def __init__(self):
# An array of accessible functions
self.functions = {
# Logarithms
'ln': ln,
'log': lambda a, b=10: dmath.log(a, b),
# Trigonometric Functions
'sin': lambda x: handle_type(sin(x)),
'cos': lambda x: handle_type(cos(x)),
'tan': lambda x: handle_type(tan(x)),
'arcsin': lambda x: handle_type(dmath.asin(x)),
'arccos': lambda x: handle_type(dmath.acos(x)),
'arctan': lambda x: handle_type(dmath.atan(x)),
'sinh': lambda x: handle_type(dmath.sinh(x)),
'cosh': lambda x: handle_type(dmath.cosh(x)),
'tanh': lambda x: handle_type(dmath.tanh(x)),
'arcsinh': lambda z: handle_type(log(z + (Integer(1)
+ z**Integer(2))**Real('0.5'))),
'arccosh': lambda z: ht(log(z + (z + Integer(1))**Real('0.5')
* (z - Integer(1))**Real('0.5'))),
'arctanh': lambda z: handle_type(log(Integer(1) + z)
- log(Integer(1) - z))/Integer(2),
'degrees': lambda x: handle_type(degrees(x)),
# Statistics
'nCr': nCr,
'nPr': nPr,
'binomialpdf': binomialpdf,
'binomialcdf': binomialcdf,
'poissonpdf': poissonpdf,
'poissoncdf': poissoncdf,
'normalcdf': normalcdf,
'mean': lambda a: a.mean(),
'median': lambda a: a.median(),
'mode': lambda a: a.mode(),
'variance': lambda a: a.variance(),
'stdev': lambda a: a.stdev(),
'sxx': lambda a: a.Sxx(),
# Manipulation of functions
'expand': expand,
'differentiate': lambda a, b=Symbol('x'):\
partial_differential(a, b),
'integrate': lambda y, a=None, b=None, x=Symbol('x'):\
partial_integral(y, x) if a == None or b == None \
else partial_integral(y, x).limit(a, b, variable=x),
'romberg': lambda f, a, b, *n: f.romberg_integral(a, b, *n),
'trapeziumrule': lambda f, a, b, *n:\
f.trapezoidal_integral(a, b, *n),
'simpsonrule': lambda f, a, b, *n: f.simpson_integral(a, b, *n),
'simpsonthreeeightrule': lambda f, a, b, *n: f.simpson38_integral(a, b, *n),
'roots': lambda a, n=1000: List(*list(a.roots(n))),
'maxima': lambda a, n=100: List(*a.maxima(n)),
'minima': lambda a, n=100: List(*a.minima(n)),
# Vectors
'norm': lambda a: a.norm(),
# Matrices
'transpose': lambda a: a.transpose(),
'order': lambda a: '{}×{}'.format(*a.order()),
'eval': lambda a, b, c=None: a(b, variable=c),
'identity': identity_matrix,
'diag': diagonal_matrix,
'inv': lambda a: a.inverse(),
'invert': lambda a: a.inverse(),
'decompose': lambda a: List(*a.LU_decomposition()),
'trace': lambda a: a.trace(),
'poly': lambda a: a.characteristic_polynomial(),
'adj': lambda a: a.adjgate(),
'zero': Matrix,
'minor': lambda a, b, c: a.minor(b, c),
'det': lambda a: a.determinant(),
'eigenvalues': lambda a: List(*a.eigenvalues()),
'rank': lambda a: a.rank(),
# Complex Numbers
're': lambda a: a.real,
'im': lambda a: a.imag,
'arg': lambda a: a.argument(),
'conj': lambda a: a.conjugate(),
# Misc
'yum': pi,
'plot': lambda f, a=-10, b=10: StrWithHtml('testing...',
'''<canvas id="{0}" onclick="new CartesianPlot('{0}').simplePlot('{1}',{2},{3})" width="600" height="600">{4}</canvas>'''.format('graph-'
+ str(random.randint(1, 1000)), f, a, b, gnuplot(f, a, b).html)),
'polarplot': lambda f, a=-pi(), b=pi(): StrWithHtml('testing...',
'''<canvas id="{0}" onclick="new PolarPlot('{0}').simplePlot('{1}',{2},{3})" width="600" height="600"></canvas>'''.format('graph-'
+ str(random.randint(1, 1000)), f, a, b)),
'testcanvas': lambda: StrWithHtml('testing...',
'''<canvas id="testcanvas" width="600" height="600"></canvas>'''),
'evalbetween': evalute_between,
'factorial': factorial,
'factors': lambda a: a.factors(),
'decimal': lambda a: Decimal(a) if not isinstance(a, List)\
else List(*list(map(Decimal, a))),
'complex': lambda a: complex(a) if not isinstance(a, List)\
else List(*list(map(complex, a))),
'round': lambda a: handle_type(round),
'list': lambda a: str(list(a)),
'gnuplot': gnuplot,
'type': lambda a: str(type(a)),
'typelist': lambda b: ', '.join(map(lambda a: str(type(a)), b)),
'typematrix': lambda c: '; '.join(map(lambda b:
', '.join(map(lambda a: str(type(a)), b)), c)),
'setprec': self.set_precision,
'setexact': self.set_exact,
'about': lambda:\
StrWithHtml('Copyright Tom Wright <*****@*****.**>',
'''<img src="./images/about.png" />
<br>This program was written by Tom Wright
<*****@*****.**>'''),
'help': help.help,
'quit': exit,
}
# An array of accessible post functions
self.post_functions = {
'!': factorial,
'degs': radians
}
# An array of standard constants
self.consts = {
'pi': pi(),
'g': Real('9.81'),
'h': Real('6.62606896e-34'),
}
# An array of miscellaneous internal variables such as ans
# which stores the previous result
self.objects = {'ans': Integer(0)}
Circle = namedtuple("Circle", "x y r")
def circle_cross((x0, y0, r0), (x1, y1, r1)):
d = vdist(Vec(x0, y0), Vec(x1, y1))
if d >= r0 + r1 or d <= abs(r0 - r1):
return []
s = (r0 + r1 + d) / D2
a = sqrt(s * (s - d) * (s - r0) * (s - r1))
h = D2 * a / d
dr = Vec(x1 - x0, y1 - y0)
dx = vscale(sqrt(r0 ** 2 - h ** 2), vnorm(dr))
ang = vangle(dr) if \
r0 ** 2 + d ** 2 > r1 ** 2 \
else pi + vangle(dr)
da = asin(h / r0)
return map(anorm, [ang - da, ang + da])
# Angles of the start and end points of the circle arc.
Angle2 = namedtuple("Angle2", "a1 a2")
Arc = namedtuple("Arc", "c aa")
arcPoint = lambda (x, y, r), a: \
vadd(Vec(x, y), Vec(r * cos(a), r * sin(a)))
arc_start = lambda (c, (a0, a1)): arcPoint(c, a0)
arc_mid = lambda (c, (a0, a1)): arcPoint(c, (a0 + a1) / D2)
arc_end = lambda (c, (a0, a1)): arcPoint(c, a1)
arc_center = lambda ((x, y, r), _): Vec(x, y)
def test_asin():
for x in range(-1, 1):
assert dmath.asin(x) == math.asin(x)
assert grad(dmath.asin)(x) == approx(1 / math.sqrt(1 - x**2))