def make_linear_eq(x="", rhs=None, var_coeffs=True):
"""
Generates linear equation in one variable, and its solution.
x : charector for the variable to be solved for. defaults to random selection
from the global list `alpha`.
OR
a list of possible charectors. A random selection will be made from them.
rhs : value to set for the right-hand side. If not given, the
right-hand side will be a randomly generated linear expression
var_coeffs : sets whether we want variables as coefficients in the problem.
defaults to True. Set to False if you want a problem with strictly
numerical coefficients.
"""
if not x:
x = random.choice(alpha)
elif isinstance(x, list):
x = random.choice(x)
exclude = [x.upper(), x.lower()]
x = sympy.Symbol(x)
c1, c2, c3, c4 = get_coefficients(4,
var_coeffs=var_coeffs,
reduce=False,
exclude=exclude)
lhs = c1 * x + c2
rhs = c3 * x + c4
e = sympy.Eq(lhs, rhs)
sols = [render(ex, x) for ex in sympy.solve(e, x)]
return "Solve for $%s$ : %s" % (x, render(e)), sols
def make_linear_eq(x="", rhs = None, var_coeffs=True):
"""
Generates linear equation in one variable, and its solution.
x : charector for the variable to be solved for. defaults to random selection
from the global list `alpha`.
OR
a list of possible charectors. A random selection will be made from them.
rhs : value to set for the right-hand side. If not given, the
right-hand side will be a randomly generated linear expression
var_coeffs : sets whether we want variables as coefficients in the problem.
defaults to True. Set to False if you want a problem with strictly
numerical coefficients.
"""
if not x:
x = random.choice(alpha)
elif isinstance(x, list):
x = random.choice(x)
exclude = [x.upper(), x.lower()]
x = sympy.Symbol(x)
c1, c2, c3, c4 = get_coefficients(4, var_coeffs=var_coeffs, reduce=False,
exclude = exclude)
lhs = c1*x + c2
rhs = c3*x + c4
e = sympy.Eq(lhs, rhs)
sols = [render(ex, x) for ex in sympy.solve(e, x)]
return "Solve for $%s$ : %s" % (x, render(e)), sols
def make_quadratic_eq(target, var="x", rhs=None, integer=[0, 1]):
"""
Generates quadratic equation problem expression and
set of solutions
x : charector for the variable to be solved for. defaults to "x".
OR
a list of possible charectors. A random selection will be made from them.
rhs : value to set for the right-hand side. If not given, the
right-hand side will be a randomly generated polynomial expression
of degree <= 2, in the same variable.
integer : determines whether generated problem will have integer roots or
not. Default is a random selection.
"""
if isinstance(var, str):
var = sympy.Symbol(var)
elif isinstance(var, list):
var = sympy.Symbol(random.choice(var))
if isinstance(integer, list):
integer = random.choice(integer)
if integer:
r1 = random.choice(digits_nozero)
r2 = target - r1
#r2 = random.choice(digits_nozero)
lhs = (var - r1) * (var - r2)
lhs = lhs.expand()
rhs = 0
else:
c1, c2, c3 = get_coefficients(3)
lhs = c1 * var**2 + c2 * var + c3
if rhs == None:
c4, c5, c6 = get_coefficients(3, first_nonzero=False)
rhs = c4 * var**2 + c5 * var + c6
e = sympy.Eq(lhs, rhs)
pvar = str(var)
sols = ', '.join(
[pvar + " = " + sympy.latex(ex) for ex in sympy.solve(e, var)])
sols = "$$" + sols + "$$"
if len(sols) == 0:
return make_quadratic_eq()
return "\\overline{" + render(e) + "}", sols
def make_quadratic_eq(var="x", rhs = None, integer=[0, 1]):
"""
Generates quadratic equation problem expression and
set of solutions
x : charector for the variable to be solved for. defaults to "x".
OR
a list of possible charectors. A random selection will be made from them.
rhs : value to set for the right-hand side. If not given, the
right-hand side will be a randomly generated polynomial expression
of degree <= 2, in the same variable.
integer : determines whether generated problem will have integer roots or
not. Default is a random selection.
"""
if isinstance(var, str):
var = sympy.Symbol(var)
elif isinstance(var, list):
var = sympy.Symbol(random.choice(var))
if isinstance(integer, list):
integer = random.choice(integer)
if integer:
r1 = random.choice(digits_nozero)
r2 = random.choice(digits_nozero)
lhs = (var - r1) * (var - r2)
lhs = lhs.expand()
rhs = 0
else:
c1, c2, c3 = get_coefficients(3)
lhs = c1*var**2 + c2*var + c3
if rhs == None:
c4, c5, c6 = get_coefficients(3, first_nonzero=False)
rhs = c4*var**2 + c5*var + c6
e = sympy.Eq(lhs, rhs)
pvar = str(var)
sols = ', '.join([pvar+" = " + sympy.latex(ex) for ex in sympy.solve(e, var)])
sols = "$$" + sols + "$$"
if len(sols) == 0:
return make_quadratic_eq()
return render(e), sols
def poly1(x):
vals = sum([k * x**i for i, k in enumerate(reversed(get_coefficients(2)))])
return vals