def testcreation2(self):
a=g.symbol("a")
b=g.symbol("b")
x=g.symbol("x")
y=g.symbol("y")
m=g.matrix([[a,0],[0,b]])
self.assertEqual(repr(m),"[[a,0],[0,b]]")
self.assertNotEqual(repr(m),"[[a,1],[0,b]]")
m=g.matrix([[0,0],[0,0]])
self.assertEqual(repr(m),"[[0,0],[0,0]]")
m[0,0]=a
self.assertEqual(repr(m),"[[a,0],[0,0]]")
m[1,1]=b
self.assertEqual(repr(m),"[[a,0],[0,b]]")
self.assertNotEqual(repr(m),"[[a,0],[b,0]]")
self.assertEqual(m[0,0],a)
self.assertNotEqual(m[0,0],b)
self.assertEqual(m[0,1],0)
self.assertNotEqual(m[0,1],b)
self.assertEqual(m[1,1],b)
self.assertNotEqual(m[1,1],0)
M=g.matrix
m[0,1]=a
self.assertEqual(m,M([[a,a],[0,b]]))
m[0,1]=b
self.assertEqual(m,M([[a,b],[0,b]]))
m[0,1]=b*a
self.assertEqual(m,M([[a,a*b],[0,b]]))
def testsubs(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4,True)
A=g.symbol("A")
e=g.indexed(A,mu)
self.assertEqual(str(e),"A~mu")
self.assertEqual(str(e.subs(mu==nu)),"A.nu")
self.assertEqual(str(e.subs(mu==0)),"A~0")
def testsimplify(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
A=g.symbol("A")
e1=g.indexed(A,mu,mu.toggle_variance())
e2=g.indexed(A,nu,nu.toggle_variance())
self.assertNotEqual(e1,e2)
self.assertEqual((e1-e2).simplify_indexed(),0)
def testvaridx3(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,mu,nu)),"A~mu~nu")
self.assertEqual(str(g.indexed(A,mu,nu.toggle_variance())),"A~mu.nu")
self.assertEqual(str(g.indexed(A,mu.toggle_variance(),nu)),"A.mu~nu")
self.failUnless(mu.is_contravariant())
self.failUnless(nu.is_contravariant())
def test_multivariate_polynomial_analyze(self):
x = symbol("x")
y = symbol("y")
p_correct = [ y**2+11*y, 5*y**2-2*y, -1, 4*y ]
PolyInp = 4*pow(x,3)*y + 5*x*pow(y,2) + 3*y - pow(x+y,2) + 2*pow(y+2,2) - 8
Poly = PolyInp.expand()
for i in xrange(Poly.ldegree(x),Poly.degree(x)+1):
self.assertEqual(Poly.coeff(x,i), p_correct[i])
self.assertEqual(Poly.collect(y), -x**2+(5*x+1)*y**2+(-2*x+4*x**3+11)*y)
def testrelat3(self):
x=g.symbol("x")
y=g.symbol("y")
r1=x/y
r2=2*(x/y)
r2/=2
self.assertEqual(r1,r2)
self.assertNotEqual(r1,r2+1)
r3=r1-r2
self.assertEqual(r3,0)
self.assertNotEqual(r3,1)
def dotest(self,s):
def t(a,b):
s(a,b)
s(b,a)
a=g.numeric(2)
b=g.numeric("1.3")
c=g.symbol("x")
d=g.symbol("y")
e=pow(c,d)*d
f=5
h=5.5
t(a,a)
t(a,b)
t(a,c)
t(a,d)
t(a,e)
t(a,f)
t(a,h)
t(b,b)
t(b,c)
t(b,d)
