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pt-c96118e682c9 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Front matter
# Sweeping Nets, Saddle Maps, & Complex Analysis
*Parker Emmerson (Yaohushuason)*
## Dedication
This book is dedicated to Yahowah the living one Allaha, who is Yeshua ben Joseph ben David.
## Publication
Published Novemb... | {
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pt-0bc464e2b9ab | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 1. Formalizing Mechanical Analysis of Sweeping Nets I (part 1 of 3)
# Chapter 1. Formalizing Mechanical Analysis of Sweeping Nets I
## Formalizing Mechanical Analysis Using Sweeping Net Methods I
Parker Emmerson
December 2023
... | {
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pt-1310a1e04336 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 1. Formalizing Mechanical Analysis of Sweeping Nets I (part 2 of 3)
$$|f_i(\phi + \delta \phi) - f_i(\phi)| \leq \max_{\phi \in \left[0, \frac{\pi}{2}\right]} |f_i'(\phi)| \delta \phi = M \delta \phi, \quad i \in \{1,2\},$$
where... | {
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pt-069fb92b6a4d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 1. Formalizing Mechanical Analysis of Sweeping Nets I (part 3 of 3)
Our approach demonstrates the robustness and stability of the sweeping nets under perturbations, as shown in Theorems 4.1, 4.2, and 4.3. The methods presented ope... | {
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pt-2e47a7ec7541 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 2. Formalizing Mechanical Analysis of Sweeping Nets II (part 1 of 3)
# Chapter 2. Formalizing Mechanical Analysis of Sweeping Nets II
## Formalizing Mechanical Analysis Using Sweeping Net Methods II: Written Without Complex Analy... | {
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pt-cd2d5410162b | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 2. Formalizing Mechanical Analysis of Sweeping Nets II (part 2 of 3)
The author would like to thank the mathematical community for the ongoing discussions and contributions that have inspired this work.
### References
- [1] Stew... | {
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pt-1780f5bcb94c | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 2. Formalizing Mechanical Analysis of Sweeping Nets II (part 3 of 3)
This script visualizes the sweeping net for $f(z) = \frac{1}{z - z_0}$ on the unit circle, highlighting the sets $A$ and $B$ that approximate the behavior near t... | {
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pt-fe04b915157e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 3. Generalizations of Sweeping Nets in Higher Dimensions (part 1 of 3)
# Chapter 3. Generalizations of Sweeping Nets in Higher Dimensions
## Generalization of Sweeping Nets to Higher-Dimensional Singularities
Parker Emmerson
Oc... | {
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pt-59a771ac2a1e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 3. Generalizations of Sweeping Nets in Higher Dimensions (part 2 of 3)
for all $x$ with $\| x - x_0 \| \leq \delta$, where $\delta$ depends on $\epsilon$.
Therefore, the net $\mathcal{N}$ approximates the hypersurface $S$ within ... | {
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pt-009b7bd7a249 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 3. Generalizations of Sweeping Nets in Higher Dimensions (part 3 of 3)
```python
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.lines import Line2D
def g(x, y):
retu... | {
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pt-90da18f6b73b | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 1 of 7)
# Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III
## Formalizing Mechanical Analysis of Sweeping Nets III
Parker Emmerson
October 2024
### 1... | {
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pt-8d8753bef69d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 2 of 7)
1. **Hessian Analysis**: Compute the Hessian matrix $H_g(x)$ of $g$ at various points $x$ on the hypersurface to analyze the curvature: $$H_g(x) = \left[ \frac{... | {
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pt-3ea0a43c8443 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 3 of 7)
```python
import numpy as np
import concurrent.futures
import matplotlib.pyplot as plt
# Define a simple function to simulate computation for a sweeping net po... | {
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pt-f72d4200aef5 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 4 of 7)
```python
import numpy as np
import matplotlib.pyplot as plt
def g(x, y):
"""A function with degenerate Hessian at the origin."""
return x**2 + y**3 #... | {
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pt-d14f5c1714d5 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 5 of 7)
1. **Comparison of $M$ and $\tilde{M}$**: The $C^k$ norm bound $\| M - \tilde{M} \|_{C^k} < \epsilon$ implies that the functions defining $M$ and $\tilde{M}$ di... | {
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pt-9108df4ecb62 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 6 of 7)
1. **Morse Function and Critical Points**: At a critical point $p$ of $g$, we have $\nabla g(p) = 0$, and the Hessian $H_g(p)$ is non-degenerate.
