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@ -1,6 +1,9 @@
import sympy as sp
import time
import random
import readline
errs = (ValueError, TypeError)
def genmatrix(rowcol, intmax, dif) :
# generate a random matrices
@ -20,7 +23,11 @@ def inmat(rowcol) :
mat[i]=input().split(" ")
for j in range(len(mat[i])) :
# convert list using nsimplify in order to take rational number symbolically
mat[i][j] = sp.nsimplify(mat[i][j])
try :
mat[i][j] = sp.nsimplify(mat[i][j])
except errs : return False
try : mat = sp.Matrix(mat)
except errs : return False
return mat
# multcheck function to check if two matrices are multiplied together
@ -28,41 +35,41 @@ def multcheck(a, b, rowcol, intmax) :
sp.pprint(b)
print("Multiply these two matrices together")
# return bool based on if input equals the two matrices multiplied together
return (sp.Matrix(inmat(rowcol)) == a*b)
return (inmat(rowcol) == a*b)
# detcheck function to check if the determinant of the matrix is correct
def detcheck(a, b, rowcol, intmax):
det = sp.det(a)
# return bool based on if input equals determinant
return (det == sp.nsimplify(input("What is the determinant of this matrix?: ")))
try : d = sp.nsimplify(input("What is the determinant of this matrix?: "))
except errs : return False
return (det == d)
# invcheck function to check if the inverse of the matrix is correct
def invcheck(a, b, rowcol, intmax):
det = a.det()
if det != 0 :
# return bool based on if input equals inverse of matrix
print("What is the inverse of this matrix?")
return (sp.Matrix(inmat(rowcol)) == a.inv())
# return bool based on if input equals inverse of matrix
print("What is the inverse of this matrix?")
return (inmat(rowcol) == a.inv())
# eigcheck function to check if the eigenvalues are correct
def eigcheck(a, b, rowcol, intmax):
eigs = a.eigenvals()
for i in range(len(eigs)) :
val = sp.nsimplify(input("Input eigenvalue: "))
if not (val in eigs and eigs[val] == sp.nsimplify(input("Input its algebraic multiplicity: "))) :
try :
val = sp.nsimplify(input("Input eigenvalue: "))
algm = sp.nsimplify(input("Input its algebraic multiplicity: "))
except errs : return False
if not (val in eigs and eigs[val] == algm) :
# return false if the eigenvalue not in dictionary and wrong alg multiplicity
return False
return True
def diagcheck(a, b, rowcol, intmax):
return (a.diagonalize()[1] == sp.Matrix(inmat(rowcol)))
return (a.diagonalize()[1] == inmat(rowcol))
# practice function
def practice(t) :
count = 0
rowcol = int(input("What size of matrix do you want to practice with? "))
intmax = int(input("What maximum size of integer do you want the matrix to be made out of? "))
dif = float(input("What difficulty (probability for a matrix of rational values between 0, 1) do you want? "))
# choose the function of the program that you want
if t == "mult" :
@ -78,6 +85,15 @@ def practice(t) :
else :
exit()
while True :
try :
rowcol = abs(int(input("What size of matrix do you want to practice with? ")))
intmax = abs(int(input("What maximum size of integer do you want the matrix to be made out of? ")))
dif = float(input("What difficulty (probability for a matrix of rational values between 0, 1) do you want? "))
break
except errs:
continue
# initialise time measurement
tic = time.perf_counter()
@ -92,6 +108,9 @@ def practice(t) :
if t == "diag" :
while not a.is_diagonalizable :
a = genmatrix(rowcol, intmax, dif)
if t == "inv" :
while a.det() == 0 :
a = genmatrix(rowcol, intmax, dif)
sp.pprint(a)
# if return of function is True
if f(a, b, rowcol, intmax) :