def test_issue_4611():
assert abs(pi._evalf(50) - 3.14159265358979) < 1e-10
assert abs(E._evalf(50) - 2.71828182845905) < 1e-10
assert abs(Catalan._evalf(50) - 0.915965594177219) < 1e-10
assert abs(EulerGamma._evalf(50) - 0.577215664901533) < 1e-10
assert abs(GoldenRatio._evalf(50) - 1.61803398874989) < 1e-10
x = Symbol("x")
assert (pi + x).evalf() == pi.evalf() + x
assert (E + x).evalf() == E.evalf() + x
assert (Catalan + x).evalf() == Catalan.evalf() + x
assert (EulerGamma + x).evalf() == EulerGamma.evalf() + x
assert (GoldenRatio + x).evalf() == GoldenRatio.evalf() + x
def test_issue1512():
assert abs(pi._evalf(50) - 3.14159265358979) < 1e-10
assert abs(E._evalf(50) - 2.71828182845905) < 1e-10
assert abs(Catalan._evalf(50) - 0.915965594177219) < 1e-10
assert abs(EulerGamma._evalf(50) - 0.577215664901533) < 1e-10
assert abs(GoldenRatio._evalf(50) - 1.61803398874989) < 1e-10
x = Symbol("x")
assert (pi+x).evalf() == pi.evalf()+x
assert (E+x).evalf() == E.evalf()+x
assert (Catalan+x).evalf() == Catalan.evalf()+x
assert (EulerGamma+x).evalf() == EulerGamma.evalf()+x
assert (GoldenRatio+x).evalf() == GoldenRatio.evalf()+x
def test_fcode_NumberSymbol():
prec = 17
p = FCodePrinter()
assert fcode(
Catalan
) == " parameter (Catalan = %sd0)\n Catalan" % Catalan.evalf(
prec)
assert fcode(
EulerGamma
) == " parameter (EulerGamma = %sd0)\n EulerGamma" % EulerGamma.evalf(
prec)
assert fcode(E) == " parameter (E = %sd0)\n E" % E.evalf(prec)
assert fcode(
GoldenRatio
) == " parameter (GoldenRatio = %sd0)\n GoldenRatio" % GoldenRatio.evalf(
prec)
assert fcode(
pi) == " parameter (pi = %sd0)\n pi" % pi.evalf(prec)
assert fcode(
pi,
precision=5) == " parameter (pi = %sd0)\n pi" % pi.evalf(5)
assert fcode(Catalan, human=False) == (
set([(Catalan, p._print(Catalan.evalf(prec)))]),
set([]),
" Catalan",
)
assert fcode(EulerGamma, human=False) == (
set([(EulerGamma, p._print(EulerGamma.evalf(prec)))]),
set([]),
" EulerGamma",
)
assert fcode(E, human=False) == (
set([(E, p._print(E.evalf(prec)))]),
set([]),
" E",
)
assert fcode(GoldenRatio, human=False) == (
set([(GoldenRatio, p._print(GoldenRatio.evalf(prec)))]),
set([]),
" GoldenRatio",
)
assert fcode(pi, human=False) == (
set([(pi, p._print(pi.evalf(prec)))]),
set([]),
" pi",
)
assert fcode(pi, precision=5, human=False) == (
set([(pi, p._print(pi.evalf(5)))]),
set([]),
" pi",
)
def test_fcode_NumberSymbol():
p = FCodePrinter()
assert fcode(
Catalan
) == ' parameter (Catalan = 0.915965594177219d0)\n Catalan'
assert fcode(
EulerGamma
) == ' parameter (EulerGamma = 0.577215664901533d0)\n EulerGamma'
assert fcode(E) == ' parameter (E = 2.71828182845905d0)\n E'
assert fcode(
GoldenRatio
) == ' parameter (GoldenRatio = 1.61803398874989d0)\n GoldenRatio'
assert fcode(pi) == ' parameter (pi = 3.14159265358979d0)\n pi'
assert fcode(pi,
precision=5) == ' parameter (pi = 3.1416d0)\n pi'
assert fcode(Catalan, human=False) == (set([
(Catalan, p._print(Catalan.evalf(15)))
]), set([]), ' Catalan')
assert fcode(EulerGamma, human=False) == (set([
(EulerGamma, p._print(EulerGamma.evalf(15)))
]), set([]), ' EulerGamma')
assert fcode(E, human=False) == (set([(E, p._print(E.evalf(15)))]),
set([]), ' E')
assert fcode(GoldenRatio, human=False) == (set([
(GoldenRatio, p._print(GoldenRatio.evalf(15)))
]), set([]), ' GoldenRatio')
assert fcode(pi, human=False) == (set([(pi, p._print(pi.evalf(15)))]),
set([]), ' pi')
assert fcode(pi, precision=5, human=False) == (set([