2. **Morse Ind... | {
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pt-5411fea3fda7 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 4. Formalizing Mechanical Analysis of Sweeping Nets III (part 7 of 7)
In this paper, we have extended the sweeping net method by proving Theorems 21 through 30, which address various advanced topics such as degenerate Hessian matr... | {
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pt-cb6f06cd575d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 5. Formalizing Mechanical Analysis of Sweeping Nets IV (part 1 of 2)
# Chapter 5. Formalizing Mechanical Analysis of Sweeping Nets IV
## Formalizing Mechanical Analysis of Sweeping Nets IV
Parker Emmerson
October 2024
**Abstra... | {
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pt-f3e81cff26af | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 5. Formalizing Mechanical Analysis of Sweeping Nets IV (part 2 of 2)
1. **Representation of the Boundary:** Let $\partial M$ denote the boundary of the manifold $M$. Near the boundary, the hypersurface $S$ and the sweeping net mus... | {
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pt-dc9e3c5cb583 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 6. Analyzing Zeros of the Riemann Zeta Function Using Sweeping Net Methods (part 1 of 3)
# Chapter 6. Analyzing Zeros of the Riemann Zeta Function Using Sweeping Net Methods
## Analyzing the Zeros of the Riemann Zeta Function Usi... | {
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pt-31aeb9d05ccf | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 6. Analyzing Zeros of the Riemann Zeta Function Using Sweeping Net Methods (part 2 of 3)
- **Relation between $P(s)$, $Q(s)$, and $C(s)$**:
- The Riemann Hypothesis asserts:
$$P(s) \cap Q(s) \subseteq C(s).$$
##### 5.2.3 Com... | {
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pt-98efc259a63d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 6. Analyzing Zeros of the Riemann Zeta Function Using Sweeping Net Methods (part 3 of 3)
We reinforce the assertion that all non-trivial zeros of $\zeta(s)$ lie on the critical line, thus supporting the Riemann Hypothesis. This co... | {
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pt-34aa38d71ac6 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 7. Proof of Riemann Hypothesis Using Set Theoretic and Sweeping Net Methods
# Chapter 7. Proof of Riemann Hypothesis Using Set Theoretic and Sweeping Net Methods
## Proof of Riemann Hypothesis Using Sweeping Nets
Parker Emmerson... | {
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pt-069968c4094d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 8. Conjecture on Perfect Numbers
# Chapter 8. Conjecture on Perfect Numbers
## Persistence of Perfect Numbers
Parker Emmerson
October 2024
### 1 Introduction
For any non-constant polynomial $P(n)$ with integer coefficients, w... | {
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pt-4cec6d21f7a3 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 9. Integration of Tensor Fields with Angular Components: An Analytical and Computational Study (part 1 of 2)
# Chapter 9. Integration of Tensor Fields with Angular Components: An Analytical and Computational Study
## Integration ... | {
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pt-7ca6e7fb5ba5 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 9. Integration of Tensor Fields with Angular Components: An Analytical and Computational Study (part 2 of 2)
The enhanced combined integrand was visualized using a 3D surface plot, providing a detailed representation of its behavi... | {
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pt-35f8d9a913ee | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 10. Optimization Paths for Energy Numbers (part 1 of 2)
# Chapter 10. Optimization Paths for Energy Numbers
## Optimization of Energy Numbers Continued
Parker Emmerson
October 2024
### 1 Introduction
### Question 3
**Polyhed... | {
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"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
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pt-132383118f98 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 10. Optimization Paths for Energy Numbers (part 2 of 2)
$$c = \inf_{x \in \mathcal{X}} \{ w^\top (\phi(x) \phi'(x)^\top) \}$$
Given that $w$ and $\phi(x)$, $\phi'(x)$ are given, perhaps our algorithm proceeds as follows:
**Algor... | {
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pt-1778cbd95cec | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 11. Cone Formation from Circle Folding: A Comprehensive Analysis
# Chapter 11. Cone Formation from Circle Folding: A Comprehensive Analysis
## Cone Formation from Circle Folding: A Comprehensive Analysis
October 20, 2024
**Abst... | {
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pt-a4fb27ff5ee2 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 13. Defining π via Infinite Densification of the Sweeping Net and Reverse Integration (part 1 of 2)
# Chapter 13. Defining π via Infinite Densification of the Sweeping Net and Reverse Integration
## Defining $\pi$ via Infinite De... | {
"chapter": "Chapter 13. Defining π via Infinite Densification of the Sweeping Net and Reverse Integration",
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pt-26c92bac15da | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 13. Defining π via Infinite Densification of the Sweeping Net and Reverse Integration (part 2 of 2)
#### 6.3 Handling Infinite Limits in Integration
When dealing with infinite limits, we use the concept of improper integrals. The... | {
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pt-dc4e52e36ee9 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 14. Non-Commutative Scalar Fields (part 1 of 2)
# Chapter 14. Non-Commutative Scalar Fields
## Non-Commutative Scalar Fields
Parker Emmerson
October 2024
### 1 Introduction
### Finite Difference Methods for Scalar Fields in N... | {
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pt-b34e8f66b024 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 2 of 7)
- 1 Introduction — 2
- 2 General Framework for Set Integration — 3
- 2.1 Defining Sets Based on Properties — 3
- 2.2 Examples of Properties — 3
- 2.3 Set Operations a... | {
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pt-a9274a91d039 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 3 of 7)
- $\operatorname{Re}(z) = c$ (a vertical line in the complex plane).
- $|z| = r$ (a circle of radius $r$).
- $|f(z)| = M$ (points where $f$ has constant modulus... | {
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pt-713e96c4ce74 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 4 of 7)
The integration of sets through set-theoretic operations involves defining sets based on certain properties or conditions and exploring their relationships using operations... | {
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pt-66d997ff47e1 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 5 of 7)
- **Function Definition**: $f(x, y) = e^{-x^2 - y^2}$.
- **Domain Definition Using Set Operations**:
- `in_circle`: Points inside the unit circle $x^2 + y^2 \leq 1$.
- `in_... | {
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pt-276228cf64e4 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 6 of 7)
In quantum mechanics, the momentum-space wave function of a particle in a potential is given by the Fourier transform of its position-space wave function. Consider a partic... | {
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pt-a1b9706b97f8 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 15. Generalized Theory of Group Integration (part 7 of 7)
In mathematical analysis, the integration over groups and sets plays a crucial role in understanding symmetry, invariants, and the behavior of functions under transformatio... | {
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pt-28baeb4f951e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 16. Math of Ghosts, Phantoms (part 1 of 4)
# Chapter 16. Math of Ghosts, Phantoms
## On the Relationship between Morphisms, Root Sets, and Interior Products in Mathematical Analysis
Parker Emmerson
October 2023
**Abstract.** W... | {
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pt-49a2709dc658 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 16. Math of Ghosts, Phantoms (part 2 of 4)
The terms **ghosts** and **phantoms** are used metaphorically to describe structures or phenomena that are not directly observable but have mathematical implications within a system. In t... | {
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pt-71d6b08aa873 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 16. Math of Ghosts, Phantoms (part 3 of 4)
where $\boldsymbol{\alpha}_\epsilon = \boldsymbol{\alpha} + \epsilon\boldsymbol{\gamma}$, with $\boldsymbol{\gamma}$ representing the differential form associated with $g(x)$.
