CoCalc -- 2713.sagews

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Below b is the number of points spent in the talent, c is the number of heals per 10 seconds you cast. The vector rs represents the probability of having a given number of stacks at any given time, i.e. the fist number in it is the probability of having no stacks, the second number is the chance to have one. The number rt is average number of stacks, so 2*rt is the average amount of wisdom gained.

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_4.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("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"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpagK45r/___code___.py", line 3
    Below b is the number of points spent in the talent, c is the number of heals per _sage_const_10  seconds you cast. The vector rs represents the probability of having a given number of stacks at any given time, i.e. the fist number in it is the probability of having no stacks, the second number is the chance to have one. The number rt is average number of stacks, so _sage_const_2 *rt is the average amount of wisdom gained.
          ^
SyntaxError: invalid syntax

b=1
c=6
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.689869781056050, 0.213949466241762, 0.0663521948085097, 0.0205778207033781, 0.00638180404012903, 0.00286893315024370) 0.896518399761301

b=2
c=6
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.464404086783941, 0.248732930962287, 0.133220341305638, 0.0713522703605406, 0.0382159844037887, 0.0440743861836764) 2.20493258637745

b=3
c=6
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.304006671423863, 0.211586615153604, 0.147262872562886, 0.102493976850706, 0.0713351241073147, 0.163314739901173) 3.83101697353324

b=4
c=6
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.192699928575918, 0.155566666102738, 0.125588980655934, 0.101387993053603, 0.0818505340337096, 0.342905897577670) 5.50568046119721

b=5
c=6
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.117648999999939, 0.103807712798946, 0.0915948391958629, 0.0808187979593089, 0.0713105471981941, 0.534819102847230) 6.97758297619505

b=5
c=5
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.168069999999948, 0.139822475099957, 0.116322511709907, 0.0967721871668228, 0.0805076856696949, 0.398505140353360) 5.95468100893164

b=5
c=4
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.240099999999941, 0.182451989999955, 0.138645267200966, 0.105356538546014, 0.0800604336411162, 0.253385770611762) 4.72596545532642

b=5
c=3
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.342999999999967, 0.225350999999978, 0.148055606999986, 0.0972725337989907, 0.0639080547059369, 0.122412804495045) 3.36195211339179

b=5
c=2
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.489999999999721, 0.249899999999858, 0.127448999999927, 0.0649989899999630, 0.0331494848999811, 0.0345025250999803) 2.00981107019885

b=5
c=1
c0=vector(((1-.06*b)^c,1-(1-.06*b)^c,0,0,0,0))
c1=vector(((1-.06*b)^c,0,1-(1-.06*b)^c,0,0,0))
c2=vector(((1-.06*b)^c,0,0,1-(1-.06*b)^c,0,0))
c3=vector(((1-.06*b)^c,0,0,0,1-(1-.06*b)^c,0))
c4=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
c5=vector(((1-.06*b)^c,0,0,0,0,1-(1-.06*b)^c))
ms=matrix(CC,[c0,c1,c2,c3,c4,c5])
ts=transpose(ms)
ns=vector((1,0,0,0,0,0))
rs=(ts^10000)*ns
rt=rs[1]+2*rs[2]+3*rs[3]+4*rs[4]+5*rs[5]
print rs,2*rt

(0.699999999999846, 0.209999999999954, 0.0629999999999862, 0.0188999999999959, 0.00566999999999876, 0.00242999999999947) 0.855059999999812