(pi, p._print(pi.evalf(5)))
]), set([]), ' pi')
def test_fcode_NumberSymbol():
assert fcode(
Catalan
) == ' parameter (Catalan = 0.915965594177219)\n Catalan'
assert fcode(
EulerGamma
) == ' parameter (EulerGamma = 0.577215664901533)\n EulerGamma'
assert fcode(E) == ' parameter (E = 2.71828182845905)\n E'
assert fcode(
GoldenRatio
) == ' parameter (GoldenRatio = 1.61803398874989)\n GoldenRatio'
assert fcode(pi) == ' parameter (pi = 3.14159265358979)\n pi'
assert fcode(pi, precision=5) == ' parameter (pi = 3.1416)\n pi'
assert fcode(Catalan, human=False) == ([('Catalan', Catalan.evalf(15))],
set([]), ' Catalan')
assert fcode(EulerGamma,
human=False) == ([('EulerGamma', EulerGamma.evalf(15))],
set([]), ' EulerGamma')
assert fcode(E, human=False) == ([('E', E.evalf(15))], set([]), ' E')
assert fcode(GoldenRatio,
human=False) == ([('GoldenRatio', GoldenRatio.evalf(15))],
set([]), ' GoldenRatio')
assert fcode(pi,
human=False) == ([('pi', pi.evalf(15))], set([]), ' pi')
assert fcode(pi, precision=5,
human=False) == ([('pi', pi.evalf(5))], set([]), ' pi')
def test_fcode_NumberSymbol():
assert fcode(Catalan) == ' parameter (Catalan = 0.915965594177219)\n Catalan'
assert fcode(EulerGamma) == ' parameter (EulerGamma = 0.577215664901533)\n EulerGamma'
assert fcode(E) == ' parameter (E = 2.71828182845905)\n E'
assert fcode(GoldenRatio) == ' parameter (GoldenRatio = 1.61803398874989)\n GoldenRatio'
assert fcode(pi) == ' parameter (pi = 3.14159265358979)\n pi'
assert fcode(pi,precision=5) == ' parameter (pi = 3.1416)\n pi'
assert fcode(Catalan,human=False) == ([('Catalan', Catalan.evalf(15))], set([]), ' Catalan')
assert fcode(EulerGamma,human=False) == ([('EulerGamma', EulerGamma.evalf(15))], set([]), ' EulerGamma')
assert fcode(E,human=False) == ([('E', E.evalf(15))], set([]), ' E')
assert fcode(GoldenRatio,human=False) == ([('GoldenRatio', GoldenRatio.evalf(15))], set([]), ' GoldenRatio')
assert fcode(pi,human=False) == ([('pi', pi.evalf(15))], set([]), ' pi')
assert fcode(pi,precision=5,human=False) == ([('pi', pi.evalf(5))], set([]), ' pi')
def test_fcode_NumberSymbol():
p = FCodePrinter()
assert fcode(Catalan) == ' parameter (Catalan = 0.915965594177219d0)\n Catalan'
assert fcode(EulerGamma) == ' parameter (EulerGamma = 0.577215664901533d0)\n EulerGamma'
assert fcode(E) == ' parameter (E = 2.71828182845905d0)\n E'
assert fcode(GoldenRatio) == ' parameter (GoldenRatio = 1.61803398874989d0)\n GoldenRatio'
assert fcode(pi) == ' parameter (pi = 3.14159265358979d0)\n pi'
assert fcode(pi,precision=5) == ' parameter (pi = 3.1416d0)\n pi'
assert fcode(Catalan,human=False) == (set([(Catalan, p._print(Catalan.evalf(15)))]), set([]), ' Catalan')
assert fcode(EulerGamma,human=False) == (set([(EulerGamma, p._print(EulerGamma.evalf(15)))]), set([]), ' EulerGamma')
assert fcode(E,human=False) == (set([(E, p._print(E.evalf(15)))]), set([]), ' E')
assert fcode(GoldenRatio,human=False) == (set([(GoldenRatio, p._print(GoldenRatio.evalf(15)))]), set([]), ' GoldenRatio')
assert fcode(pi,human=False) == (set([(pi, p._print(pi.evalf(15)))]), set([]), ' pi')
assert fcode(pi,precision=5,human=False) == (set([(pi, p._print(pi.evalf(5)))]), set([]), ' pi')
def test_fcode_NumberSymbol():
prec = 17
p = FCodePrinter()
assert fcode(
Catalan
) == ' parameter (Catalan = %sd0)\n Catalan' % Catalan.evalf(
prec)
assert fcode(
EulerGamma
) == ' parameter (EulerGamma = %sd0)\n EulerGamma' % EulerGamma.evalf(
prec)
