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)](Images/MapleConf2022-MatrixTimesMatrix.gif)
![(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)](Images/MapleConf2022-CreateTensor.gif)
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)
The Process: Maple Computations Then (Transport) Visualization
![(left) Correct Maple Computations are the Most Important (right) Export Maple Output for Application and Visualization](Images/MapleConf2022-Transport.gif)
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 Areas](Images/Caveats-Gauss1.gif)
![Gauss Curvature Illustration: A Ratio of Areas](Images/Caveats-Gauss2.gif)
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)](Images/Caveats-CurvatureStoryFig1.png)
![Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)](Images/Caveats-CurvatureStoryFig4.gif)
![Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)](Images/Caveats-CurvatureStoryFig3.png)
Figure 5: Gauss Curvature as an Animated Graphic Novel: Find “A Curvature Story” on Apple Books (shorturl.at/EGOXY)
![](Images/MapleConf2022-Motivation-1-Annotated.png)
![](Images/MapleConf2022-Motivation-2-Annotated.png)
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![Screenshots from tensorAddOns[RiemannCurvatureOnSurface] and tensorAddOns[SurfaceData] which Shows how the Riemann Curvature Defines the Gauss Curvature.](Images/MapleConf2022-Motivation-7-Annotated.png)
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
![](Images/MapleConf2022-Ex1-0-Annotated.png)
![](Images/MapleConf2022-Ex1-1-Annotated.png)
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![](Images/MapleConf2022-Ex1-6.png)
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![](Images/MapleConf2022-Ex1-15.png)
![](Images/MapleConf2022-Ex1-16-Annotated.png)
![A tensorAddOns vs. Physics package Comparison of the Computation of the Riemann Curvature Tensor of the Schwarzschild Metric](Images/MapleConf2022-Ex1-17-Annotated.png)
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?
![](Images/MapleConf2022-Ex2-0.png)
![](Images/MapleConf2022-Ex2-1.png)
![](Images/MapleConf2022-Ex2-2.png)
![](Images/MapleConf2022-Ex2-3.png)
![](Images/MapleConf2022-Ex2-4.png)
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![](Images/MapleConf2022-Ex2-6.png)
![](Images/MapleConf2022-Ex2-7.png)
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![tensorAddOns Computes the Riemann and Ricci Curvature Tensors in an Orthonormal, Anholonomic Frame](Images/MapleConf2022-Ex2-9.png)
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.
![](Images/tensorAddOns-MoreInfo.png)
![For more technical details, see the post tensorAddOns on our blog unconcisemath.com by jason M. Osborne.](Images/tensorAddOns-MoreInfo2.png)
Figure 9: For more technical details, see the post tensorAddOns on our blog unconcisemath.com by jason M. Osborne.