- Python is used as a teaching tool in mathematics education due to its simplicity and readability. It helps students visualize and understand mathematical concepts through coding.
import math
!pip install vectors
dino_vectors = [(6,4), (3,1), (1,2),
(-1,5), (-2,5), (-3,4), (-4,4),
# insert 16 remaining vectors here
]
from math import sqrtdef length(v):
return sqrt(v[0]**2 + v[1]**2)
from math import sin, cos
def to_cartesian(polar_vector):
length, angle = polar_vector[0],
polar_vector[1]
return (length*cos(angle),
length*sin(angle))
from math import pi
angle = 37*pi/180
to_cartesian((5,angle))
(3.993177550236464, 3.0090751157602416)
from math import asin
sin(1)
0.8414709848078965
asin(0.8414709848078965)
1.0
from math import sqrt
asin(3/sqrt(13))
0.9827937232473292
math.asin
from math import acos
acos(-2/sqrt(13))
2.1587989303424644
import matplotlib
import numpy as np
from matplotlib.patches import Polygon
from matplotlib.collections
import PatchCollection
from vectors import *
def plane_equation(p1,p2,p3):
parallel1 = subtract(p2,p1)
parallel2 = subtract(p3,p1)
a,b,c = cross(parallel1, parallel2)
d = dot((a,b,c), p1)
return a,b,c,d
data = np.arange(9).reshape(3, 3)
data
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
np.transpose(data)
array([[0, 3, 6],
[1, 4, 7],
[2, 5, 8]])
A = np.arange(1, 7).reshape(2, 3)
A
array([[1, 2, 3],
[4, 5, 6]])
B = np.arange(1, 7).reshape(3, 2)
B
array([[1, 2],
[3, 4],
[5, 6]])
np.dot(A, B)
array([[22, 28],
[49, 64]])
np.dot(B, A)
array([[ 9, 12, 15],
[19, 26, 33],
[29, 40, 51]])
# SYMPY
import sympy
sympy.init_printing()
from sympy import I, pi, oo
sympy.symbols("x")
x
import numpy as np
data = np.array([[1, 2], [3, 4], [5, 6]])
type(data)
numpy.ndarray
data
array([[1, 2],
[3, 4],
[5, 6]])
data.ndim
2
data.shape
(3,2)
data.size
6
data.dtype
dtype('int64')
data.nbytes
48
np.array([1, 2, 3], dtype=np.int)
array([1, 2, 3])
np.array([1,2,3],dtype=np.float)
array([1., 2., 3.])
np.array([1,2,3],dtype=np.complex)
array([1.+0.j, 2.+0.j, 3.+0.j])
data.imag
array([[0, 0],
[0, 0],
[0, 0]])
#Array Created from Lists and
Other Array- Like Objects,
Onedimention
np.array([1,2,3,4])
array([1, 2, 3, 4])
np.array([[1,2],[3,4]])
array([[1, 2],
[3, 4]])
np.zeros((5,3))
array([[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.]])
np.ones((5,3))
array([[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.]])
x1=5.4*np.ones(10)
x1
array([5.4, 5.4, 5.4, 5.4,
5.4, 5.4, 5.4, 5.4, 5.4, 5.4])
x1=np.empty(5)
x1
array([0. , 0.25, 0.5 , 0.75, 1. ])
x1.fill(3.0)
x1
array([3., 3., 3., 3., 3.])
x2=np.full(5,3.0)
x2
array([3., 3., 3., 3., 3.])
np.arange(0.0,10,1)
array([0., 1., 2., 3., 4., 5., 6.,
7., 8., 9.])
np.linspace(0,10,11)
array([ 0., 1., 2., 3., 4., 5.,
6., 7., 8., 9., 10.])