t(b,e)
t(b,f)
t(b,h)
t(c,c)
t(c,d)
t(c,e)
t(c,f)
t(c,h)
t(d,d)
t(d,e)
t(d,f)
t(d,h)
t(e,e)
t(e,f)
t(e,h)
t(f,f)
t(f,h)
t(h,h)
def __init__(self, name = 'x'):
if isinstance(name, str):
self.data = _g.symbol(name)
elif isinstance(name, _g.symbol):
self.data = name
else:
raise ValueError, "Can not construct a Symbol from a %s" % type(name)
self.spatial_symbs = [self.data]
self.time = None
def testlorentz(self):
mu=g.varidx(g.symbol("mu"),4)
e=g.delta_tensor(g.varidx(0,4),mu.toggle_variance())*\
g.lorentz_g(mu,g.varidx(0,4))
self.assertEqual(e.simplify_indexed(),1)
e=g.delta_tensor(g.varidx(0,4),mu.toggle_variance())*\
g.lorentz_g(mu,g.varidx(0,4),True)
self.assertEqual(e.simplify_indexed(),-1)
def test_basic_print(self):
a = g.symbol('a','\\alpha')
self.assertEqual(str(a), "a")
a.set_print_context('tex')
self.assertEqual(str(a), "\\alpha")
b = a-a+g.Pi
b.set_print_context('tex')
self.assertEqual(str(b), "\\pi")
b.set_print_context('c')
self.assertEqual(str(b), "Pi")
def testsimplify(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("i"),3)
A=g.symbol("A")
B=g.symbol("B")
C=g.symbol("C")
sp=g.scalar_products()
sp.add(A,B,0)
sp.add(A,C,0)
sp.add(A,A,4)
e=g.indexed(A+B,i)*g.indexed(A+C,i)
self.assertEqual(e.expand(g.expand_options.expand_indexed).
simplify_indexed(sp),4+g.indexed(C,i)*g.indexed(B,i))
self.assertEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),4+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed)),4+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),5+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),4+g.indexed(C,i)*g.indexed(B,j))
def testsymm(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
l=g.idx(g.symbol("l"),3)
A=g.symbol("A")
e=g.indexed(A,i,j)
e=g.indexed(A,g.sy_none(), i,j)
e=g.indexed(A,g.sy_none(0, 1), i,j)
e=g.indexed(A,g.sy_none(g.symmetry(0), g.symmetry(1)), i,j)
e=g.indexed(A,g.sy_symm(), i,j,k)
e=g.indexed(A,g.sy_symm(0,1,2), i,j,k)
e=g.indexed(A,g.sy_symm(2,0,1), i,j,k)
e=g.indexed(A,g.sy_symm(0,1), i,j,k)
e=g.indexed(A,g.sy_none(g.sy_symm(0,1),2), i,j,k)
e=g.indexed(A,g.sy_anti(0,2), i,j,k)
e=g.indexed(A,g.sy_none(g.sy_anti(0,2),1), i,j,k)
e=g.indexed(A,g.sy_symm(g.sy_anti(0,1),g.sy_anti(2,3)), i,j,k,l)
e=g.indexed(A,g.sy_cycl(), i,j,k)
e=g.indexed(A,g.sy_cycl(0,1,2), i,j,k)
#this is a deadlock... bug in ginac?