Expanding ... | {
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pt-a33d0480d63c | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 16. Math of Ghosts, Phantoms (part 4 of 4)
**Exterior Derivatives:**
Compute the exterior derivatives:
$$dN = \frac{\partial N}{\partial r}dr + \frac{\partial N}{\partial s}ds,$$
$$dD = \frac{\partial D}{\partial r}dr + \frac{\... | {
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pt-2bf7fc7b2c11 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 17. Fractal Morphisms and the World Sheet (part 1 of 2)
# Chapter 17. Fractal Morphisms and the World Sheet
## Fractal Morphisms of the World Sheet
Parker Emmerson
October 2024
### 1 Introduction
Quantum Mechanics:
1. Hilber... | {
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"author": "Parker Emmerson (Yaohushuason)"
} |
pt-fbc4a4fdc0af | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 17. Fractal Morphisms and the World Sheet (part 2 of 2)
- Quantum and Fractal Combinatorics: The tensor product $\otimes$ suggests combining different aspects or scales of the system in a way that respects the quantum and fractal ... | {
"chapter": "Chapter 17. Fractal Morphisms and the World Sheet",
"source": "book",
"piece": 2,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-5c2f0cbf063e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 18. Fractals (part 1 of 3)
# Chapter 18. Fractals
## Fractals
Parker Emmerson
November 2024
### 1 Introduction
These fractals are from interpretations of the following pseudo-code for the iterations:
$$\begin{aligned}
& \the... | {
"chapter": "Chapter 18. Fractals",
"source": "book",
"piece": 1,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-707bd019586e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 18. Fractals (part 2 of 3)
```python
import numpy as np
import matplotlib.pyplot as plt
from numba import jit
import warnings
# Suppress warnings from invalid operations (e.g., overflow)
warnings.filterwarnings("ignore", category... | {
"chapter": "Chapter 18. Fractals",
"source": "book",
"piece": 2,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-4a63828e754f | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 18. Fractals (part 3 of 3)
```python
import numpy as np
import matplotlib.pyplot as plt
from numba import jit
# Define the custom fractal function with the iterative function
@jit(nopython=True)
def compute_fractal_with_hold_cons... | {
"chapter": "Chapter 18. Fractals",
"source": "book",
"piece": 3,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-2373b1d5412c | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 19. Hypersphere (part 1 of 2)
# Chapter 19. Hypersphere
## The Mathematics of Hyperspheres and Generalizations of the Reverse Double Integral
Parker Emmerson
**Abstract.** Hyperspheres are fundamental objects in higher-dimensio... | {
"chapter": "Chapter 19. Hypersphere",
"source": "book",
"piece": 1,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-f47b2e8afa69 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 19. Hypersphere (part 2 of 2)
```python
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider
from mpl_toolkits.mplot3d import Axes3D
# Parameters
R = 1.0 # Initial radius of the sphere
... | {
"chapter": "Chapter 19. Hypersphere",
"source": "book",
"piece": 2,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-7404eded8fde | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic (part 1 of 5)
# Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the ... | {
"chapter": "Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic",
"source": "book",
"piece": 1,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-c63ba44f38e4 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic (part 2 of 5)
```mathematica
(*Define the constants and functions*)
r = 0.5;(*Radius of the \
circle*)K = 1;(*Con... | {
"chapter": "Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic",
"source": "book",
"piece": 2,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-2489a1bd052e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic (part 3 of 5)
```python
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
i... | {
"chapter": "Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic",
"source": "book",
"piece": 3,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-115d9b449c96 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic (part 4 of 5)
*[Figure 20 (Tessellations PDF page 28): It stands to reason that logical associations that form a ... | {
"chapter": "Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic",
"source": "book",
"piece": 4,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-f6e6f62307d0 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason)
Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic (part 5 of 5)
The code structure and style discussed herein adeptly marry the abstract with the procedural, unvei... | {
"chapter": "Chapter 20 (supplement, not in the printed book). Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic",
"source": "book",
"piece": 5,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-23ebe48270af | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook 5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb (part 1 of 5)
## Notebook `5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb`
Code cell 1:
```python
import matplotlib.pyplot as plt
import networkx as ... | {
"chapter": null,
"notebook": "5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb",
"source": "notebook",
"piece": 1,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-1ec36110b996 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook 5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb (part 2 of 5)
Code cell 6:
```python
