def printGreenPen(penName, funcs, file=sys.stdout, docstring=None):
if docstring is not None:
print('"""%s"""' % docstring)
print(
'''from fontTools.pens.basePen import BasePen, OpenContourError
try:
import cython
except ImportError:
# if cython not installed, use mock module with no-op decorators and types
from fontTools.misc import cython
if cython.compiled:
# Yep, I'm compiled.
COMPILED = True
else:
# Just a lowly interpreted script.
COMPILED = False
__all__ = ["%s"]
class %s(BasePen):
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
'''% (penName, penName), file=file)
for name,f in funcs:
print(' self.%s = 0' % name, file=file)
print('''
def _moveTo(self, p0):
self.__startPoint = p0
def _closePath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
self._lineTo(self.__startPoint)
def _endPath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
# Green theorem is not defined on open contours.
raise OpenContourError(
"Green theorem is not defined on open contours."
)
''', end='', file=file)
for n in (1, 2, 3):
subs = {P[i][j]: [X, Y][j][i] for i in range(n+1) for j in range(2)}
greens = [green(f, BezierCurve[n]) for name,f in funcs]
greens = [sp.gcd_terms(f.collect(sum(P,()))) for f in greens] # Optimize
greens = [f.subs(subs) for f in greens] # Convert to p to x/y
defs, exprs = sp.cse(greens,
optimizations='basic',
symbols=(sp.Symbol('r%d'%i) for i in count()))
print()
for name,value in defs:
print(' @cython.locals(%s=cython.double)' % name, file=file)
if n == 1:
print('''\
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
def _lineTo(self, p1):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
''', file=file)
elif n == 2:
print('''\
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
@cython.locals(x2=cython.double, y2=cython.double)
def _qCurveToOne(self, p1, p2):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
''', file=file)
elif n == 3:
print('''\
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
@cython.locals(x2=cython.double, y2=cython.double)
@cython.locals(x3=cython.double, y3=cython.double)
def _curveToOne(self, p1, p2, p3):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
''', file=file)
for name,value in defs:
print(' %s = %s' % (name, value), file=file)
print(file=file)
for name,value in zip([f[0] for f in funcs], exprs):
print(' self.%s += %s' % (name, value), file=file)
print('''
if __name__ == '__main__':
from fontTools.misc.symfont import x, y, printGreenPen
printGreenPen('%s', ['''%penName, file=file)
for name,f in funcs:
print(" ('%s', %s)," % (name, str(f)), file=file)
print(' ])', file=file)
def __missing__(self, i): args = ['p%d'%d for d in range(i+1)] f = green(self._symfunc, BezierCurve[i]) f = sp.gcd_terms(f.collect(sum(P,()))) # Optimize return sp.lambdify(args, f)
def printGreenPen(penName, funcs, file=sys.stdout):
print(
'''from fontemon_blender_addon.fontTools.misc.py23 import *
from fontemon_blender_addon.fontTools.pens.basePen import BasePen
class %s(BasePen):
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
'''%penName, file=file)
for name,f in funcs:
print(' self.%s = 0' % name, file=file)
print('''
def _moveTo(self, p0):
self.__startPoint = p0
def _closePath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
self._lineTo(self.__startPoint)
