def tZ05():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
A = pt.Product( [pt.CoefficientFloat( 1.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn )] )
B = pt.Product( [pt.CoefficientFloat( 2.0 ), pt.TermA(), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn )] )
C = pt.areTermsCommon(A, B)
return str( C )
def tZ07():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
Dup = pt.MatrixK( "up" )
Dup.fourierTransform()
Ddn = pt.MatrixK( "dn" )
Ddn.fourierTransform()
A = pt.Product( [pt.CoefficientFloat( 1.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Ddn, Dup ] )
B = pt.Product( [pt.CoefficientFloat( 2.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Ddn ] )
C = pt.areTermsCommon(A, B)
return str( C )
def tZ08():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
Dup = pt.MatrixK( "up" )
Dup.fourierTransform()
Ddn = pt.MatrixK( "dn" )
Ddn.fourierTransform()
F1 = pt.FourierSum( [0,1,0,1], 4 )
F2 = pt.FourierSum( [0,0,1,1], 4 )
A = pt.Product( [pt.CoefficientFloat( 1.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Ddn, Dup, F1 ] )
B = pt.Product( [pt.CoefficientFloat( 2.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Ddn, F2 ] )
C = pt.areTermsCommon(A, B)
return str( C )
def tY01():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
Dup = pt.MatrixK( "up" )
Dup.fourierTransform()
Dup.indices = 0
Ddn = pt.MatrixK( "dn" )
Ddn.fourierTransform()
Ddn.indices = 0
A = pt.Product( [pt.CoefficientFloat( 1.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Ddn, Dup ] )
B = pt.Product( [pt.CoefficientFloat( 2.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Ddn ] )
C = pt.Sum( [ A, B ] )
D = pt.combineLikeTerms( C )
D.simplify()
return str( D )
def tY04():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
Dup = pt.MatrixK( "up" )
Dup.fourierTransform()
Dup.indices = 0
Ddn = pt.MatrixK( "dn" )
Ddn.fourierTransform()
Ddn.indices = 0
A1 = pt.Product( [pt.CoefficientFloat( 1.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Ddn, Dup ] )
A2 = pt.Product( [pt.CoefficientFloat( 9.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Dup ] )
A3 = pt.Product( [pt.CoefficientFloat( 2.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Ddn ] )
A4 = pt.Product( [pt.CoefficientFloat( 5.0 ), pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn ), Dup, Dup ] )
D = pt.Sum( [ A3, A2, A4, A1 ] )
E = pt.combineLikeTerms( D )
E.simplify()
return str( E )
D2dn.setAsNoninteracting()
D3up.setAsNoninteracting()
D3dn.setAsNoninteracting()
D4up.setAsNoninteracting()
D4dn.setAsNoninteracting()
# D5up.setAsNoninteracting()
# D5dn.setAsNoninteracting()
# D6up.setAsNoninteracting()
# D6dn.setAsNoninteracting()
# D7up.setAsNoninteracting()
# D7dn.setAsNoninteracting()
# D8up.setAsNoninteracting()
# D8dn.setAsNoninteracting()
print "Calculating spin-up partition function..."
Zup = pt.Sum([detMup, pt.Product([ pt.TermA(), D1up ]), pt.Product([ pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,2), D2up ]) , \
pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,6), D3up]), \
pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,24), D4up])])#, \
#pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,120), D5up]), \
#pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,720), D6up]), \
#pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,5040), D7up]),
#pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,40320), D8up]) ])
Zup = Zup.getExpandedExpr()
Zup.reduceTree()
print "Calculating spin-down partition function..."
Zdn = pt.Sum([detMdn, pt.Product([ pt.TermA(), D1dn ]), pt.Product([ pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,2), D2dn ]), \
pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,6), D3dn]), \
pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,24), D4dn])])#, \
#pt.Product([pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.TermA(), pt.CoefficientFraction(1,120), D5dn]), \
def tZ02():
Mup = pt.MatrixM( False, "up" )
Mdn = pt.MatrixM( False, "dn" )
A = pt.Product( [pt.TermA(), pt.DetM( Mup ), pt.DetM( Mdn )] )
B = pt.areTermsCommon(A, A)
return str( B )
