eng8 = [solve(eng==(k-1)*md*Vm1^2/(2*Patm*Vs*((Pc-(P2*s6))-(Pc-(P2*s6))^(1/k))),Vm1) for s6 in srange(r9,r10,s5,include_endpoint=1)]
v4=[v[0].rhs().n() for v in eng8]
v5=[v for v in v4 if v >= 0]

I can't seem to get v5 to output both real and positive numbers, only an empty list. All the inputs are positive, and I know the square root of the squared gives both positive and negative output. Any help?

Thanks. That clears it right up.

The first step in debugging is to look to see what the first argument actually is. I'm assuming that you did n = var("n") or something at some point. So we can get the first element:

sage: Pps = np.arange(103421.359,1013529,6895.75729) 
sage: Pps[0]
103421.359
sage: Pp = Pps[0]
sage: Pp * Vt
144.05561095109999
sage: Pp * Vt == n
False
sage: Pp * Vt == n*r*t
False

.. and we see that Sage is automatically evaluating the expression, and since it can't prove that it's true -- which is good, because it's not true in general -- it's saying that it's False.

Ultimately this is because

sage: type(Pp)
<type 'numpy.float64'>

Pp is a numpy float, which doesn't interact too well with the Sage types. As soon as the __eq__ method of the float is called, the game's over. You can work around this in some fragile ways, such as flipping the order:

sage: n*r*t == Pp*Vt  
2446.62193200810*n == 144.055610951
sage: solve(n*r*t == Pp*Vt, n)
[n == (52361895020038/889307677165161)]

But a better and more robust way would be to avoid getting numpy involved at all, and stick with Sage-native objects. For example, you can use srange and sxrange:

srange(start, end=None, step=1, universe=None, check=True, include_endpoint=False, endpoint_tolerance=1e-05)
    Return list of numbers ``a, a+step, ..., a+k*step``,
    where ``a+k*step < b`` and ``a+(k+1)*step >= b`` over
    exact rings, and makes a best attempt for inexact rings 
    (see note below).

which would give:

sage: s = srange(103421.359,1013529,6895.75729)
sage: len(s)
132
sage: s[:5]
[103421.359000000, 110317.116290000, 117212.873580000, 124108.630870000, 131004.388160000]

and then

sage: eng5= [solve(Pp*Vt == n*r*t,n) for Pp in srange(103421.359,1013529,6895.75729)]
sage: len(eng5)
132
sage: eng5[:3]
[[n == (52361895020038/889307677165161)], [n == (56778965120683/904048017111831)], [n == (74168281138961/1111449736506101)]]

Short version: don't use numpy unless you need to, and here you don't.

Could you elaborate on when one might use srange, xrange or np.arange? Why did someone request using np.arange on this problem: http://ask.sagemath.org/question/1725/unexpected-solve-errors I see that srange() works there, but xrange() does not. Is it because srange and np.arange both generate a list output, but xrange does it dynamically? Thanks for the clarification!

Ideal Gas Law[Relates Pressure and Volume]

Definitions v3

#Main Tank Pressure[Pascals]
#Pp=1013529.32 
#Tank Volume[m^3]
Vt=0.0013929
#Moles of Air
#n= 0
#Gas Constant
r=8.3144621
#Ambient Temperature[Kelvin][70F]
t= 294.261
eng5= [solve(Pp*Vt == n*r*t,n) for Pp in np.arange(103421.359,1013529,6895.75729)]

Why does this say:

TypeError: The first argument must be a symbolic expression or a list of
symbolic expressions.

I have the variables defined elsewhere[Pp =var('Pp')] but I'm not sure why this won't work. Thanks

That works pretty well, but with 0 as the start it throws an empty list, which screws up my list comprehension. It works pretty well. Do you know about the other problem or why

#Area [m^2]
Ab = 0.00313659226
#CB Ratio
cb = 0.262
eng4 =[solve(cb == Vc/(Ab*Lb),Lb) for Vc in xrange(0.000001,0.00002)]
print(eng4)

This returns an empty list [] and I have no idea why. And this one:

#Ideal Gas Law[Relates Pressure and Volume]
#Definitions v3
#Main Tank Pressure[Pascals]
Pp=1013529.32 
#Tank Volume[m^3]
Vt=0.0013929
#Moles of Air
#Gas Constant
r=8.3144621
#Ambient Temperature[Kelvin][70F]
t= 294.261

eng5= solve(Pp*Vt == n*r*t,n,solution_dict=1)
v3=eng5[0]
v4=n(v3)
n(v4)

__main__:18: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) See http://trac.sagemath.org/5930 for details. 75589949342674/131001015929725

Or it just shows the fraction. It's been acting weird lately

Why?

Your solve syntax has two minor problems. First, Sage uses == for equality, not =, and second, the parentheses aren't balanced. You're missing ")". After correcting these:

sage: solve(eng==(k-1)*md*Vm^2/(2*Patm*Vc*(Pc-Pc^(1/k))),Vc)                           
[Vc == (1821842000000/164304225615681)]

#Pneumatic Air Gun Calculations
import matplotlib.pyplot as plt

#Variables Outlined

#Muzzle Velocity
Vm=var('Vm')
#Atmospheric Pressure
Patm=var('Patm')
#Gas Chamber Volume
Vc=var('Vc')
#Barrel Area[Internal]
Ab=var('Ab')
#Barrel Length
Lb=var('Lb')
#Specific Heat of Air
k=var('k')
#CB Ratio[see table]
cb=var('cb')
#formula variable
eng=var('eng')
#2nd Formula Variable
eng2=var('eng2')
#Mass of the Projectile
md=var('md')
#Operating Pressure in atm
Pc=var('Pc')

#Definitions
k = 1.4
Patm = 101235
cb = 0.261208
#m/s^2
Vm= 91.44
md=2
Pc=10
eng=0.618081

#Main Formula
solve(eng=(k-1)*md*Vm^2/(2*Patm*Vc*(Pc-Pc^(1/k)),Vc)

Can anyone tell me why this is giving a syntax error and pointing to my variable definition Vm? It's really bugging me!