Revision history [back]

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

from sympy import symbols, Poly, solve from sympy.plotting import plot

Define the function f and the variable x

x = symbols('x') f = x5 - 13x3 - x2 + 10x + 170

Convert f to a polynomial

f_poly = Poly(f, x)

Find all the roots

roots = solve(f_poly, domain='CC')

Print all roots

print("All roots:") for root in roots: root_approx = root.evalf() print(root_approx)

Filter real and complex roots

real_roots = [root for root in roots if root.is_real] complex_roots = [root for root in roots if not root.is_real]

Print real roots

print("Real roots:") for root in real_roots: root_approx = root.evalf() print(root_approx)

Print complex roots

print("Complex roots:") for root in complex_roots: root_approx = root.evalf() print(root_approx)

Print the number of real roots

num_real_roots = len(real_roots) print("Number of real roots:", num_real_roots)

Plot the real part of the function f

p1 = plot(f, (x, -5, 5), title='Graph of f(x)', real=True) help for Gerschgorin-Circle

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

from sympy import symbols, Poly, solve from sympy.plotting import plot

# Define the function f and the variable x
x x = symbols('x') f = x5 - 13x3 - x2 + 10x + 170 x**5 - 13*x**3 - x**2 + 10*x + 170 # Convert f to a polynomial polynomial f_poly = Poly(f, x) x) # Find all the roots roots roots = solve(f_poly, domain='CC') domain='CC') # Print all roots roots print("All roots:") for root in roots: root_approx = root.evalf() print(root_approx) print(root_approx) # Filter real and complex roots roots real_roots = [root for root in roots if root.is_real] complex_roots = [root for root in roots if not root.is_real] Print real roots root.is_real] # Print real roots print("Real roots:") for root in real_roots: root_approx = root.evalf() print(root_approx) print(root_approx) # Print complex roots roots print("Complex roots:") for root in complex_roots: root_approx = root.evalf() print(root_approx) print(root_approx) # Print the number of real roots roots num_real_roots = len(real_roots) print("Number of real roots:", num_real_roots) num_real_roots) # Plot the real part of the function f
f p1 = plot(f, (x, -5, 5), title='Graph of f(x)', real=True)
help for Gerschgorin-Circle

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

help for Gerschgorin-Circle

from sympy import symbols, Poly, solve
 from sympy.plotting import plot
 plot

# Define the function f and the variable x
x = symbols('x')
f = x**5 - 13*x**3 - x**2 + 10*x + 170

# Convert f to a polynomial
f_poly = Poly(f, x)

# Find all the roots
roots = solve(f_poly, domain='CC')

# Print all roots
print("All roots:")
for root in roots:
    root_approx = root.evalf()
    print(root_approx)

# Filter real and complex roots
real_roots = [root for root in roots if root.is_real]
complex_roots = [root for root in roots if not root.is_real]

# Print real roots
print("Real roots:")
for root in real_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print complex roots
print("Complex roots:")
for root in complex_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print the number of real roots
num_real_roots = len(real_roots)
print("Number of real roots:", num_real_roots)

# Plot the real part of the function f
p1 = plot(f, (x, -5, 5), title='Graph of f(x)', real=True)
  help for Gerschgorin-Circle

          4    None 
      
    
        
        updated 2023-06-06 15:00:36 +0200  
    slelievre 
 17674  ●22 ●160 ●349  
        http://carva.org/samue...
         
 
 
 
  
 
 
 
  Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter
 I need help for Gerschgorin-Circlewith the Gerschgorin circles root localisation.
 Consider the following function:
  $f = x^5 - 13 x^3 - x^2 + 10 x + 170$
 
 Visualize the roots using Gerschgorin-Circle. Include a plot
of the function itself, complete with labels and title,
in your report in a SageMath  Jupyter notebook.
 from sympy import symbols, Poly, solve
from sympy.plotting import plot

# Define the function f and the variable x
x = symbols('x')
f = x**5 - 13*x**3 - x**2 + 10*x + 170

# Convert f to a polynomial
f_poly = Poly(f, x)

# Find all the roots
roots = solve(f_poly, domain='CC')

# Print all roots
print("All roots:")
for root in roots:
    root_approx = root.evalf()
    print(root_approx)

# Filter real and complex roots
real_roots = [root for root in roots if root.is_real]
complex_roots = [root for root in roots if not root.is_real]

# Print real roots
print("Real roots:")
for root in real_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print complex roots
print("Complex roots:")
for root in complex_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print the number of real roots
num_real_roots = len(real_roots)
print("Number of real roots:", num_real_roots)

# Plot the real part of the function f
p1 = plot(f, (x, -5, 5), title='Graph of f(x)', real=True)
 
 
 
          5    None 
      
    
        
        updated 2023-06-06 15:00:56 +0200  
    slelievre 
 17674  ●22 ●160 ●349  
        http://carva.org/samue...
         
 
 
 
  
 
 
 
  Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter
 I need help with the Gerschgorin circles root localisation.
 Consider the following function:
  $f = x^5 - 13 x^3 - x^2 + 10 x + 170$
 
 Visualize the roots using Gerschgorin-Circle. Include a plot
of the function itself, complete with labels and title,
in your report in a SageMath  Jupyter notebook.
 from sympy import symbols, Poly, solve
from sympy.plotting import plot

# Define the function f and the variable x
x = symbols('x')
f = x**5 - 13*x**3 - x**2 + 10*x + 170

# Convert f to a polynomial
f_poly = Poly(f, x)

# Find all the roots
roots = solve(f_poly, domain='CC')

# Print all roots
print("All roots:")
for root in roots:
    root_approx = root.evalf()
    print(root_approx)

# Filter real and complex roots
real_roots = [root for root in roots if root.is_real]
complex_roots = [root for root in roots if not root.is_real]

# Print real roots
print("Real roots:")
for root in real_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print complex roots
print("Complex roots:")
for root in complex_roots:
    root_approx = root.evalf()
    print(root_approx)

# Print the number of real roots
num_real_roots = len(real_roots)
print("Number of real roots:", num_real_roots)

# Plot the real part of the function f
p1 = plot(f, (x, -5, 5), title='Graph of f(x)', real=True)

Revision history [back]

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

Define the function f and the variable x

Convert f to a polynomial

Find all the roots

Print all roots

Filter real and complex roots

Print real roots

Print complex roots

Print the number of real roots

Plot the real part of the function f

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

`# Define the function f and the variable x`

x**5 - 13x3 - x2 + 10x + 170 # Convert f to a polynomial

x) # Find all the roots

domain='CC') # Print all roots

print(root_approx) # Filter real and complex roots

Print real roots

print(root_approx) # Print complex roots

print(root_approx) # Print the number of real roots

num_real_roots) # Plot the real part of the function f

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter

Consider a function a follows: f = x^5 - 13x^3 - x^2 + 10x + 170 .Visualize the roots using Gerschgorin-Circle. Include a plot of the function itself, complete with labels and title in your report.in sage math notebook jupyter