'use strict' """ copyright belongs to: Amichai Etzion Dael Winograd 2020 """ # v. 6.7.6 """ Created by The amazing super developers: Amichai Etzion Dael Winograd This code takes an equation (equality), inequality or an expression, and returns its solutions. Any equation is accepted as long as it is possible to solve. Any parentheses (brackets) are allowed. List of accepted equations: - Any polynomial up to 4th degree at their final form. For example: 4.5x^4+2x^3-7x^2+4x+1 = 0 x^2*(x-3) = (x+5)/(6-x)+1 - Any polynomial in a final form of x^a=b. For example: x^100 = 1 - Equations in which it's possible to lower the degree by setting another parameter. For example: x^16+x^8+ix^4=1 (this equation can be simplified by using another parameter [t=x^4]) - Multiplications of forms like the above that equal zero. For example: (x^2+5x-7)(8x^3-4x^2+2) = 0 - Some other possible equations are allowed, and more equations will be supported in the future. - Inequalities are supported as long as their equality form is from the above. For example: 5x^4-3x^2 <= 7x^3-2 (x^3-7x+5)/(x+3) > 2+(x+2)^3 Any expression can be simplified! For example: (x^2-5)/(x^3+17x-2)+3x^5 Becomes: (3x^8+51x^6-6x^5+x^2-5)/(x^3+17x-2) (Hint: try also "(x+1)^50") The main method - "solve", takes 3 arguments: solve(eq, show=False, way=False) - eq {string}: This is the equality/inequality/expression in a string form. - show {boolean}: If show is True, solve will show the final answers/simplified expression, in addition of returning it. - way {boolean}: If way is True, solve will show the solution step by step, all the way to the final answers. """ def solve(eq, show=False, way=False): p = par(eq.lower()) #parameter eq = edit(eq, p) #equation tp = [] #To Print ne = [] #nonExistence way = show and way if '=' in eq: ans = equality(eq, p, show, way, tp, ne, True) elif any([i in eq for i in (chr(8804),chr(8805),'<','>')]): ans = inequality(eq, p, show, way, tp, ne) else: if show: sd(eq+'=', p, tp, True) if p not in eq: sd(str(fix(eval(eq.replace('^','**').replace(')j',')*1j'))))+'=', p, tp, True) if p in eq: ans = sograim(eq, p, True, way, tp, True) #if way: # sd(''.join(['('+p+('-'+a if a!='0' else '')+')' for a in equality(ans+'=0',p,False,False,tp,ne,True)])+'=',p,tp,True) else: ans = eval(eq.replace('^','**').replace(')j',')*1j')) for i in range(len(tp)): tp[i] = tp[i][:tp[i].index(" ")] if show: if len(open(__file__).read())==39945: print(chr(8226)*34,'| Amichai Etzion & Dael Winograd |',chr(8226)*34,'',sep='\n') print('\n'.join(erase(tp))) return ans def equality(eq, p, show, way, tp, ne, final): if show: sd(eq, p, tp, True) if p == '?': eq = eq.split('=') else: eq = moveHandSides(eq, '=') eq[0],eq[1] = remUns(eq[0],True),remUns(eq[1],True) if way: sd('='.join(eq), p, tp, True) ans = [] splitEq = splitChar(eq[0], '*') if len(splitEq) > 1 and len(splitChar(eq[0],'+')) == 1 and p!='?': for exp in splitEq: if way: sd('-'*len(tp[-1]), p, tp, False) ans+=equality(exp+'=0', p, way, way, tp, ne, False) if way: sd('-'*len(tp[-1]), p, tp, False) elif p != '?': eq[0] = sograim(eq[0], p, False, way, tp) if eq[0][0][2][0][0]!={0:1}: ne += equality(stringifyer(eq[0][0][2],p)+'=0',p,False,False,None,[],True) eq[0] = eq[0][0][0] if isPoly(eq[0][0]) and len(eq[0][0][0]) and min(eq[0][0][0]): m = min(eq[0][0][0]) if len(eq[0][0][0]) > 1: eq[0] = '1'+p+('^'+str(m) if m!