Hi all,
I am new to Sage and I don't quite understand how to convert my code
to cython code to speed up my program. I am doing a lot of symbolic
manipulations and using the PolynomialRing object. Below I have some
of my code so that you can see the types of manipulations I hope to
speed up:
Ring=PolynomialRing(ZZ,'q,t')
q,t=Ring.gens()
A=PolynomialRing(Ring,'x1,x1L,x1R,x2,x2L,x2R')
x1,x1L,x1R,x2,x2L,x2R=A.gens()
xnplus3=[]
xnegn=[]
zn=[]
def qnumber(n):
g(q,t)=(q^n-t^n)/(q-t)
return g
def qfactorial(n):
prod(q,t)=1
for k in range(n):
prod(q,t)=prod*qnumber(k+1)
return prod
def quantumBinomial(n,k):
f(q,t)=factor(qfactorial(n)/(qfactorial(k)*qfactorial(n-k)))
return f(q,q^(-1))
def L(x1x2_expr):
f=x1x2_expr.substitute({x1:x1L,x2:x2L})
return f
def R(x1x2_expr):
f=x1x2_expr.substitute({x1:x1R,x2:x2R})
return f
def x_nplus3(n):
s=X(-n-1,n+2) #x1^(-n-1)*x2^(n+2)
for p in range(n+1):
for r in range(n+1-p):
b1=quantumBinomial(n-r,p)
b2=quantumBinomial(n+1-p,r)
s=s+b1*b2*X(2*p-n-1,2*r-n)
return s
def commute(LR_expr):
Sum=0
Coeffs=LR_expr.coeffs(x2L)
for Term in Coeffs:
Term[0]=Term[0].substitute({x1L:x1,x1R:q^(-Term[1])
*x1,x2R:x2})
Sum=Sum+Term[0]*x2^(Term[1])
Coeffs=Sum.coeffs(x1)
Sum=0
for Term in Coeffs:
coeffs=Term[0].coeffs(x2)
for term in coeffs:
p=q^(-term[1]*Term[1]/2)
adj_qterm=term[0]/p
qcoeffs=adj_qterm.coeffs(q)
new_qterm=0
for qterm in qcoeffs:
if qterm[1]>=0:
new_qterm=new_qterm+qterm[0]*q^(qterm[1])
if qterm[1]<0:
new_qterm=new_qterm+qterm[0]*t^(-qterm[1])
Sum=Sum+factor(new_qterm)*p*x1^(Term[1])*x2^(term[1])
return Sum.substitute({t:q^(-1)})
I am hoping to get a few pointers and suggestions for making my code
compatible with cython.
Thank you for your time.
Dylan
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