# -*- coding: utf-8 -*-
from sympy.core.function import Function
from sympy.integrals.integrals import Integral
from sympy.printing.latex import latex
from sympy.printing.pretty import pretty as xpretty
from sympy.vector import CoordSys3D, Del, Vector, express
from sympy.abc import a, b, c
from sympy.testing.pytest import XFAIL
def pretty(expr):
"""ASCII pretty-printing"""
return xpretty(expr, use_unicode=False, wrap_line=False)
def upretty(expr):
"""Unicode pretty-printing"""
return xpretty(expr, use_unicode=True, wrap_line=False)
# Initialize the basic and tedious vector/dyadic expressions
# needed for testing.
# Some of the pretty forms shown denote how the expressions just
# above them should look with pretty printing.
N = CoordSys3D('N')
C = N.orient_new_axis('C', a, N.k) # type: ignore
v = []
d = []
v.append(Vector.zero)
v.append(N.i) # type: ignore
v.append(-N.i) # type: ignore
v.append(N.i + N.j) # type: ignore
v.append(a*N.i) # type: ignore
v.append(a*N.i - b*N.j) # type: ignore
v.append((a**2 + N.x)*N.i + N.k) # type: ignore
v.append((a**2 + b)*N.i + 3*(C.y - c)*N.k) # type: ignore
f = Function('f')
v.append(N.j - (Integral(f(b)) - C.x**2)*N.k) # type: ignore
upretty_v_8 = """\
⎛ 2 ⌠ ⎞ \n\
j_N + ⎜x_C - ⎮ f(b) db⎟ k_N\n\
⎝ ⌡ ⎠ \
"""
pretty_v_8 = """\
j_N + / / \\\n\
| 2 | |\n\
|x_C - | f(b) db|\n\
| | |\n\
\\ / / \
"""
v.append(N.i + C.k) # type: ignore
v.append(express(N.i, C)) # type: ignore
v.append((a**2 + b)*N.i + (Integral(f(b)))*N.k) # type: ignore
upretty_v_11 = """\
⎛ 2 ⎞ ⎛⌠ ⎞ \n\
⎝a + b⎠ i_N + ⎜⎮ f(b) db⎟ k_N\n\
⎝⌡ ⎠ \
"""
pretty_v_11 = """\
/ 2 \\ + / / \\\n\
\\a + b/ i_N| | |\n\
| | f(b) db|\n\
| | |\n\
\\/ / \
"""
for x in v:
d.append(x | N.k) # type: ignore
s = 3*N.x**2*C.y # type: ignore
upretty_s = """\
2\n\
3⋅y_C⋅x_N \
"""
pretty_s = """\
2\n\
3*y_C*x_N \
"""
# This is the pretty form for ((a**2 + b)*N.i + 3*(C.y - c)*N.k) | N.k
upretty_d_7 = """\
⎛ 2 ⎞ \n\
⎝a + b⎠ (i_N|k_N) + (3⋅y_C - 3⋅c) (k_N|k_N)\
"""
pretty_d_7 = """\
/ 2 \\ (i_N|k_N) + (3*y_C - 3*c) (k_N|k_N)\n\
\\a + b/ \
"""
def test_str_printing():
assert str(v[0]) == '0'
assert str(v[1]) == 'N.i'
assert str(v[2]) == '(-1)*N.i'
assert str(v[3]) == 'N.i + N.j'
assert str(v[8]) == 'N.j + (C.x**2 - Integral(f(b), b))*N.k'
assert str(v[9]) == 'C.k + N.i'
assert str(s) == '3*C.y*N.x**2'
assert str(d[0]) == '0'
assert str(d[1]) == '(N.i|N.k)'
assert str(d[4]) == 'a*(N.i|N.k)'
assert str(d[5]) == 'a*(N.i|N.k) + (-b)*(N.j|N.k)'
assert str(d[8]) == ('(N.j|N.k) + (C.x**2 - ' +
'Integral(f(b), b))*(N.k|N.k)')
@XFAIL
def test_pretty_printing_ascii():
assert pretty(v[0]) == '0'
assert pretty(v[1]) == 'i_N'
assert pretty(v[5]) == '(a) i_N + (-b) j_N'
assert pretty(v[8]) == pretty_v_8
assert pretty(v[2]) == '(-1) i_N'
assert pretty(v[11]) == pretty_v_11
assert pretty(s) == pretty_s
assert pretty(d[0]) == '(0|0)'
assert pretty(d[5]) == '(a) (i_N|k_N) + (-b) (j_N|k_N)'
assert pretty(d[7]) == pretty_d_7
assert pretty(d[10]) == '(cos(a)) (i_C|k_N) + (-sin(a)) (j_C|k_N)'
def test_pretty_print_unicode_v():
assert upretty(v[0]) == '0'