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from ipywidgets import interact, IntSlider, Flo... | {
"chapter": null,
"notebook": "5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb",
"source": "notebook",
"piece": 2,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-b652900b50cb | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook 5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb (part 3 of 5)
Code cell 9:
```python
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
from ipywidgets import interact, FloatSlider
fr... | {
"chapter": null,
"notebook": "5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb",
"source": "notebook",
"piece": 3,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-ca7eea94f385 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook 5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb (part 4 of 5)
Code cell 11:
```python
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
from ipywidgets import interact, FloatSlider, ... | {
"chapter": null,
"notebook": "5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb",
"source": "notebook",
"piece": 4,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-2cb9aac61405 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook 5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb (part 5 of 5)
Code cell 13:
```python
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
from ipywidgets import interact, FloatSlider, ... | {
"chapter": null,
"notebook": "5D_Logic_Particle_(Incomplete_Cohesive_Vectron).ipynb",
"source": "notebook",
"piece": 5,
"pieces": 5,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-669111404075 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook And_Or_Games.ipynb
## Notebook `And_Or_Games.ipynb`
Code cell 1:
```python
import numpy as np
import matplotlib.pyplot as plt
# Define the symbolic logic operations as per the provided description
class LogicO... | {
"chapter": null,
"notebook": "And_Or_Games.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-e3d5c3715425 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Commutative_Diagrams.ipynb (part 2 of 3)
Code cell 8:
```python
import matplotlib.pyplot as plt
import networkx as nx
def draw_commutative_diagram():
# Create graph object
G = nx.DiGraph()
# Define... | {
"chapter": null,
"notebook": "Commutative_Diagrams.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-d1aebdafd2d0 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Commutative_Diagrams.ipynb (part 3 of 3)
*[Plot: images/notebooks/Commutative_Diagrams_cell14_15.png]*
Code cell 16:
```python
import networkx as nx
import matplotlib.pyplot as plt
# Create a balanced tree of ... | {
"chapter": null,
"notebook": "Commutative_Diagrams.ipynb",
"source": "notebook",
"piece": 3,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-3d633a7fdec3 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Computational_Notebook_for_M_Posit_Transforms_on_Spinors.ipynb (part 1 of 2)
## Notebook `Computational_Notebook_for_M_Posit_Transforms_on_Spinors.ipynb`
Code cell 1:
```python
# Import necessary libraries
impo... | {
"chapter": null,
"notebook": "Computational_Notebook_for_M_Posit_Transforms_on_Spinors.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-5ea84605632e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Computational_Notebook_for_M_Posit_Transforms_on_Spinors.ipynb (part 2 of 2)
Code cell 5:
```python
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider, IntSlider
def... | {
"chapter": null,
"notebook": "Computational_Notebook_for_M_Posit_Transforms_on_Spinors.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-30bf34110fbe | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Connected_Prime_Digit_Factorial_Occurrences_to_The_Riemann_Zeta_Function_10_5281_zenodo_12837958.ipynb
## Notebook `Connected_Prime_Digit_Factorial_Occurrences_to_The_Riemann_Zeta_Function_10_5281_zenodo_1283795... | {
"chapter": null,
"notebook": "Connected_Prime_Digit_Factorial_Occurrences_to_The_Riemann_Zeta_Function_10_5281_zenodo_12837958.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-8c69d5dd1318 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook DiGraph_Code.ipynb (part 1 of 2)
## Notebook `DiGraph_Code.ipynb`
Code cell 1:
```python
from graphviz import Digraph
# Create a new directed graph
dot = Digraph()
# Set graph attributes
dot.attr('node'... | {
"chapter": null,
"notebook": "DiGraph_Code.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-3a65b523f42d | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook DiGraph_Code.ipynb (part 2 of 2)
Printed output:
```text
Optimal Gamma for m=1, i=1: 0.36787944117144233
Optimal Gamma for m=2, i=1: 0.1353352832366127
Optimal Gamma for m=2, i=2: 0.1353352832366127
Optimal Gamm... | {
"chapter": null,
"notebook": "DiGraph_Code.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-fe3e8e6de162 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Direction_Fields_of_Numeric_Energy_Integral_Mapped_to_Reals.ipynb
## Notebook `Direction_Fields_of_Numeric_Energy_Integral_Mapped_to_Reals.ipynb`
Code cell 1:
```python
import numpy as np
import matplotlib.pypl... | {
"chapter": null,
"notebook": "Direction_Fields_of_Numeric_Energy_Integral_Mapped_to_Reals.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-8fca1fe54432 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook E_Approximata.ipynb
## Notebook `E_Approximata.ipynb`
Code cell 1:
```python
import math
import random
from sympy import symbols, Sum, factorial, exp, pi, diff, oo, Function, simplify
# Unique Symbols Generati... | {
"chapter": null,
"notebook": "E_Approximata.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-44904b6b10d7 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Folding_Circle_into_Cone_Code.ipynb