def _endPath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
# Green theorem is not defined on open contours.
raise NotImplementedError
''', end='', file=file)
for n in (1, 2, 3):
if n == 1:
print('''
def _lineTo(self, p1):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
''', file=file)
elif n == 2:
print('''
def _qCurveToOne(self, p1, p2):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
''', file=file)
elif n == 3:
print('''
def _curveToOne(self, p1, p2, p3):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
''', file=file)
subs = {P[i][j]: [X, Y][j][i] for i in range(n+1) for j in range(2)}
greens = [green(f, BezierCurve[n]) for name,f in funcs]
greens = [sp.gcd_terms(f.collect(sum(P,()))) for f in greens] # Optimize
greens = [f.subs(subs) for f in greens] # Convert to p to x/y
defs, exprs = sp.cse(greens,
optimizations='basic',
symbols=(sp.Symbol('r%d'%i) for i in count()))
for name,value in defs:
print(' %s = %s' % (name, value), file=file)
print(file=file)
for name,value in zip([f[0] for f in funcs], exprs):
print(' self.%s += %s' % (name, value), file=file)
print('''
if __name__ == '__main__':
from fontemon_blender_addon.fontTools.misc.symfont import x, y, printGreenPen
printGreenPen('%s', ['''%penName, file=file)
for name,f in funcs:
print(" ('%s', %s)," % (name, str(f)), file=file)
print(' ])', file=file)
def test_simplify_matrix_expressions():
# Various simplification functions
assert type(gcd_terms(C*D + D*C)) == MatAdd
a = gcd_terms(2*C*D + 4*D*C)
assert type(a) == MatMul
assert a.args == (2, (C*D + 2*D*C))
def test_simplify_matrix_expressions():
# Various simplification functions
assert type(gcd_terms(C*D + D*C)) == MatAdd
a = gcd_terms(2*C*D + 4*D*C)
assert type(a) == MatMul
assert a.args == (2, (C*D + 2*D*C))
print(Sum(1,(i,0,n-1)).doit())
T = Sum((-1)**(n-j) * C(j,k), (j,0,n-1))
T2 = T.subs(n, 2*n)
T3 = T.subs(n,2*n+1)
print(T2)
print(T3)
for i in range(0,5):
D = -2*factorial(i)
a2 = T2.subs(k,i).doit().simplify() #.expand(force=True)
#print(factor(a))
b2 = a2.subs(n, n/2)
print('[even n]: {} = ({})/{}'.format(factor(b2), (b2*D).expand(), D))
a3 = T3.subs(k,i).doit().simplify()
b3 = a3.subs(n, (n-1)/2)
print('[odd n]: {} = {}'.format(factor(b3), gcd_terms(b3.expand())))
raise
f = T - (1-(-1)**n)/(-2)**(k+1)
f *= -2*factorial(k) / Product(n-2*i, (i, 0, floor(k/2)))
print(f)
for i in range(0,8):
a = f.subs(k,i).doit().simplify() #.expand(force=True)
print(factor(a))
'''
-2*(-(-2)**(-k - 1)*(-(-1)**n + 1) + Sum((-1)**(-j + n)*binomial(j, k), (j, 0, n - 1)))*k!/Product(-2*i + n, (i, 0, floor(k/2)))
0
1
1
def Stirling_subset_polynomial(n, z):
'Stirling_polynomial(n, z) = Stirling{z, z-n}/fall(z, n+1), for [int n>0]'
assert n > 0
r = Stirling_subset_tail(n, z) / ff(z, n + 1)
return gcd_terms(factor(r.simplify()))
def Stirling_polynomial(n, z):
'Stirling_polynomial(n, z) = Stirling[z, z-n]/fall(z, n+1), for [int n>0]'
assert n > 0
r = Stirling_circle_tail(n, z) / ff(z, n + 1)
return gcd_terms(factor(r.simplify()))
def __missing__(self, i): args = ['p%d'%d for d in range(i+1)] f = green(self._symfunc, BezierCurve[i]) f = sp.gcd_terms(f.collect(sum(P,()))) # Optimize return sp.lambdify(args, f)
def printGreenPen(penName, funcs, file=sys.stdout):
print(
'''from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
from fontTools.pens.basePen import BasePen
class %s(BasePen):
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
'''%penName, file=file)
for name,f in funcs:
print(' self.%s = 0' % name, file=file)
print('''
def _moveTo(self, p0):
self.__startPoint = p0
def _closePath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
self._lineTo(self.__startPoint)
def _endPath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
# Green theorem is not defined on open contours.
raise NotImplementedError
''', end='', file=file)
for n in (1, 2, 3):
if n == 1:
print('''
def _lineTo(self, p1):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
''', file=file)
elif n == 2:
print('''
def _qCurveToOne(self, p1, p2):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
''', file=file)
elif n == 3:
print('''
def _curveToOne(self, p1, p2, p3):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
''', file=file)
subs = {P[i][j]: [X, Y][j][i] for i in range(n+1) for j in range(2)}
greens = [green(f, BezierCurve[n]) for name,f in funcs]
greens = [sp.gcd_terms(f.collect(sum(P,()))) for f in greens] # Optimize
greens = [f.subs(subs) for f in greens] # Convert to p to x/y
defs, exprs = sp.cse(greens,
optimizations='basic',
symbols=(sp.Symbol('r%d'%i) for i in count()))
for name,value in defs:
print(' %s = %s' % (name, value), file=file)
print(file=file)
for name,value in zip([f[0] for f in funcs], exprs):
print(' self.%s += %s' % (name, value), file=file)
print('''
if __name__ == '__main__':
from fontTools.misc.symfont import x, y, printGreenPen
printGreenPen('%s', ['''%penName, file=file)
for name,f in funcs:
print(" ('%s', %s)," % (name, str(f)), file=file)
print(' ])', file=file)
def int_cs_gh(d, s, r):
g, h = find_gh(d, s, r, z)
g = gcd_terms(g)
h = gcd_terms(h)
return g, h