=1 else '')+'*('+dictToStr(dict([(n[0]-m,n[1]) for n in eq[0][0][0].items()]),p)+')' ans += equality(eq[0]+'=0',p,way,way,tp,ne,False) else: if way: sd('1'+p+('^'+str(m) if m!=1 else '')+'=0',p,tp,True) sd('1'+p+'=0',p,tp,True) ans += ['0'] else: ans += formula(eq[0],p,way,tp) else: eq[0], eq[1] = str(fix(eval(eq[0].replace('^','**').replace('j','*1j')))), str(fix(eval(eq[1].replace('^','**').replace('j','*1j')))) if way: sd('='.join(eq), p, tp, True) ans += ['Any '+p if eq[0]==eq[1] else 'No Solution'] ans = checkSolution(list(set(ans)), p, ne, show, tp, final) return ans def checkSolution(ans, p, ne, show, tp,final): if 'No Solution' in ne: ne.remove('No Solution') if 'No Solution' in ans and len(ans)>1: ans.remove('No Solution') if 'Any '+p in ne: ans = ['No Solution'] ne = [] if 'Any '+p in ans and len(ans)>1: ans = ['Any '+p] if 'Any '+p in ans and len(ne): ans[0] += ',but' + p + chr(8800) + (','+p+chr(8800)).join(ne) ne = [] for n in ne: if n in ans: del ans[ans.index(n)] if not len(ans): ans = ['No Solution'] if p == '?': ans = [str(ans[0]=='Any '+p)] if len(ans) > 1: ans = list(map(lambda s: s.replace('i','j').replace('+-','-'),ans)) ans = list(map(complex,ans)) ans = list(map(fix,ans)) ans = [filter(lambda n: type(n)!=complex,ans),filter(lambda n: type(n)==complex and not n.real,ans),filter(lambda n: type(n)==complex and n.real,ans)] ans = list(map(lambda l: sorted(l,key=abs),ans)) ans = ans[0]+ans[1]+ans[2] ans = list(map(str,ans)) ans = list(map(lambda s: s.replace('j','i'),ans)) if show: if final: sd('='*len(tp[-1]),p,tp,False) answ = ans[:] if len(answ) > 1: for i in range(len(answ)): if answ[i] not in ('No Solution', 'Any '+p): answ[i] = p+tiny(str(i+1),'sub')+' = '+answ[i] elif answ[0] not in ('No Solution','True','False') and 'Any' not in answ[0]: answ[0] = p+'='+answ[0] sd('\n'.join(answ), p, tp, True) return ans def moveHandSides(eq, sign): eq = eq.split(sign) if eq[1] != '0': if len(splitChar(eq[1],'+')) == 1: if eq[1][0] == '-': eq[0] += '+'+eq[1][1:] elif eq[1][0] != '(': eq[0] += '+-'+eq[1] else: eq[0] += '+-1*'+eq[1] else: eq[0] += '+-1*('+eq[1]+')' eq[1] = '0' return eq def calcPoly(eq, p, strBack=False, way=False, tp=None): pows = {} for e in eq: e = checkPower(e, p) if pows.get(e[0]) == None: pows[e[0]] = [] pows[e[0]].append(e[1]) for k in pows: pows[k] = fix(eval('+'.join(list(map(str,pows[k]))).replace('^','**').replace('i','j'))) pows = dict(sorted(pows.items(),reverse=True)) while 0 in pows.values() or '0' in pows.values(): for i in pows: if not pows[i] or pows[i]=='0': del pows[i] break if strBack or way: string = dictToStr(pows, p) if way: sd(string+' = 0', p, tp, True) if strBack: return string return pows def rootFormula(a, b, c, p, way=False, tp=None): if way: if all([a,b,c]): if p not in ('a','b','c'): sd(f'a = {a}, b = {b}, c = {c}', p, tp, True) sd(p+' = ('+str(fix(-b))+chr(177)+chr(8730)+'(('+str(b)+')^2+-4*'+str(a)+'*'+str(c)+')) / (2*'+str(a)+')', p, tp, True) sd(p+' = ('+str(fix(-b))+chr(177)+chr(8730)+'('+str(fix(b**2-4*a*c))+')) / '+str(fix(2*a)), p, tp, True) sd(p+' = ('+str(fix(-b))+chr(177)+str(fix((b**2-4*a*c)**.5))+') / '+str(fix(2*a)), p, tp, True) elif a and b: sd(p+'('+str(a)+p+'+'+str(b)+') = 0', p, tp, True) elif a and c: sd(str(a)+p+'^2 = '+str(fix(-c)), p, tp, True) sd(p+'^2 = '+str(fix(-c/a)), p, tp, True) sd(p+' = '+chr(177)+chr(8730)+'('+str(fix(-c/a))+')', p, tp, True) if b**2-4*a*c == 0: return [str(fix(-b/(2*a)))] return [str(fix((-b+(b**2-4*a*c)**.5)/(2*a))),str(fix((-b-(b**2-4*a*c)**.5)/(2*a)))] def edit(eq, p): eq = eq.replace(' ','').lower().replace('-','+-').replace('×','*').replace('÷','/').replace('*+-','*-').replace('/+-','/-').replace(')(',')*(').replace('(+-','(-').replace('-(','-1*(').replace('<=',chr(8804)).replace('=<',chr(8804)).replace('=>',chr(8805)).replace('>=',chr(8805)).replace('^+-','^-') #)))) #if 'i' in eq.replace(p, ''): #eq = eq.replace('i','j').replace(p.replace('i','j'), p) for idx in range(len(eq)): if eq[idx]=='i': if not ((idx and eq[idx-1].isalpha()) or (idx!=len(eq)-1 and eq[idx+1].isalpha())) or (idx=6 while cont: if len(eq)<5: cont = False for x in range(2,len(eq)-2): if eq[x:x+2] ==')^': power = fix(float(eq[x+2:fs(eq,x+2,1,True)+1])) if type(power)==int: if power>0: if x==len(eq)-3: cont=False continue elif power==0: rp = '(1)' else: rp = '(1/('+eq[fs(eq,x,-1):x+2]+str(-power)+'))' eq = rplc(eq,fs(eq,x,-1),fs(eq,x+2,1,True),rp,p) break if x^() ': if s not in ps: ps.append(s) s = '' mid = False else: s += p elif p in 'abcdefghijklmnopqrstuvwxyz': s += p mid = True if mid and s not in ps: ps.append(s) if 'i' in ps: ps.remove('i') if 'j' in ps: ps.remove('j') if not ps: ps.append('?') for idx in range(len(ps)): if (ps[idx][0]=='i' and ps[idx][1:] in ps) or ((ps[idx]+'(') in eq) or ((')'+ps[idx]) in eq): ps[idx] = None while None in ps: del ps[ps.index(None)] return ps[0] def sd(s, p, tp, toEdit): if toEdit: s = unEdit(s, p) for string in s.split('\n'): tp.append(string) def unEdit(s, p): s = remUns(s.replace('÷','/')) if '=0' in s and unnecesog(s.split('=')[0]) and s[0]=='(': s = s.split('=')[0][1:-1]+'=0' cont = len(s)>=4 while cont: for i in range(2,len(s)): if s[i:].startswith(p) and s[i-1]=='1' and (i-2<0 or not ord(s[i-2]) in list(range(ord('0'),ord('9')+1))+[ord('.')]): s = rplc(s,i-1,i-1+len(p),p,p) break if i==len(s)-1: cont = False if s[1:].startswith(p) and s[0]=='1': s = rplc(s,0,len(p),p,p) while '^' in s: for i in range(1, len(s)): if s[i] == '^': s = rplc(s,i,fs(s,i+1,1,True),tiny(s[i+1:fs(s,i+1,1,True)+1],'sup'),p) break s = s.replace(' ','').replace(',',', ').replace('NoSolution','No Solution').replace('Any','Any ').replace('but','but ').replace('+-','-').replace('-1*(','-(').replace('or',' or ').replace('j','i') for sign in '<>='+chr(8804)+chr(8805)+chr(8800): s = s.replace(sign, f' {sign} ') if s.startswith('1i'): s = s[1:] cont = len(s)>=3 while cont: for i in range(2, len(s)): if s[i] == 'i' and s[i-1]=='1' and s[i-2] not in '0123456789.': s = rplc(s, i-1, i, 'i', p) break if i == len(s)-1: cont = False return s def erase(tp): isEq = any(['==' in t for t in tp]) tpc = [] ft = 0 for t in range(len(tp)): if '--' in tp[t] or '==' in tp[t]: if tp[ft:t]: tpc.append(tp[ft:t]) ft = t+1 if tp[ft:]: tpc.append(tp[ft:]) ansLen = len(tpc[-1]) cont = True while cont: for t in range(len(tpc)): if isIncluded(tpc,t) or tiny('1','sub') in tpc[t][0] and (isEq or t!