Maple Conference 2022

A Demonstration of the Maple package tensorAddOns by Jason M. Osborne.
For additional technical detail please see the post tensorAddOns.

Last Updated: Wednesday, January 03, 2024 - 12:28:44.


The Goal: In Maple As On Paper

(left) Matrix Multiplication in Tensor Notation (right) New tensorAddOns Functionality CreateTensor, DescribeTensor, and MatrixView (Note: prod is existing, but deprecated, functionality of the package tensor)(left) Matrix Multiplication in Tensor Notation (right) New tensorAddOns Functionality CreateTensor, DescribeTensor, and MatrixView (Note: prod is existing, but deprecated, functionality of the package tensor)

Figure 1: (left) Matrix Multiplication in Tensor Notation (right) New tensorAddOns Functionality CreateTensor, DescribeTensor, and MatrixView (Note: prod is existing, but deprecated, functionality of the package tensor)
















What is… A Tensor

Think of a Tensor as a Storage Mechanism for Higher Dimensional Data

Figure 2: Think of a Tensor as a Storage Mechanism for Higher Dimensional Data
















The Process: Maple Computations Then (Transport) Visualization

(left) Correct Maple Computations are the Most Important (right) Export Maple Output for Application and Visualization

Figure 3: (left) Correct Maple Computations are the Most Important (right) Export Maple Output for Application and Visualization
















Math Motivation and Coding Philosophy: Gauss to Riemann Curvature

Gauss Curvature Illustration: A Ratio of AreasGauss Curvature Illustration: A Ratio of Areas

Figure 4: Gauss Curvature Illustration: A Ratio of Areas

Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)

Figure 5: Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)

Screenshots from tensorAddOns[RiemannCurvatureOnSurface] and tensorAddOns[SurfaceData] which Shows how the Riemann Curvature Defines the Gauss Curvature.

Figure 6: Screenshots from tensorAddOns[RiemannCurvatureOnSurface] and tensorAddOns[SurfaceData] which Shows how the Riemann Curvature Defines the Gauss Curvature.
















A Comparison: The Packages tensorAddOns and Physics

A tensorAddOns vs. Physics package Comparison of the Computation of the Riemann Curvature Tensor of the Schwarzschild Metric

Figure 7: A tensorAddOns vs. Physics package Comparison of the Computation of the Riemann Curvature Tensor of the Schwarzschild Metric
















The Question: An Example Only tensorAddOns Can Do?

tensorAddOns Computes the Riemann and Ricci Curvature Tensors in an Orthonormal, Anholonomic Frame

Figure 8: tensorAddOns Computes the Riemann and Ricci Curvature Tensors in an Orthonormal, Anholonomic Frame
















More Info: Check out our blog unconcisemath.com

  • Currently 36 functions in the package tensorAddOnsTools and tensorAddOnsComps.
  • Many documentation examples have been written that are in need of testing and demonstration.
For more technical details, see the post tensorAddOns on our blog unconcisemath.com by jason M. Osborne.

Figure 9: For more technical details, see the post tensorAddOns on our blog unconcisemath.com by jason M. Osborne.