assert fcode(E) == ' parameter (E = %sd0)\n E' % E.evalf(prec)
assert fcode(
GoldenRatio
) == ' parameter (GoldenRatio = %sd0)\n GoldenRatio' % GoldenRatio.evalf(
prec)
assert fcode(
pi) == ' parameter (pi = %sd0)\n pi' % pi.evalf(prec)
assert fcode(
pi,
precision=5) == ' parameter (pi = %sd0)\n pi' % pi.evalf(5)
assert fcode(Catalan, human=False) == (set([
(Catalan, p._print(Catalan.evalf(prec)))
]), set([]), ' Catalan')
assert fcode(EulerGamma, human=False) == (set([
(EulerGamma, p._print(EulerGamma.evalf(prec)))
]), set([]), ' EulerGamma')
assert fcode(E, human=False) == (set([(E, p._print(E.evalf(prec)))]),
set([]), ' E')
assert fcode(GoldenRatio, human=False) == (set([
(GoldenRatio, p._print(GoldenRatio.evalf(prec)))
]), set([]), ' GoldenRatio')
assert fcode(pi, human=False) == (set([(pi, p._print(pi.evalf(prec)))]),
set([]), ' pi')
assert fcode(pi, precision=5, human=False) == (set([
(pi, p._print(pi.evalf(5)))
]), set([]), ' pi')
def test_fcode_NumberSymbol():
prec = 17
p = FCodePrinter()
assert fcode(Catalan) == ' parameter (Catalan = %sd0)\n Catalan' % Catalan.evalf(prec)
assert fcode(EulerGamma) == ' parameter (EulerGamma = %sd0)\n EulerGamma' % EulerGamma.evalf(prec)
assert fcode(E) == ' parameter (E = %sd0)\n E' % E.evalf(prec)
assert fcode(GoldenRatio) == ' parameter (GoldenRatio = %sd0)\n GoldenRatio' % GoldenRatio.evalf(prec)
assert fcode(pi) == ' parameter (pi = %sd0)\n pi' % pi.evalf(prec)
assert fcode(
pi, precision=5) == ' parameter (pi = %sd0)\n pi' % pi.evalf(5)
assert fcode(Catalan, human=False) == (set(
[(Catalan, p._print(Catalan.evalf(prec)))]), set([]), ' Catalan')
assert fcode(EulerGamma, human=False) == (set([(EulerGamma, p._print(
EulerGamma.evalf(prec)))]), set([]), ' EulerGamma')
assert fcode(E, human=False) == (
set([(E, p._print(E.evalf(prec)))]), set([]), ' E')
assert fcode(GoldenRatio, human=False) == (set([(GoldenRatio, p._print(
GoldenRatio.evalf(prec)))]), set([]), ' GoldenRatio')
assert fcode(pi, human=False) == (
set([(pi, p._print(pi.evalf(prec)))]), set([]), ' pi')
assert fcode(pi, precision=5, human=False) == (
set([(pi, p._print(pi.evalf(5)))]), set([]), ' pi')
def main():
setup_matplotlib_rc()
expr = get_CRAM_from_cache(degree, prec)
c = 1 / GoldenRatio.evalf() * degree
# Get the translated approximation on [-1, 1]. This is similar logic from CRAM_exp().
n, d = map(Poly, fraction(expr))
inv = -c * (t + 1) / (t - 1)
p, q = map(lambda i: Poly(i, t), fraction(inv))
n, d = n.transform(p, q), d.transform(p, q)
rat_func = n / d.TC() / (d / d.TC())
rat_func = rat_func.evalf(prec)
plt.clf()
fig, (ax1, ax2) = plt.subplots(1, 2, sharey=False)
fig.set_size_inches(1.5 * 6.4, 1.5 / 2 * 4.8)
plot_in_terminal(rat_func - exp(-inv), (-1, 1.01),
prec=prec,
points=points,
axes=ax1)
ax1.set_xlabel(r'$t$')
ax1.set_ylabel(
r'$\hat{r}_{14, 14}\left (c\frac{t+1}{t-1}\right ) - e^{-c\frac{t+1}{t-1}}$'
)
plot_in_terminal(expr - exp(-t), (0, 100),
prec=prec,
points=points,
axes=ax2)
ax2.set_xlabel(r'$t$')
ax2.set_ylabel(r'$\hat{r}_{14, 14}(t) - e^{-t}$')
plt.tight_layout()
plt.savefig('cram-plot.pgf')
def test_GoldenRatio_expand():
assert GoldenRatio.expand(func=True) == S.Half + sqrt(5)/2
def test_GoldenRatio_expand():
assert GoldenRatio.expand(func=True) == S.Half + sqrt(5)/2
def test_golden_ratio_rewrite_as_sqrt():
assert GoldenRatio.rewrite(sqrt) == S.Half + sqrt(5)*S.Half
def test_golden_ratio_rewrite_as_sqrt():
assert GoldenRatio.rewrite(sqrt) == S.Half + sqrt(5) * S.Half