assert upretty(v[1]) == 'i_N'
assert upretty(v[5]) == '(a) i_N + (-b) j_N'
# Make sure the printing works in other objects
assert upretty(v[5].args) == '((a) i_N, (-b) j_N)'
assert upretty(v[8]) == upretty_v_8
assert upretty(v[2]) == '(-1) i_N'
assert upretty(v[11]) == upretty_v_11
assert upretty(s) == upretty_s
assert upretty(d[0]) == '(0|0)'
assert upretty(d[5]) == '(a) (i_N|k_N) + (-b) (j_N|k_N)'
assert upretty(d[7]) == upretty_d_7
assert upretty(d[10]) == '(cos(a)) (i_C|k_N) + (-sin(a)) (j_C|k_N)'
def test_latex_printing():
assert latex(v[0]) == '\\mathbf{\\hat{0}}'
assert latex(v[1]) == '\\mathbf{\\hat{i}_{N}}'
assert latex(v[2]) == '- \\mathbf{\\hat{i}_{N}}'
assert latex(v[5]) == ('\\left(a\\right)\\mathbf{\\hat{i}_{N}} + ' +
'\\left(- b\\right)\\mathbf{\\hat{j}_{N}}')
assert latex(v[6]) == ('\\left(\\mathbf{{x}_{N}} + a^{2}\\right)\\mathbf{\\hat{i}_' +
'{N}} + \\mathbf{\\hat{k}_{N}}')
assert latex(v[8]) == ('\\mathbf{\\hat{j}_{N}} + \\left(\\mathbf{{x}_' +
'{C}}^{2} - \\int f{\\left(b \\right)}\\,' +
' db\\right)\\mathbf{\\hat{k}_{N}}')
assert latex(s) == '3 \\mathbf{{y}_{C}} \\mathbf{{x}_{N}}^{2}'
assert latex(d[0]) == '(\\mathbf{\\hat{0}}|\\mathbf{\\hat{0}})'
assert latex(d[4]) == ('\\left(a\\right)\\left(\\mathbf{\\hat{i}_{N}}{\\middle|}' +
'\\mathbf{\\hat{k}_{N}}\\right)')
assert latex(d[9]) == ('\\left(\\mathbf{\\hat{k}_{C}}{\\middle|}' +
'\\mathbf{\\hat{k}_{N}}\\right) + \\left(' +
'\\mathbf{\\hat{i}_{N}}{\\middle|}\\mathbf{' +
'\\hat{k}_{N}}\\right)')
assert latex(d[11]) == ('\\left(a^{2} + b\\right)\\left(\\mathbf{\\hat{i}_{N}}' +
'{\\middle|}\\mathbf{\\hat{k}_{N}}\\right) + ' +
'\\left(\\int f{\\left(b \\right)}\\, db\\right)\\left(' +
'\\mathbf{\\hat{k}_{N}}{\\middle|}\\mathbf{' +
'\\hat{k}_{N}}\\right)')
def test_issue_23058():
from sympy import symbols, sin, cos, pi, UnevaluatedExpr
delop = Del()
CC_ = CoordSys3D("C")
y = CC_.y
xhat = CC_.i
t = symbols("t")
ten = symbols("10", positive=True)
eps, mu = 4*pi*ten**(-11), ten**(-5)
Bx = 2 * ten**(-4) * cos(ten**5 * t) * sin(ten**(-3) * y)
vecB = Bx * xhat
vecE = (1/eps) * Integral(delop.cross(vecB/mu).doit(), t)
vecE = vecE.doit()
vecB_str = """\
⎛ ⎛y_C⎞ ⎛ 5 ⎞⎞ \n\
⎜2⋅sin⎜───⎟⋅cos⎝10 ⋅t⎠⎟ i_C\n\
⎜ ⎜ 3⎟ ⎟ \n\
⎜ ⎝10 ⎠ ⎟ \n\
⎜─────────────────────⎟ \n\
⎜ 4 ⎟ \n\
⎝ 10 ⎠ \
"""
vecE_str = """\
⎛ 4 ⎛ 5 ⎞ ⎛y_C⎞ ⎞ \n\
⎜-10 ⋅sin⎝10 ⋅t⎠⋅cos⎜───⎟ ⎟ k_C\n\
⎜ ⎜ 3⎟ ⎟ \n\
⎜ ⎝10 ⎠ ⎟ \n\
⎜─────────────────────────⎟ \n\
⎝ 2⋅π ⎠ \
"""
assert upretty(vecB) == vecB_str
assert upretty(vecE) == vecE_str
ten = UnevaluatedExpr(10)
eps, mu = 4*pi*ten**(-11), ten**(-5)
Bx = 2 * ten**(-4) * cos(ten**5 * t) * sin(ten**(-3) * y)
vecB = Bx * xhat
vecB_str = """\
⎛ -4 ⎛ 5⎞ ⎛ -3⎞⎞ \n\
⎝2⋅10 ⋅cos⎝t⋅10 ⎠⋅sin⎝y_C⋅10 ⎠⎠ i_C \
"""
assert upretty(vecB) == vecB_str
def test_custom_names():
A = CoordSys3D('A', vector_names=['x', 'y', 'z'],
variable_names=['i', 'j', 'k'])
assert A.i.__str__() == 'A.i'
assert A.x.__str__() == 'A.x'
assert A.i._pretty_form == 'i_A'
assert A.x._pretty_form == 'x_A'
assert A.i._latex_form == r'\mathbf{{i}_{A}}'
assert A.x._latex_form == r"\mathbf{\hat{x}_{A}}"