"""

Calculates the Greenberg transform of

  x^2 + (a0,a1,a2)*x + (b0,b1,b2)

in 3 different ways:

* Precompute polynomials for Witt Sum and Prod. (in the most efficient way),
  then use them to perform sums and prod.

* Perform sums and prods using recursion.

* Use the formulas for the GT.


Best to cut and paste....

We include the times obtained (in boole) as comments.


  ***  TESTED!!!  -- compared the results and they all match!  ***


"""

####################################################################

# FIRST WAY: Precompute polynomials for Witt Sum and Prod.

load 'memory.py' # to check memory usage
load 'witt2_fun.sage'

m0=memory()

# #######################
# choose char.
p=11
# #######################

vecS=WittSum2Pol(p)
vecP=WittProd2Pol(p)

PR.<a0,a1,a2,b0,b1,b2,x0,x1,x2>=PolynomialRing(GF(p))

a=[a0,a1,a2]
b=[b0,b1,b2]
x=[x0,x1,x2]

GT=WittSum22(b,WittProd22(a,x, vecP=vecP), vecS=vecS)
GT=WittSum22(GT,WittProd22(x,x, vecP=vecP), vecS=vecS)

print "Total memory usage: " + str(memory(m0)/(1024)^2) + "MB"

"""
p=5 gives:
Total memory usage: 2.3203125MB
Exiting SAGE (CPU time 0m0.26s, Wall time 0m29.49s).

p=7 gives:
Total memory usage: 4.8203125MB
Exiting SAGE (CPU time 0m0.89s, Wall time 0m22.13s).

p=11 gives:
Total memory usage: 50.3203125MB
Exiting SAGE (CPU time 1m57.84s, Wall time 2m4.28s).

######## sage 4.3.1. ################

p=11 gives:
Total memory usage: 50.3203125MB
Exiting SAGE (CPU time 1m57.77s, Wall time 2m26.30s).

#####################################


p=13 gives:
Total memory usage: 153.3203125MB
Exiting SAGE (CPU time 13m53.49s, Wall time 14m14.26s).

p=17 gives:
Total memory usage: 922.921875MB
Exiting SAGE (CPU time 259m19.63s, Wall time 3834m3.13s).

"""


####################################################################

# SECOND WAY: Perform sums and prods using recursion.

load 'memory.py' # to check memory usage
load 'witt2_fun.sage'

m0=memory()

###########################
# choose char.
p=11
###########################


PR.<a0,a1,a2,b0,b1,b2,x0,x1,x2>=PolynomialRing(GF(p))

a=[a0,a1,a2]
b=[b0,b1,b2]
x=[x0,x1,x2]

GT2=WittSum2(b,WittProd2(a,x))
GT2=WittSum2(GT2,WittProd2(x,x))


print "Total memory usage: " + str(memory(m0)/(1024)^2) + "MB"

"""

p=5 gives:
Total memory usage: 2.3203125MB
Exiting SAGE (CPU time 0m0.24s, Wall time 0m2.02s)

p=7 gives:
Total memory usage: 5.3203125MB
Exiting SAGE (CPU time 0m0.31s, Wall time 0m1.97s).

p=11 gives:
Total memory usage: 70.8203125MB
Exiting SAGE (CPU time 0m7.96s, Wall time 0m13.68s).

######## sage 4.3.1. ################

Total memory usage: 70.3203125MB
Exiting SAGE (CPU time 0m6.14s, Wall time 0m15.37s).

#####################################

p=13 gives:
Total memory usage: 217.8203125MB
Exiting SAGE (CPU time 0m40.47s, Wall time 1m7.91s).

p=17 gives:
Total memory usage: 1354.3203125MB
Exiting SAGE (CPU time 11m8.95s, Wall time 12m27.87s).

p=19 gives:
Total memory usage: 2907.3203125MB
Exiting SAGE (CPU time 34m52.06s, Wall time 407m24.24s).

"""


####################################################################

# THIRD WAY: Use the formulas for GT

load 'memory.py' # to check memory usage
load 'witt2_fun.sage'

m0=memory()

########################
# choose char.
p=11
########################


PR.<a0,a1,a2,b0,b1,b2,x0,x1,x2>=PolynomialRing(GF(p),9)


f=b0+a0*x0+x0^2
cc2=f.derivative(x0)^p*x1+ b1+a1*x0^p+SpcFct(f)

cc3=f.derivative(x0)^(p^2)*x2 +(-NextCoord(2,p)*x0^p+a1)^p*x1^p +x1^(2*p)+(b2+a2*x0^(p^2)) + SpcFct(f.derivative(x0)^p*x1+ b1+a1*x0^p) + fSpcFct(f.derivative(x0)^p*x1+ b1+a1*x0^p,SpcFct(f)) + Spc4Fct(f)

# GT3=[f,cc2,cc3]

# len(cc3.monomials())

print "Total memory usage: " + str(memory(m0)/(1024)^2) + "MB"


"""

p=5 gives:
Total memory usage: 2.3203125MB
Exiting SAGE (CPU time 0m0.24s, Wall time 0m2.49s).

p=7 gives:
Total memory usage: 4.3203125MB
Exiting SAGE (CPU time 0m0.29s, Wall time 0m3.10s).

p=11 gives:
Total memory usage: 27.3203125MB
Exiting SAGE (CPU time 0m1.22s, Wall time 0m3.45s).

######## sage 4.3.1. ################

Total memory usage: 27.3203125MB
Exiting SAGE (CPU time 0m1.21s, Wall time 0m5.20s).

#####################################

p=13 gives:
Total memory usage: 78.3203125MB
Exiting SAGE (CPU time 0m3.64s, Wall time 0m5.50s).

p=17 gives:
Total memory usage: 458.8203125MB
Exiting SAGE (CPU time 0m49.43s, Wall time 1m0.55s).

p=19 gives:
Total memory usage: 976.3203125MB
Exiting SAGE (CPU time 2m22.43s, Wall time 4m53.32s).

p=23 gives:
Total memory usage: 3570.12109375MB
Exiting SAGE (CPU time 10m33.81s, Wall time 11m27.72s).

# number of monomials
sage: len(cc3.monomials())
_43 = 65553940


"""