=len(tpc)-2): del tpc[t] break if t >= len(tpc)-2: cont = False break for t in range(len(tpc)): while len(tpc[t]) > len(set(tpc[t])): for i in tpc[t]: if i in tpc[t][tpc[t].index(i)+1:]: tpc[t] = tpc[t][:tpc[t].index(i)] + tpc[t][-1-tpc[t][::-1].index(i):] break tp.clear() if len(tpc) >= 4: for t in range(len(tpc)): tp += tpc[t] if t == len(tpc)-2: tp.append('='*len(tp[-1])) elif t!=len(tpc)-2: tp.append('-'*len(tp[-1])) del tp[-1] else: if len(tpc[-1]) == 1 and len(tpc)>1 and tpc[-1][0] == tpc[-2][-1]: del tpc[-1] for t in range(len(tpc)): tp += tpc[t] return tp def isIncluded(lst, idx): for i in range(idx+1,len(lst)): if all([n in lst[i] for n in lst[idx]]): return True return False def tiny(string, scriptType): script = {'0':[8304,8320], '1':[185,8321], '2':[178,8322], '3':[179,8323], '4':[8308,8324], '5':[8309,8325], '6':[8310,8326], '7':[8311,8327], '8':[8312,8328], '9':[8313,8329],'a':[7491,8336], 'b':[7495,63], 'c':[7580,63], 'd':[7496,63], 'e':[7497,8337], 'f':[7584,63], 'g':[7501,63], 'h':[688,8341], 'i':[8305,7522], 'j':[690,11388], 'k':[7503,8342], 'l':[737,8343], 'm':[7504,8344], 'n':[8319,8345], 'o':[7506,8338], 'p':[7510,8346], 'q':[63,63], 'r':[691,7523], 's':[738,8347], 't':[7511,8348], 'u':[7512,7524], 'v':[7515,7525], 'w':[695,63], 'x':[739,8339], 'y':[696,63], 'z':[7611,63], '+':[8314,8330], '-':[8315,8331], '=':[8316,8332], '(':[8317,8333], ')':[8318,8334], '/':[5151,63], '.':[5159,63], '*':[5441,63], '^':[5487,63]} if scriptType == 'sup': scriptType = 0 elif scriptType == 'sub': scriptType = 1 result = '' for ch in string: result += chr(script[ch][scriptType]) return result def cubicFormula(a, b, c, d): q = (3*a*c-b**2)/(9*a**2) r = (9*a*b*c-27*a**2*d-2*b**3)/(54*a**3) s = (r+(q**3+r**2)**.5)**(1/3) if s: t = -q/s else: t = (r-(q**3+r**2)**.5)**(1/3) x1 = s+t-b/(3*a) x2 = -.5*(s+t)-b/(3*a)+(3**.5)/2*(s-t)*1j x3 = -.5*(s+t)-b/(3*a)-(3**.5)/2*(s-t)*1j ans = list(map(fix,[x1,x2,x3])) for i in range(3): ans[i] = str(ans[i]).replace('j','i') return sorted(list(set(ans))) def quarticFormula(a,b,c,d,e,par,way,tp): f,g,h,i = b/a,c/a,d/a,e/a p = g-3/8*f**2 q = 1/8*f**3-f*g/2+h r = i-h*f/4+1/16*g*f**2-3*f**4/256 A2 = cubicFormula(1,2*p,p**2-4*r,-q**2) A = list(map(lambda s: fix(complex(s.replace('i','j'))**.5),A2)) A = [n for n in A if type(n)!=complex] if not len(A): A = fix(complex(A2[0].replace('i','j')))**.5 else: A = A[0] if A: B = (p+A**2-q/A)/2 C = (p+A**2+q/A)/2 else: B = (p+A**2-((p+A**2)**2-4*r)**.5)/2 C = (p+A**2+((p+A**2)**2-4*r)**.5)/2 if way: sd(dictToStr({4:1,3:fix(f),2:fix(g),1:fix(h),0:fix(i)},par)+' = 0',par,tp,True) ans = equality('('+dictToStr({2:1,1:fix(f/2+A),0:fix(f**2/16+f/4*A+B)},par)+')*('+dictToStr({2:1,1:fix(f/2-A),0:fix(f**2/16-f*A/4+C)},par)+')=0',par,way,way,tp,[],False) return ans def linearFormula(m, b, p, way, tp): if m: if b and way: sd(str(m)+p+'='+str(fix(-b)), p, tp, True) return [str(fix(-b/m))] if b: return ['No Solution'] return ['Any '+p] def formula(expression, p, way, tp): if isPoly(expression[0]): return formulaPoly(expression[0][0],p,way,tp) else: return ['No Solution (Can\'t find.)'] def formulaPoly(dic, p, way, tp): pow = gcd(*dic) if pow > 1 and not (len(dic)==2 and min(dic)==0): return letFormula(dic, pow, p, way, tp) elif not len(dic) or max(dic)<=1: return linearFormula(dic.get(1,0),dic.get(0,0),p,way,tp) elif max(dic) == 2: return rootFormula(dic.get(2),dic.get(1,0),dic.get(0,0),p,way,tp) elif max(dic) == 3: return cubicFormula(dic.get(3),dic.get(2,0),dic.get(1,0),dic.get(0,0)) elif max(dic) == 4: return quarticFormula(dic.get(4),dic.get(3,0),dic.get(2,0),dic.get(1,0),dic.get(0,0),p,way,tp) elif len(dic)==1 or len(dic)==2 and dic.get(0)!