods for simplifying and converting to decimal and percent forms.
2. Matrix: A class that represents a matrix and provides methods for performing matrix operations such as addition, subtraction, multiplication, and inversion.
3. Polynomial: A class that represents a polynomial and provides methods for adding, subtracting, multiplying, and dividing polynomials, as well as methods for finding roots and derivatives.
4. Vector: A class that represents a vector and provides methods for performing vector operations such as addition, subtraction, multiplication, and normalization.
5. Graph: A class that represents a graph and provides methods for adding, deleting, and modifying vertices and edges, as well as methods for finding shortest paths and spanning trees.
6. BigInteger: A class that represents an arbitrarily large integer and provides methods for performing arithmetic operations and comparing numbers of any size.
7. BigDecimal: A class that represents an arbitrarily precise decimal number and provides methods for performing arithmetic operations and comparing numbers with high precision.
8. DateInterval: A class that represents an interval of time between two dates and provides methods for calculating the duration, finding overlapping intervals, and converting to different units of time.
9. ComplexNumber: A class that represents a complex number and provides methods for performing arithmetic operations and conversions to different forms, such as polar and rectangular.
10. Quaternion: A class that represents a quaternion and provides methods for performing arithmetic operations and conversions to different forms, such as axis-angle and Euler angles.
11. FractionalNumber: A class that represents a number in fractional form and provides methods for performing arithmetic operations and conversions to different forms, such as decimal and percent.
12. Interval: A class that represents an interval of numbers and provides methods for testing whether a number is within the interval and finding intersections with other intervals.
13. Permutation: A class that represents a permutation and provides methods for composing, inverting, and comparing permutations.
14. Partition: A class that represents a partition of a set and provides methods for testing whether a set is a partition, finding equivalent partitions, and merging partitions.
15. PowerSet: A class that represents the power set of a set and provides methods for generating all subsets, testing whether a set is a subset, and finding the cardinality of the power set.

very advanced

1. Circuit: A class that represents a digital logic circuit and provides methods for analyzing and simulating the behavior of the circuit.
2. Image: A class that represents a digital image and provides methods for processing and analyzing the image, such as filtering, segmentation, and feature extraction.
3. Audio: A class that represents an audio signal and provides methods for processing and analyzing the signal, such as filtering, resampling, and Fourier analysis.
4. Video: A class that represents a video signal and provides methods for processing and analyzing the signal, such as compression, motion estimation, and object tracking.
5. GeneticSequence: A class that represents a DNA or RNA sequence and provides methods for analyzing and comparing sequences, such as finding common motifs and calculating evolutionary distances.
6. ChemicalCompound: A class that represents a chemical compound and provides methods for analyzing and synthesizing compounds, such as calculating molecular properties and designing reactions.
7. GeometricShape: A class that represents a geometric shape and provides methods for computing geometric properties, such as area, perimeter, and centroid.
8. StatisticalDistribution: A class that represents a statistical distribution and provides methods for generating random samples, computing moments, and fitting data.
9. OptimizationProblem: A class that represents an optimization problem and provides methods for solving the problem using various algorithms, such as gradient descent and genetic algorithms.
10. Automaton: A class that represents a finite-state automaton and provides methods for analyzing and simulating the behavior of the automaton.
11. Robot: A class that represents a robotic system and provides methods for controlling the motion and sensing of the robot, as well as simulating its behavior.
12. NeuralNetwork: A class that represents a neural network and provides methods for training and testing the network, as well as analyzing its behavior.
13. DigitalSignalProcessing: A class that provides methods for processing digital signals, such as filtering, resampling, and spectral analysis.
14. Graph: A class that represents a graph and provides methods for analyzing and manipulating the graph, such as finding shortest paths and computing centrality measures.
15. ProbabilityDistribution: A class that represents a probability distribution and provides methods for generating random samples, computing moments, and fitting data.
16. MachineLearningModel: A class that represents a machine learning model and provides methods for training and testing the model, as well as analyzing its performance and interpretability.
17. TimeSeries: A class that represents a time series and provides methods for processing and analyzing the series, such as smoothing, trend detection, and anomaly detection.
18. GeometricObject: A class that represents a geometric object and provides methods for computing geometric properties, such as area, perimeter, and centroid.
19. SimulationModel: A class that represents a simulation model and provides methods for running and analyzing simulations, as well as optimizing model parameters.
20. PhysicalSystem: A class that represents a physical system and provides methods for modeling and simulating the behavior of the system, such as solving differential equations and simulating control systems.