Simple example | Core content | B-spline library | Graphical user interface | An interactive Shiny GUI is available: | Python port

Introduction | Basic Polynomial Operations | Polynomial Multiplication | Polynomial Addition | Polynomial Evaluation | Polynomial Differentiation | Polynomial Reduction | Taylor Basis Change | Piecewise Polynomial (PP) Form | Creating a PP Object | Non-Callable PP Objects | Callable PP Objects | Create a callable PP | Evaluate directly | Print shows information | Can be used in plots | Extrapolating values | PP with two intervals: x^2 on [0,1], 2x-1 on [1,2] | Evaluate inside and outside the knot range | The values at -0.5 and 2.5 are extrapolated | Advanced: PP Form Manipulation | Extracting a Single Interval Polynomial | Combining PP Objects | Visualizing PP with Basis Functions | Comparison: PP vs B-spline | Summary | Displaying polynomial in a human readable form | Basic Usage | Canonical Basis (Default) | Working with Local Bases | Display in Local Basis | Converting Between Bases | Examples with Different Bases | Positive and Negative Centers | Controlling Output Format | Number of Digits | Working with B-splines | Integration with show_pp() | Summary show_pp()

Introduction | Available Demos | Uniform Constraints | Monotonicity Constraints | Convexity Constraints | Third Derivative Constraints | Constraints by Degree | Partial Constraints | Partial Monotonicity | Partial Convexity | Mixed Constraints | Constraints with Multiple Knots | Recap: Visualizing Constraint Effects | Karlin-Studden SOCP Formulation | Practical Considerations | When to Use Shape Constraints | Constraint Strength | Choosing the Degree | Summary

Introduction | 1. Quantile Constrained Regression | 1.1 Quantile Regression | 1.2 Shape Constraints | 1.3 Karlin-Studden Characterization | 1.4 SOCP formulation and CVXR implementation | 2. B-spline Construction with De Boor's Formula | 2.1 B-spline Definition | 2.3 De Boor's Algorithm for Coefficient Computation | 2.4 Implementation Details | 2.5 (Advanced) Knot Multiplicity and Regularity | References | Further Reading

Introduction | Building a B-spline Basis | Basic Construction | Visualizing the Basis | Understanding the Extended Knot Sequence | Visualizing B-spline Bases | Visualizing a B-spline Basis | Visualizing Different Degrees | Customizing Visualization | Differentiating a B-spline Basis | Visualizing Derivative Bases | Differentiating a B-spline Function | Method 1: Using spline_eval() with der Parameter | Method 2: Using Bspline_deriv() to Get Derivative Coefficients | Method 3: Step-by-step evaluation using basis derivatives | 1. Compute the derivative basis | 2. Evaluate the basis at points using bs_direct | 3. Use matrix multiplication with coefficients | PP-form Conversion | Callable PP Objects | Callable Splines | Creating Callable Splines | Non-Callable Splines | Getting Parameters | Advanced: Knot Multiplicity and Regularity | Creating B-splines with Multiple Knots | Effect of Multiplicity on Regularity | Derivatives at Knots | Simple Example: Coherence of Derivative Evaluation Methods (Degree 5) | Summary