=None: return complexFormula(dic,p,way,tp) def dictToStr(dic, p): while 0 in dic.values() or '0' in dic.values(): for i in dic: if not dic[i] or dic[i]=='0': del dic[i] break string = [] for k in dic: if not k: string.append(str(dic[k])) elif k == 1: string.append(str(dic[k])+p) else: string.append(str(dic[k])+p+'^'+str(k)) if not len(string): string.append('0') string = '+'.join(string) return string def gcd(*args): from math import gcd g = 0 for i in args: g = gcd(g, i) return g def complexFormula(eq, p, way, tp): from math import sin,cos,pi,atan pow = max(eq) if not 0 in eq.keys(): eq[0] = 0 if way: sd(str(eq[pow])+p+'^'+str(pow)+'='+str(-eq[0]),p,tp,True) sd(p+'^'+str(pow)+'='+str(fix(-eq[0]/eq[pow])),p,tp,True) sd(p+'='+tiny(str(pow),'sup')+chr(8730)+'('+str(fix(-eq[0]/eq[pow]))+')',p,tp,True) eq[0] = -eq[0]/eq[pow] if type(eq[0])==complex: sangle = atan(eq[0].imag/eq[0].real) if eq[0].real else pi/2 if eq[0].imag>0 else -pi/2 elif eq[0]<0: sangle = pi else: sangle = 0 length = abs(eq[0])**(1/pow) angle = 0 ans = [] for i in range(pow): angle = (sangle+i*2*pi)/pow im = fix(length*sin(angle)) re = fix(length*cos(angle)) ans.append(str(re)+'+'+str(im)+'i') return list(set(ans)) def letFormula(dic, pow, p, way, tp): newP = 't' if p!='t' else 'x' if way: sd('---',p,tp,False) sd('Let '+newP+' = '+p+tiny(str(pow),'sup'), p, tp, False) tempAns = equality(dictToStr(dict([(n[0]//pow, n[1]) for n in dic.items()]),newP)+'=0', newP, way, way, tp, [], False) if way: sd('---',p,tp,False) ans = [] for x in tempAns: currAns = complexFormula({pow:1,0:-fix(complex(x.replace('i','j')))},p,way,tp) if way: currAns = checkSolution(currAns, p, [], way, tp, False) sd('---',p,tp,False) ans += currAns return ans def sograim(s,p,strBack=False,way=False,tp=None,showDenom=False): s = innerDiv(s) s,d = tuple(calcdiv(s,p,way,tp).split('/')) s,d = calc(s,p,False),calc(d,p,False) s,d = calcmul(s,p,way,tp,s,True,d if showDenom else [({0:1},'^1')]),calcmul(d,p,False,tp,d,True) if way: if showDenom: if stringifyer(d,p)!='1': sd('('+stringifyer(s,p)+')/('+stringifyer(d,p)+')=',p,tp,True) else: sd(stringifyer(s,p)+'=',p,tp,True) else: sd(stringifyer(s,p)+'=0',p,tp,True) if strBack: return stringifyer([(s,'/',d)] if d!=[({0:1},'^1')] else s,p) return [(s,'/',d)] def calcmul(exp,p,way,tp,ori,first=False,d=[({0:1},'^1')]): ans = [] for e in range(len(exp)): if not isPoly(exp[e]) and isIntPower(exp[e]): ret = intPower(exp[e]) ans.extend(ret) ori = eval(str(ori).replace(str(exp[e]),str(ret)[1:-1])) elif exp[e][1]=='*': ret = [] for a in exp[e][0]: for b in exp[e][2]: ret.append(calcmulRes(a,b,p,way,tp,ori,d)) ans.extend(ret) ori = eval(str(ori).replace(str(exp[e]),str(ret)[1:-1])) else: ans.append(exp[e]) if way: sd('('+stringifyer(ori,p)+')'+('/('+stringifyer(d,p)+')' if d!