#but nobody really needs that, so I don't care
#g.sy_symm(0,1,2,3).add(4).add(5)
e=g.indexed(A,g.sy_symm(),i,j)+g.indexed(A,g.sy_symm(),j,i)
self.assertEqual(e,2*g.indexed(A,g.sy_symm(), i,j))
e=g.indexed(A,g.sy_anti(),i,j)+g.indexed(A,g.sy_anti(),j,i)
self.assertEqual(e,0)
e=g.indexed(A,g.sy_anti(),i,j,k)+g.indexed(A,g.sy_anti(),j,i,k)
self.assertEqual(e,0)
def testmetric(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
A=g.symbol("A")
e=g.metric_tensor(mu,nu)*g.indexed(A,nu.toggle_variance(),rho)
self.assertEqual(e.simplify_indexed(),g.indexed(A,mu,rho))
self.assertNotEqual(e.simplify_indexed(),g.indexed(A,nu,rho))
e=g.delta_tensor(mu,nu.toggle_variance())*g.metric_tensor(nu,rho)
self.assertEqual(e.simplify_indexed(),g.metric_tensor(mu,rho))
e=g.metric_tensor(mu.toggle_variance(),nu.toggle_variance())*\
g.metric_tensor(nu,rho)
self.assertEqual(e.simplify_indexed(),
g.delta_tensor(mu.toggle_variance(),rho))
e=g.metric_tensor(nu.toggle_variance(),rho.toggle_variance())*\
g.metric_tensor(mu,nu)*(g.delta_tensor(mu.toggle_variance(),rho)+\
g.indexed(A,mu.toggle_variance(),rho))
self.assertEqual((e-(4+g.indexed(A,rho.toggle_variance(),rho))).
simplify_indexed(),0)
def testdelta(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
l=g.idx(g.symbol("l"),3)
A=g.symbol("A")
B=g.symbol("B")
e=g.indexed(A,i,j)*g.indexed(B,k,l)*g.delta_tensor(i,k)*\
g.delta_tensor(j,l)
self.assertEqual((e-g.indexed(A,k,l)*g.indexed(B,k,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(B,k,l)*g.indexed(A,k,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(A,i,l)*g.indexed(B,i,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(A,i,j)*g.indexed(B,i,j)).
simplify_indexed(),0)
self.assertNotEqual((e-g.indexed(A,i,i)*g.indexed(B,k,k)).
simplify_indexed(),0)
self.assertEqual(g.delta_tensor(i,i),3)
self.assertNotEqual(g.delta_tensor(i,i),4)
def __init__(self, name = 'x'):
self.data = _g.symbol(name)
self.spatial_symbs = [self.data]
self.time = None
def test_autodoc(self):
res = 0
x = g.symbol('x')
if not (x.__doc__ == 'Proxy of C++ GiNaC::symbol class'): res += 1
self.assertEqual(res, 0)
ginac_routine = args.ginac_routine
print 'Start preparing ' + file_name
MyTestGenerator = TestGenerator()
MyListCreator = listcreator.ListCreator()
dirac_gamma = swiginac.dirac_gamma
dirac_slash = swiginac.dirac_slash
dirac_gamma5 = swiginac.dirac_gamma5
dirac_gammaR = swiginac.dirac_gammaR
dirac_gammaL = swiginac.dirac_gammaL
simplify_indexed = swiginac.simplify_indexed
dirac_trace = swiginac.dirac_trace
D = swiginac.symbol("D")
i = swiginac.varidx(swiginac.symbol("i"), 4)
j = swiginac.varidx(swiginac.symbol("j"), 4)
k = swiginac.varidx(swiginac.symbol("k"), 4)
l = swiginac.varidx(swiginac.symbol("l"), 4)
m = swiginac.varidx(swiginac.symbol("m"), 4)
n = swiginac.varidx(swiginac.symbol("n"), 4)
o = swiginac.varidx(swiginac.symbol("o"), 4)
p = swiginac.varidx(swiginac.symbol("p"), 4)
iD = swiginac.varidx(swiginac.symbol("iD"), D)
jD = swiginac.varidx(swiginac.symbol("jD"), D)
kD = swiginac.varidx(swiginac.symbol("kD"), D)
lD = swiginac.varidx(swiginac.symbol("lD"), D)
def testdummy(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
l=g.idx(g.symbol("l"),3)
A=g.symbol("A")
B=g.symbol("B")
C=g.symbol("C")
