2022-09-04 11:47:27 +0100 received badge ● Famous Question (source) 2022-02-07 12:03:21 +0100 received badge ● Notable Question (source) 2022-02-07 12:03:21 +0100 received badge ● Popular Question (source) 2020-09-24 18:13:02 +0100 asked a question Anyone who has computing power and can run some code for me? Hello, I am running the following code (which should be correct because it works and gives results when applied to E7, E6, up to a couple of modification, A6 and A5 for instance), and on my laptop it takes ages, and actually has not even started to compute the first 5000 cases. Can anyone just help me by running it on some more powerful computer? Is there any other website where I could ask for this kind of help? : a1 = vector((1/2, -1/2, -1/2, -1/2, -1/2, -1/2, -1/2, 1/2)) a2 = vector((1, 1, 0, 0, 0, 0, 0, 0)) a3 = vector((-1, 1, 0, 0, 0, 0, 0, 0)) a4 = vector((0, -1, 1, 0, 0, 0, 0, 0)) a5 = vector((0, 0, -1, 1, 0, 0, 0, 0)) a6 = vector((0, 0, 0, -1, 1, 0, 0, 0)) a7 = vector((0, 0, 0, 0, -1, 1, 0, 0)) a8 = vector((0, 0, 0, 0, 0, -1, 1, 0)) def proj(t, ai): myLone = vector(ai) result= t - myLone.dot_product(t) / (ai.dot_product(ai))*myLone return result # produce all combinaisons in myL of five vectors, and apply the procedure to them: the procedure consists in writing # the Weyl group associated to any five elements in myL (call any myLel) def gensi(t, projai): myLone = projai result = t- 2*myLone.dot_product(t)/(projai.dot_product(projai))*myLone return result def decompose(g, mylength): # g is a str(aa) where aa belongs to list(WeylGroup ...) listg = [g[3*i]+ g[3*i+1] for i in range(0, mylength)] return listg def letsapply(listg, alist, p1, p2, p3, p4, p5, p6, p7): mylistg = listg mylistg.reverse() for si in mylistg: if si == 's1': alist = map(lambda w: gensi(w, p1), alist) elif si == 's2': alist = map(lambda w: gensi(w, p2), alist) elif si == 's3': alist = map(lambda w: gensi(w, p3), alist) elif si == 's4': alist = map(lambda w: gensi(w, p4), alist) elif si == 's5': alist = map(lambda w: gensi(w, p5), alist) elif si == 's6': alist = map(lambda w: gensi(w, p6), alist) elif si == 's7': alist = map(lambda w: gensi(w, p7), alist) else: print("Wrong input in letsapply!!") alistt = [tuple(v) for v in alist] alistts = set(alistt) return alistts import sys from timeit import default_timer as timer def main(): starttime = timer() W = WeylGroup(["A", 7], prefix="s") listW = list(W) # We remove the first element which is 1: listW.pop(0) listWdecomposed = [decompose(str(g), g.length()) for g in listW] e = RootSystem(['E',8]).ambient_space() Roots = e.roots() ## get all projections of roots in E6 myR = [vector(v) for v in Roots] myL = [proj(x, a2) for x in myR] myL = [pp for pp in myL if pp != zero_vector(8)] print("myL = ", myL) print("myL has ", len(myL), " components.") print(len(Combinations(myL, 7).list())) print("End of precomputations, beginning of the loop.") WhenToTell = 5000 # Every WhenToTell, the program writes something CounterToTell = 0 for myLel in Combinations(myL, 7): #print("Next element of myLlist ...") [proja1, proja2, proja3, proja4, proja5, proja6, proja7] = myLel res = set(tuple(v) for v in myLel) CounterToTell += 1 # We add 1 ShouldTakeNextmyLel = False ### NONONO print("Trying ", myLel) for listg in listWdecomposed: res = res.union(letsapply(listg, myLel, proja1, proja2, proja3, proja4, proja5, proja6, proja7)) #sys.stdout.write(".")