=[({0:1},'^1')] else '')+'=0',p,tp,True) return calcAdd(ans,p,way,tp,first,d) def calcmulRes(a,b,p,way,tp,ori,d): if isMul(a) or inExpression([a],isIntPower): a = calcmul([a],p,way,tp,ori,False,d)[0] if isMul(b) or inExpression([b],isIntPower): b = calcmul([b],p,way,tp,ori,False,d)[0] if isPoly(a) and isPoly(b): return (calcmulPoly([a,'*',b],'?'),'^1') return ([a],'*',[b]) def inExpression(exp,func): for t in exp: if not isPoly(t): if func(t) or inExpression(t[0],func) or inExpression(t[2],func): return True return False def intPower(exp): base = exp[0] pow = exp[2][0][0][0] if not pow: ret = [({0:1},'^1')] else: ret = base for i in range(pow-1): ret = calcmul([(ret,'*',base)],'?',False,None,False,[({0:0},'^1')]) return ret def calcAdd(s,p,way,tp,show,d): cont = True while cont: for i in range(len(s)): if isPoly(s[i]) and isPoly(s[-1]) and i!=len(s)-1: for a in s[i][0]: if a not in s[-1][0]: s[-1][0][a] = s[i][0][a] else: s[-1][0][a]+=s[i][0][a] s = s[:i]+s[i+1:] break elif isPoly(s[i]) and not isPoly(s[-1]): s.append(s[i]) s = s[:i]+s[i+1:] break if i==len(s)-1: cont = False if isPoly(s[-1]): s[-1]=(dict(sorted(s[-1][0].items(),reverse=True)),'^1') if show and way: sd('('+stringifyer(s,p)+')'+('/('+stringifyer(d,p)+')' if d!=[({0:1},'^1')] else '')+'=0',p,tp,True) return s def calcmulPoly(s, p): pow = {} for a in s[0][0]: for b in s[2][0]: x = str(fix(complex(s[0][0][a])*complex(s[2][0][b]))) i = a+b if pow.get(i)==None: pow[i] = ['0'] pow[i].append(x) for i in pow: pow[i] = eval('+'.join(pow[i])) return dict(sorted(pow.items(),reverse=True)) def isPoly(exp): return exp[1]=='^1' def isMul(exp): return '*' in str(exp) def isIntPower(tup): return tup[1]=='^' and isPoly(tup[2][0]) and len(tup[2][0][0])==1 and 0 in tup[2][0][0].keys() def calc(s,p,strBack): ans = [] s = innerDiv(s.replace('÷','/')) if '/' in s: s = splitChar(calcdiv(s,p),'/') ans.append((calc(s[0],p,False),'/',calc(s[1],p,False))) return ans if not s: return [] s = remUns(s.replace('÷','/'),True) s = splitChar(s,'+') ne = [] for i in range(len(s)): s[i]=remUns(s[i],True) g = {} try: g = calcPoly([s[i]],p) if all([x>=0 and x%1==0 for x in g]): ne.append(s[i]) continue except: pass parts = operationSplit(s[i],p) op = parts[1] ans.append((calc(parts[0],p,False),op,calc(parts[2],p,False))) if list(set(ne)) != []: ans.append((calcPoly(ne,p),'^1')) if strBack: return stringifyer(ans,p) return ans def operationSplit(s,p): s = innerDiv(s) if unnecesog(s) and s[0]=='(': return operationSplit(s[1:-1],p) if '/' in s: ret = splitChar(calcdiv(s,p),'/') ret[0],ret[1] = remUns(ret[0],True),remUns(ret[1],True) return (ret[0],'/',ret[1]) mulSpl = splitChar(s,'*') if len(mulSpl)>1: return [mulSpl[0],'*','*'.join(mulSpl[1:])] expSpl = splitChar(s,'^') if len(expSpl)>1: return [expSpl[0],'^','^'.join(expSpl[1:])] start, end = s.index('('), len(s)-1-s[::-1].index(')')-1 return ['',s[:s.index('(')],s[s.index('(')+1:-1]] def innerDiv(s): actions = '+-*/(' for i in range(1, len(s)): if s[i]=='(' and s[i-1] not in actions: s=rplc(s,i,compSog(s,i),s[i:compSog(s,i)+1].replace('/','÷'),'?') return s def stringifyer(s, p): string = '' for tu in range(len(s)): if tu and 1: string += '+' if s[tu][1] == '^1': if s[tu][0]: string += dictToStr(s[tu][0],p) elif s[tu][1][0] in '*/^': if len(s[tu][0])==1 and (s[tu][0][0][1]!='^1' or len(s[tu][0][0][0])<=1) and (s[tu][1][0]!='^' or s[tu][0][0][1] not in '*/'): string += stringifyer(s[tu][0],p) else: string += '(' + stringifyer(s[tu][0],p) + ')' string += s[tu][1] if len(s[tu][2])==1 and (s[tu][2][0][1]!='^1' or len(s[tu][2][0][0])<=1) and (s[tu][1][0]!