## Notebook `Folding_Circle_into_Cone_Code.ipynb`
Code cell 1:
```python
import numpy as np
from ipywidgets import interact, FloatSlider, ColorPicker
from matplotlib import c... | {
"chapter": null,
"notebook": "Folding_Circle_into_Cone_Code.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-634b921a56f4 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Fractal_Partitioning_with_Zeta_Function.ipynb (part 1 of 2)
## Notebook `Fractal_Partitioning_with_Zeta_Function.ipynb`
Code cell 1:
```python
import mpmath
import numpy as np
import matplotlib.pyplot as plt
#... | {
"chapter": null,
"notebook": "Fractal_Partitioning_with_Zeta_Function.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-978a760ab8bb | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Fractal_Partitioning_with_Zeta_Function.ipynb (part 2 of 2)
Code cell 4:
```python
import mpmath
import numpy as np
import matplotlib.pyplot as plt
# Initialize mpmath to higher precision
mpmath.mp.dps = 25 # ... | {
"chapter": null,
"notebook": "Fractal_Partitioning_with_Zeta_Function.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 2,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-8544f8ae8051 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Genetic Fragment.ipynb
## Notebook `Genetic Fragment.ipynb`
Code cell 1:
```python
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Constants and functions
r = 0.5 ... | {
"chapter": null,
"notebook": "Genetic Fragment.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-235ea6a524fb | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Hypercone.ipynb
## Notebook `Hypercone.ipynb`
Code cell 1:
```python
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider
from mpl_toolkits.mplot3d import Axes3D
# Pa... | {
"chapter": null,
"notebook": "Hypercone.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 1,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-6b2c620443d5 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 1 of 14)
## Notebook `Limbertwig_V_4_Ultra.ipynb`
Text cell 1:
Fractal Morphisms: The fractal morphisms are mappings between metric spaces that preserve the fractal structure. ... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-0f410a29ad71 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 3 of 14)
Code cell 13:
```python
from sympy import symbols, sin, cos, pi, tanh, sqrt, exp, Function, Integral
import numpy as np
# Define symbols
theta, gamma, alpha, beta, l, r... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 3,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-a180a90755b4 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 4 of 14)
Code cell 21:
```python
import sympy as sp
# Define symbols
theta, psi, n, l, R, Omega_Lambda, prod_Lambda_h = sp.symbols('theta psi n l R Omega_Lambda prod_Lambda_h')
... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 4,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-ae436bee7835 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 5 of 14)
Printed output:
```text
Requirement already satisfied: ipywidgets in /usr/local/lib/python3.10/dist-packages (7.7.1)
Requirement already satisfied: matplotlib in /usr/lo... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 5,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-9ddb5d5c03c9 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 6 of 14)
Printed output:
```text
Field Equation for Generalized Aftereffect Morphism:
... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 6,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-eabadac8d03e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 9 of 14)
Code cell 38:
```python
import sympy as sp
# Category theory classes
class Category:
def __init__(self, name):
self.name = name
self.objects = set()... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 9,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-ead29e41584b | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 10 of 14)
Code cell 41:
```python
import sympy as sp
# Define symbols used throughout all programs
symbols_dict = {
'n': sp.symbols('n'),
'r': sp.symbols('r'),
'm': ... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 10,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-424ae3c08e11 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 11 of 14)
Code cell 47:
```python
import sympy as sp
# Define symbols for elements in the vector space
V = sp.symbols('V') # V as a symbol representing a vector space
t = sp.sy... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 11,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-192d16a344c9 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 12 of 14)
Error:
```text
ValueError: Invalid limits given: ((idx, Lambda),)
---------------------------------------------------------------------------
ValueError ... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 12,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-8968acc3f67c | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 13 of 14)
Error:
```text
SympifyError: SympifyError: 'A'
---------------------------------------------------------------------------
SympifyError Tr... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 13,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-c7ee57b09c88 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Limbertwig_V_4_Ultra.ipynb (part 14 of 14)
Code cell 59:
```python
import numpy as np
# Define a virtual life form as a list of genes (parameters)
class VirtualLifeForm:
def __init__(self, genes):
s... | {
"chapter": null,
"notebook": "Limbertwig_V_4_Ultra.ipynb",
"source": "notebook",
"piece": 14,
"pieces": 14,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-3964f82aa6eb | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Kernel_3.ipynb (part 1 of 3)
