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8d55ddb | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | #!/usr/bin/env python
""" extp.py: Print p-forms and exterior products.
"""
from sympy import (symbols, Symbol)
from sympy.printing import (latex, print_latex)
from sympy.printing.latex import LatexPrinter
from sympy.diffgeom import Differential
from sympy.diffgeom.rn import R3_r
def _print_BaseScalarField(self, field):
string = field._coord_sys._names[field._index]
return f'{self._print(Symbol(string))}'
def _print_Differential(self, diff):
field = diff._form_field
if hasattr(field, '_coord_sys'):
string = field._coord_sys._names[field._index]
return rf'\dd {self._print(Symbol(string))}'
else:
return rf'\dd({self._print(field)})'
for m in (_print_BaseScalarField, _print_Differential):
setattr(LatexPrinter, m.__name__, m)
def main():
a, b, c = symbols('a b c', real=True)
x, y, z = R3_r.coord_functions()
dx, dy, dz = R3_r.base_oneforms()
ex, ey, ez = R3_r.base_vectors()
fx = a* x * y * z
fy = b * x ** 2 * z
fz = -3 * x**2 * y
omega = fx * dx + fy * dy + fz * dz
print_latex(omega)
domega = Differential(omega)
print_latex(domega)
print_latex(domega(ey, ez)) # for WedgeProduct(dy, dz)
print_latex(domega(ez, ex)) # for WedgeProduct(dz, dx)
print_latex(domega(ex, ey)) # for WedgeProduct(dx, dy)
if __name__ == '__main__':
main()
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