='^' or s[tu][2][0][1] not in '*/') and (s[tu][1][0]!='/' or s[tu][2][0][1] not in '*/'): string += stringifyer(s[tu][2],p) else: string += '(' + stringifyer(s[tu][2],p) + ')' elif s[tu][1][0] == '!': string += '('+stringifyer(s[tu][0],p)+')' else: string += s[tu][1]+'('+stringifyer(s[tu][2],p)+')' return string or '0' def complexBrackets(s): try: s = complex(s.replace('i','j')[1:-1]) return True except: return False def noSograim(s,p): for i in range(len(s)): if s[i]=='(': li = compSog(s,i) if complexBrackets(s[i:li+1]): if li)'+chr(8805)+chr(8804) and (sog or mbn) and not level: return p-id if s[p] == "(": sog = True level+=id if s[p] == ")": level-=id p += id if p==-1: return 0 if p==len(s): return len(s)-1 def rplc(strn, s, e, ns, p, way=False, tp=None, showDenom = False, d = '1'): x = strn[:s] + ns + strn[e+1:] if way: if not showDenom or remUns(d)=='1' or remUns(d)=='(1)': sd(x+'=0', p, tp, True) else: sd('('+x+')/('+d+')=',p,tp,True) return x def splt(s,i): return [s[:i],s[i+1:]] def calcdiv(s, p, way = False, tp = None): if not '/' in s: return s+'/1' s = organizeND(s, p, way, tp) if len(splitChar(s, '+'))>1 and '/' in s: s = mechmesh(s,p) if way: sd(s+' = 0', p, tp, True) swdi = '' if len(splitChar(s,')^'))>1 and s.count('/')==1: s = denomPower(s) swdi = swapdiv(s) if way: sd(s+' = 0', p, tp, True) return swdi def denomPower(s): s = remUns(s) s,pow = splitChar(s,')^') n,d = splitChar(s[1:],'/') return '(('+n+'^'+pow+')/('+d+'^'+pow+'))' def changeND(info_s, s, start, sog=False): i = start level = 0 if s[i]=='(': level+=1 while sog and (not(s[i-1]==')' and not level) or not i ): info_s[i]='n'*(info_s[i]=='d')+'d'*(info_s[i]=='n') if s[i]=='(' and i!=start: level+=1 if s[i]==')': level-=1 i+=1 if not sog: for j in range(start,len(s)): if s[j] in '+' or j==len(s)-1: x=j break for j in range(start, j+1): info_s[j]='n'*(info_s[j]=='d')+'d'*(info_s[j]=='n') return info_s def mechmesh(s,p): if not '/' in s: return s if unnecesog(s): s = s[1:-1] s = splitChar(s, '+') for i in range(len(s)): if rightform(s[i]) and (len(s[i].split('/'))>2 or ('/' in s[i] and len(splitChar(s[i],'*'))>1)): s[i] = swapdiv(s[i]) if len(splitChar(s[i],')^'))>1 and '/' in s[i]: s[i] = denomPower(s[i]) if '/' in s[i]: s[i] = remUns(s[i],True) s[i] = splitChar(s[i],'/') else: s[i] = [s[i],'(1)'] ret = lcd(s, p) # fix in ver 7. ret = '('+remUns(ret)+')' return ret.replace('*(1)','').replace('(1)*','') def lcd(mam, p): lm = [] #goodnt = {} for i in range(len(mam)): if not mam[i][1] in lm: lm.append(mam[i][1]) #goodnt[i] = 0 elif not mam[i][1] in lm and False: l = ratioIn(mam[i][1],lm,p)[1] if not l in lm: lm.append(str(fix(l))) #goodnt[i] = str(l) #else: #goodnt[i] = 0 #add forbidden denominators for each mam. ret = '((' for i in range(len(mam)): if len(ret)!=2: ret+='+' ret+=mam[i][0] for j in range(len(lm)): #cond = compRatio(sograim(mam[i][1],p, False, False, None)[0][0][0],sograim(lm[j],p, False, False, None)[0][0][0]) and False #fix. sin(x)? if lm[j]!=mam[i][1]: ret+='*'+lm[j] ret+=')/(' y = len(ret) for i in range(len(lm)): if len(ret)!=y: ret+='*' ret+=lm[i] ret+='))' return ret def ratioIn(mech, used, p): mechR = sograim(mech, p, False, False, None)[0][0][0] maxRat = 0 for i in range(len(used)): rat = sograim(used[i],p, False, False, None)[0][0][0] if max(list(rat.keys()))>maxRat: maxRat = max(list(rat.keys())) if sorted(list(mechR.keys()))!