np.logspace(0,2,5)
array([ 1. , 3.16227766, 10. , 31.6227766 ,
100. ])
x=np.array([-1,0,1])
y=np.array([-2,0,2])
z=np.array([-3,0,3])
x
array([-1, 0, 1])
y
array([-2, 0, 2])
z
array([-3, 0, 3])
X,Y,Z=np.meshgrid(x,y,z)
X,Y,Z
(array([[[-1, -1, -1],
[ 0, 0, 0],
[ 1, 1, 1]],
[[-1, -1, -1],
[ 0, 0, 0],
[ 1, 1, 1]],
[[-1, -1, -1],
[ 0, 0, 0],
[ 1, 1, 1]]]),
array([[[-2, -2, -2],
[-2, -2, -2],
[-2, -2, -2]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[ 2, 2, 2],
[ 2, 2, 2],
[ 2, 2, 2]]]),
array([[[-3, 0, 3],
[-3, 0, 3],
[-3, 0, 3]],
[[-3, 0, 3],
[-3, 0, 3],
[-3, 0, 3]],
[[-3, 0, 3],
[-3, 0, 3],
[-3, 0, 3]]]))
P=(X+Y)**2
P
array([[[9, 9, 9],
[4, 4, 4],
[1, 1, 1]],
[[1, 1, 1],
[0, 0, 0],
[1, 1, 1]],
[[1, 1, 1],
[4, 4, 4],
[9, 9, 9]]])
X**2
array([[[1, 1, 1],
[0, 0, 0],
[1, 1, 1]],
[[1, 1, 1],
[0, 0, 0],
[1, 1, 1]],
[[1, 1, 1],
[0, 0, 0],
[1, 1, 1]]])
Y**2
array([[[4, 4, 4],
[4, 4, 4],
[4, 4, 4]],
[[0, 0, 0],
[0, 0, 0],
[0, 0, 0]],
[[4, 4, 4],
[4, 4, 4],
[4, 4, 4]]])
Z**2
array([[[9, 0, 9],
[9, 0, 9],
[9, 0, 9]],
[[9, 0, 9],
[9, 0, 9],
[9, 0, 9]],
[[9, 0, 9],
[9, 0, 9],
[9, 0, 9]]])
2*X*Y
array([[[ 4, 4, 4],
[ 0, 0, 0],
[-4, -4, -4]],
[[ 0, 0, 0],
[ 0, 0, 0],
[ 0, 0, 0]],
[[-4, -4, -4],
[ 0, 0, 0],
[ 4, 4, 4]]])
np.empty(3, dtype=np.float)
array([58., 15., 3.])
def f(x):
y = np.ones_like(x)
return y
x=2
x
2
np.eye(3,k=1)
array([[0., 1., 0.],
[0., 0., 1.],
[0., 0., 0.]])
np.diag(np.arange(0, 20, 5))
array([[ 0, 0, 0, 0],
[ 0, 5, 0, 0],
[ 0, 0, 10, 0],
[ 0, 0, 0, 15]])a = np.arange(0, 11)
a
array([ 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10])
data = np.array([[1,2],[3,4],[5,6]])
#Trigonometry
x = np.linspace(-1, 1, 11)
x
array([-1. , -0.8, -0.6, -0.4,
-0.2, 0. , 0.2, 0.4, 0.6, 0.8, 1. ])
y = np.sin(np.pi * x)
y'
array([-1.22464680e-16, -5.87785252e-01, -9.51056516e-01, -9.51056516e-01,
-5.87785252e-01, 0.00000000e+00, 5.87785252e-01, 9.51056516e-01,
9.51056516e-01, 5.87785252e-01, 1.22464680e-16])
np.round(y, decimals=4)
array([-0. , -0.5878, -0.9511, -0.9511, -0.5878, 0. , 0.5878,
0.9511, 0.9511, 0.5878, 0. ])
np.add(np.sin(x) ** 2, np.cos(x) ** 2)
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])
np.sin(x) ** 2 + np.cos(x) ** 2
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])
np.subtract(np.sin(x)**2,np.cos(x)**2)
array([ 0.41614684, 0.02919952, -0.36235775, -0.69670671, -0.92106099,
-1. , -0.92106099, -0.69670671, -0.36235775, 0.02919952,
0.41614684])
data = np.random.normal(size=(15,15))
np.mean(data)
import sympy
np.alltrue(np.einsum("mk,kn", A, B) == np.dot(A, B))
True
x = sympy.Symbol("x")
expr = 1 + 2 * x**2 + 3 * x**3
expr
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