# That's print without a return if len(res) > 56: ShouldTakeNextmyLel = True break # No use continuing with this myLel if ShouldTakeNextmyLel: next # On reconvertit : res = [vector(v) for v in res] res = list(res) #print("End") if len(res) == 56: LLL =[] lst=[] for a in myLel: for b in myLel: R = a.dot_product(b) lst.append(R) #print(a, lst, "lst") if (lst.count(-1)==1 or lst.count(-1)==2) and lst.count(1)==0 and lst.count(2) ==1 and (lst.count(0)==4 or lst.count(0)==5): LLL.append(lst) lst=[] else: break if len(LLL) ==7: print("myLel = ", myLel) print("res = ", res) print(LLL, "LLL") #else: #print("not the basis of root system") #break # Exceptional exit from "for" loop #else: # print("too many vectors in this subspace") ## Give some info on the running: if CounterToTell%WhenToTell == 0: endtime = timer() print("We used ", endtime - starttime, " seconds for ", WhenToTell, " cases.") starttime = endtime return 0 main()  2020-09-10 17:25:00 +0100 asked a question checking a list of vectors constitute the basis of a root system In this area of Sage link text is there a command to check a set of vectors satisfy the conditions to be a basis of a root system? 2020-08-25 11:51:27 +0100 commented answer Root systems algorithm: "TypeError: 'str' object is not callable" Cool. Merci :) 2020-08-20 09:51:44 +0100 commented answer Root systems algorithm: "TypeError: 'str' object is not callable" This code along with the main function below work fine: def main(): W = WeylGroup(["A", 5], prefix="s") listW = list(W) # We remove the first element which is 1: listW.pop(0) listWdecomposed = [decompose(str(g), g.length()) for g in listW] res = set(tuple(v) for v in myP) for listg in listWdecomposed: res = res.union(letsapply(listg, myP)) # On reconvertit : res = [vector(v) for v in res] res.sort() return(len(res), res)  Now, I am trying to do a loop where I apply this function 'main' to the list of all sets of five random vectors in myL, this is why I have added the p1,p2... in the letsapply function. 2020-08-20 09:45:08 +0100 commented answer Root systems algorithm: "TypeError: 'str' object is not callable" Hi, the si applied is the si defined here: myP = [proj(x, a6) for x in Lini] [proja1, proja2, proja3, proja4, proja5] = myP def si(t, projai): myLone = projai result = t- 2*myLone.dot_product(t)/(projai.dot_product(projai))*myLone return result  2020-08-19 22:54:59 +0100 asked a question Root systems algorithm: "TypeError: 'str' object is not callable" I am rather new to Sage and formal language. I am running the following code which works fine with a slighty simpler version (where the variables p1, p2, ..., p5 in the function letsapply are fixed). Here is the original function that works fine: def letsapply(listg, alist): mylistg = listg mylistg.reverse() for si in mylistg: if si == 's1': alist = map(s1, alist) elif si == 's2': alist = map(s2, alist) elif si == 's3': alist = map(s3, alist) elif si == 's4': alist = map(s4, alist) elif si == 's5': alist = map(s5, alist) elif si == 's6': alist = map(s6, alist) else: print("Wrong input in letsapply!!") alistt = [tuple(v) for v in alist] alistts = set(alistt) return alistts  Below, I am getting the following TypeError: 'str' object is not callable  Could anyone help me fix this? Thanks a lot! e = RootSystem(['E',6]).ambient_space() Roots = e.roots() a1 = vector((1/2, -1/2, -1/2, -1/2, -1/2, -1/2, -1/2, 1/2)) a2 = vector((1, 1, 0, 0, 0, 0, 0, 0)) a3 = vector((-1, 1, 0, 0, 0, 0, 0, 0)) a4 = vector((0, -1, 1, 0, 0, 0, 0, 0)) a5 = vector((0, 0, -1, 1, 0, 0, 0, 0)) a6 = vector((0, 0, 0, -1, 1, 0, 0, 0)) Lini = [a1, a2, a3, a4, a5] # alist is the set of all projections of roots in E6 myR = [vector(v) for v in Roots] def proj(t, ai): myLone = vector(ai) result= t - myLone.dot_product(t) / (ai.dot_product(ai))*myLone return result myL = [proj(x, a6) for x in myR] def si(t, projai): myLone = projai result = t- 2*myLone.dot_product(t)/(projai.dot_product(projai))*myLone return result def decompose(g, mylength): # g is a str(aa) where aa belongs to list(WeylGroup ...) listg = [g[3*i]+ g[3*i+1] for i in range(0, mylength)] return listg def letsapply(listg, alist, p1, p2, p3, p4, p5): mylistg = listg mylistg.reverse() for si in mylistg: if si == 's1': alist = map(lambda w: si(w, p1), alist) elif si == 's2': alist = map(lambda w: si(w, p2), alist) elif si == 's3': alist = map(lambda w: si(w, p3), alist) elif si == 's4': alist = map(lambda w: si(w, p4), alist) elif si == 's5': alist = map(lambda w: si(w, p5), alist) else: print("Wrong input in letsapply!!") alistt = [tuple(v) for v in alist] alistts = set(alistt) return alistts def main(): W = WeylGroup(["A", 5], prefix="s") listW = list(W) # We remove the first element which is 1: listW.pop(0) listWdecomposed = [decompose(str(g), g.length()) for g in listW] e = RootSystem(['E',6]).ambient_space() Roots = e.roots() ## get all projections of roots in E6 myR = [vector(v) for v in Roots] myL = [proj(x, a6) for x in myR] print("myL =", myL) # produce all combinaisons in myL of five vectors, # and apply the procedure to them: the procedure consists first in writing # the Weyl group associated to any five elements in myL (call any : myLel), # then applying these elements si to myLel myLlist= Combinations(myL, 5).list() for myLel in myLlist: [proja1, proja2, proja3, proja4, proja5] = myLel res = set(tuple(v) for v in myLel) for listg in listWdecomposed: res = res.union(letsapply(listg, myLel, proja1, proja2, proja3, proja4, proja5)) # Reconvert res = [vector(v) for v in res] res.sort() if len(res)< 30: return(len(res), res) else: print("too many vectors in this subspace") return 0 main()  2020-08-19 20:31:16 +0100 commented answer An algorithm on root systems' vectors "ValueError: too many values to unpack " Yes, my bad, I wanted : if len(myLset1) >= 5: [proja1, proja2, proja3, proja4, proja5] = myLset1 Thanks! 2020-08-19 20:29:01 +0100 received badge ● Supporter (source) 2020-08-19 20:12:37 +0100 received badge ● Editor (source) 2020-08-19 16:00:59 +0100 received badge ● Student (source) 2020-08-19 15:49:27 +0100 asked a question An algorithm on root systems' vectors "ValueError: too many values to unpack " While finishing a math project, I need to run the following code, and get an error message which seems related to Sage calculation capacity, could anyone help me through this? (I am quite new to Sage.) If there is no way to handle that in Sage, could anyone recommend me another software with similar language where this code could be run properly? e = RootSystem(['E', 6]).ambient_space() Roots = e.roots() a1 = vector((1/2, -1/2, -1/2, -1/2, -1/2, -1/2, -1/2, 1/2)) a2 = vector((1, 1, 0, 0, 0, 0, 0, 0)) a3 = vector((-1, 1, 0, 0, 0, 0, 0, 0)) a4 = vector((0, -1, 1, 0, 0, 0, 0, 0)) a5 = vector((0, 0, -1, 1, 0, 0, 0, 0)) a6 = vector((0, 0, 0, -1, 1, 0, 0, 0)) Lini = [a1, a2, a3, a4, a5] def proj(t, ai): myLone = vector(ai) result= t - myLone.dot_product(t) / (ai.dot_product(ai))*myLone return result myP = [proj(x, a6) for x in Lini] [proja1, proja2, proja3, proja4, proja5] = myP myR = [vector(v) for v in Roots] myL = [proj(x, a6) for x in myR] len(myL) myPlist1= Combinations(myP, 3).list() myLlist1= Combinations(myL, 2).list() # alternatively: produce all combinaisons in myL of five vectors # (all to be used in a function where these combinaisons are variables: # this does not work either # myLlist = Combinations(myL, 5).list() def letsapply(listg, alist): for listel in listg: myPset1= set(tuple(v) for v in listel) print(myPset1) for listel2 in alist: myLset1 = set(tuple(v) for v in listel2) print(myLset1) myLset1 = myLset1.union(myPset1) if len(myLset1) >= 5: print(myLset1, "myLset1") if len(myLset1) >= 5: for myLel in myLset1: [proja1, proja2, proja3, proja4, proja5] = myLel print(myLel) print(letsapply(myPlist1, myLlist1))