e=g.indexed(A,i,j)*g.indexed(B,j,k)+g.indexed(C,k,l,i,l)
#can vary from run to run
#self.assertEqual(str(e),"C.k.l.i.l+B.j.k*A.i.j")
f=e.get_free_indices()
self.failUnless(type(f)==list)
self.failUnless(f==[i,k] or f==[k,i])
self.failUnless(str(f)=="[.i, .k]" or str(f)=="[.k, .i]")
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
sigma=g.varidx(g.symbol("sigma"),4)
e=g.indexed(A,mu,nu)*g.indexed(B,nu.toggle_variance(),rho)+\
g.indexed(C,mu,sigma,rho,sigma.toggle_variance())
self.failUnless(e.get_free_indices()==[mu,rho] or
e.get_free_indices()==[rho,mu])
e=g.indexed(A,mu,mu)
self.assertEqual(e.get_free_indices(),[mu])
self.assertNotEqual(e.get_free_indices(),[mu.toggle_variance()])
def testeps(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
sig=g.varidx(g.symbol("sig"),4)
lam=g.varidx(g.symbol("lam"),4)
bet=g.varidx(g.symbol("bet"),4)
e=g.lorentz_eps(mu,nu,rho,sig)*g.lorentz_eps(mu.toggle_variance(),
nu.toggle_variance(),lam,bet)
g.simplify_indexed(e)
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
A=g.symbol("A")
B=g.symbol("B")
e=g.epsilon_tensor(i,j,k)*g.indexed(A,j)*g.indexed(B,k)
self.assertNotEqual(g.simplify_indexed(e),0)
e=g.epsilon_tensor(i,j,k)*g.indexed(A,j)*g.indexed(A,k)
self.assertEqual(g.simplify_indexed(e),0)
ginac_routine = args.ginac_routine
print 'Start preparing ' + file_name
MyTestGenerator = TestGenerator()
MyListCreator = listcreator.ListCreator()
dirac_gamma = swiginac.dirac_gamma
dirac_slash = swiginac.dirac_slash
dirac_gamma5 = swiginac.dirac_gamma5
dirac_gammaR = swiginac.dirac_gammaR
dirac_gammaL = swiginac.dirac_gammaL
simplify_indexed = swiginac.simplify_indexed
dirac_trace = swiginac.dirac_trace
D = swiginac.symbol("D")
i = swiginac.varidx(swiginac.symbol("i"), 4)
j = swiginac.varidx(swiginac.symbol("j"), 4)
k = swiginac.varidx(swiginac.symbol("k"), 4)
l = swiginac.varidx(swiginac.symbol("l"), 4)
m = swiginac.varidx(swiginac.symbol("m"), 4)
n = swiginac.varidx(swiginac.symbol("n"), 4)
o = swiginac.varidx(swiginac.symbol("o"), 4)
p = swiginac.varidx(swiginac.symbol("p"), 4)
iD = swiginac.varidx(swiginac.symbol("iD"), D)
jD = swiginac.varidx(swiginac.symbol("jD"), D)
kD = swiginac.varidx(swiginac.symbol("kD"), D)
lD = swiginac.varidx(swiginac.symbol("lD"), D)
def testvaridx1(self):
i=g.varidx(g.symbol("i"),3)
j=g.varidx(g.symbol("j"),3)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,i,j)),"A~i~j")
# # If we initialize a set of symbols, we might want to use a loop rather than a # lot of lines with individual assignments. # # We can use the feature that the dictionary returned by the built-in function # `globals` can be manipulated # # >>> for name in ['gamma', 'delta', 'epsilon']: # ... globals()[name] = swiginac.symbol(name) # # To define the small latin letters a-z as symbols in this module, :: import string as _string for name in _string.lowercase: globals()[name] = swiginac.symbol(name) # Which results in # # >>> print type(delta), type(x) # <class 'swiginac.symbol'> <class 'swiginac.symbol'> # # # Numbers # ------- # # The ``numeric`` class can manipulate arbitrary precision integers in a very # fast way. # # Rational numbers are automatically converted to fractions of coprime # integers.
def testidx(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,i,j)),"A.i.j")