## Notebook `Logic_Kernel_3.ipynb`
Code cell 1:
```python
import sympy as sp
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from graphviz import Digr... | {
"chapter": null,
"notebook": "Logic_Kernel_3.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-bd9ccce81b0e | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Kernel_3.ipynb (part 2 of 3)
Code cell 2:
```python
# Import necessary libraries
import sympy as sp
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from graphviz import Digraph
fro... | {
"chapter": null,
"notebook": "Logic_Kernel_3.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-fd8b2dccb863 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Kernel_3.ipynb (part 3 of 3)
Code cell 3:
```python
# Import necessary libraries
import sympy as sp
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from graphviz import Digraph
fro... | {
"chapter": null,
"notebook": "Logic_Kernel_3.ipynb",
"source": "notebook",
"piece": 3,
"pieces": 3,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-51fdf2c03a97 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 1 of 9)
## Notebook `Logic_Vector_9.ipynb`
Code cell 1:
```python
import ipywidgets as widgets
from IPython.display import display, clear_output
import numpy as np
import matplotlib.p... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 1,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-0cf629fd6901 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 2 of 9)
*[Plot: images/notebooks/Logic_Vector_9_cell02_8.png]*
*[Plot: images/notebooks/Logic_Vector_9_cell02_9.png]*
*[Plot: images/notebooks/Logic_Vector_9_cell02_10.png]*
*[Plot:... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 2,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-ee3dc52f0525 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 3 of 9)
Code cell 7:
````python
Sure! Let's design an integrated application that consolidates various aspects of the previous programs into a comprehensive and multi-functional applic... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 3,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-8c32a4ea1560 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 4 of 9)
Error:
```text
SyntaxError: unterminated string literal (detected at line 1) (<ipython-input-10-64038dd85f26>, line 1)
File "<ipython-input-10-64038dd85f26>", line 1
Sur... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 4,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-c2c3c9e90318 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 5 of 9)
Code cell 9:
````python
Certainly! It seems there was some corruption in the previous execution. Let's break down and correct the pieces to ensure the entire application works ... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 5,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-cea0f966f023 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 6 of 9)
Code cell 10:
```python
import os
import subprocess
import re
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
from graphviz import Digraph
import networkx... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 6,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-f2428dd3dabc | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 7 of 9)
Printed output:
```text
digraph CJTree {
root [label="$\mathbf{s_{s}^\Omega}=\mathrm{F}(\phi.)$: \ $\mathbf{\star_{\overline{\infty}}}:$" shape=none]
A [label="$s_s^\Omega+\o... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 7,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-6674a6bd73bb | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 8 of 9)
Code cell 11:
```python
import os
import subprocess
import re
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import RegularPolygo... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 8,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-93b97bde985b | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Logic_Vector_9.ipynb (part 9 of 9)
Printed output:
```text
Integrated Application Menu
1: Side-by-side Diff
2: Unified Diff
3: Prevent The Silver Searcher from Searching Irrelevant Files
4: Sum Numbers
5: newj ... | {
"chapter": null,
"notebook": "Logic_Vector_9.ipynb",
"source": "notebook",
"piece": 9,
"pieces": 9,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-22c4a22ff1df | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb (part 1 of 6)
## Notebook `Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb`
Code cell 1:
```python
import sympy as sp
# Define symbols
I = sp.I # Imagin... | {
"chapter": null,
"notebook": "Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb",
"source": "notebook",
"piece": 1,
"pieces": 6,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-18d403dd9a35 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb (part 2 of 6)
Code cell 5:
```python
import numpy as np
import matplotlib.pyplot as plt
import sympy as sp
# Define symbolic variables
nu_E, theta, alpha, rho... | {
"chapter": null,
"notebook": "Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb",
"source": "notebook",
"piece": 2,
"pieces": 6,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
pt-4862dbaf8557 | Sweeping Nets, Saddle Maps, & Complex Analysis by Parker Emmerson (Yaohushuason) — code collection
Notebook Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb (part 3 of 6)
Printed output:
```text
⎡ ⎛ ⎛ 2 2⎞ ⎛ 2.0⋅ν_E ⎞ ↪
⎢⎛ ____ ____... | {
"chapter": null,
"notebook": "Matrix_Method_Analysis_of_String_Theory_2 (1).ipynb",
"source": "notebook",
"piece": 3,
"pieces": 6,
"book": "Sweeping Nets, Saddle Maps, & Complex Analysis",
"author": "Parker Emmerson (Yaohushuason)"
} |
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