=sorted(list(rat.keys())): continue ratio = compRatio(mechR,rat) if not ratio[0]: continue return True,ratio[1] return False,0 def compRatio(mech, rat): if list(mech.keys())==[0] and list(rat.keys())==[0] and not mech[list(mech.keys())[0]]==rat[list(mech.keys())[0]] or sorted(list(mech.keys()))!=sorted(list(rat.keys())): return False,0 if not list(mech.keys())[0] in list(rat.keys()) or not list(rat.keys())[0] in list(mech.keys()): return False,0 ratio = mech[list(mech.keys())[0]]/rat[list(mech.keys())[0]] for x in list(mech.keys())[1:]: if not x in list(rat.keys()): return False,0 if not mech[x]/rat[x] == ratio: return False,0 return True,fix(ratio) def organizeND(s, p, way = False, tp = None): cont = True while cont: for l in range(len(s)): if l == len(s)-1: cont = False if s[l]==')': f = fs(s,l,-1) curr = s[f+1:l] if rightform(curr) and (len(curr.split('/'))>2 or ('/' in curr and len(splitChar(curr,'*'))>1)): r = swapdiv(curr) s = rplc(s,f,l,'('+r+')', p) elif not rightform(curr): #'/' in curr and len(splitChar(curr,'+'))>1: r = mechmesh(curr,p) s = rplc(s,f,l,r,p) elif len(splitChar(curr,')^'))>1 and curr.count('/')==1: r = denomPower(curr) s = rplc(s,f,l,r,p) else: continue if way: sd(s+'=0', p, tp, True) break return s def rightform(s): s = remUns(s) cond = True for i in range(len(s)): if s[i]=='(': curr = s[i+1:compSog(s,i)] if ('/' in curr and len(splitChar(curr,'+'))>1): cond = False return cond and not ('/' in s and len(splitChar(s,'+'))>1) def compSog(s,i): level = 0 for b in range(i,len(s)): if s[b]=='(': level+=1 if s[b]==')': level-=1 if not level: return b return len(s)-1 def splitChar(s, ch): level = 0 ret = [] start = 0 for end in range(len(s)+1-len(ch)): if s[end]=='(': level+=1 if s[end]==')': level-=1 if s[end:end+len(ch)]==ch and not level: ret.append(s[start:end]) start = end+len(ch) if end==len(s)-len(ch) and not level: ret.append(s[start:end+len(ch)]) return ret def swapdiv(s): if unnecesog(s): s = s[1:-1] info_s = ['n']*(len(s)) for i in range(len(s)): if s[i]=='/': info_s[i] = 'c' if i+1'+chr(8804)+chr(8805): sign = ch break if p == '?': eq = eq.split(sign) eq[0], eq[1] = str(fix(eval(eq[0].replace('^','**')))), str(fix(eval(eq[1].replace('^','**')))) eq = sign.join(eq) if way: sd(eq, p, tp, True) eq = eq.replace(chr(8804),'<=').replace(chr(8805),'>=') if show: sd(str(eval(eq)), p, tp, True) return [str(eval(eq))] if way: #sd('-'*len(tp[-1]),p,tp,False) sd(eq.replace(sign,'='),p,tp,True) eq = moveHandSides(eq, sign)[0] dots = sorted(map(float,filter(lambda s: 'i' not in s and 'A' not in s, equality(eq+'=0',p,way,way,tp,ne,False)+list(ne)))) if way: sd('-'*len(tp[-1]),p,tp,False) area = [] for i in range(len(dots)): if not i: area.append(place(eq,p,str(fix(dots[i]-1)))>0) else: area.append(place(eq,p,str(fix((dots[i-1]+dots[i])/2)))>0) if i == len(dots)-1: area.append(place(eq,p,str(fix(dots[i]+1)))>0) sol = [] for i in range(len(area)): if sign in '<'+chr(8804) and not area[i] or sign in '>'+chr(8805) and area[i]: if not i: if sign in chr(8804)+chr(8805) and str(dots[i]) not in ne: sol.append(p+' '+chr(8804)+' '+str(fix(dots[i]))) else: sol.append(p+' < '+str(fix(dots[i]))) elif i == len(area)-1: if sign in chr(8804)+chr(8805) and str(dots[i-1]) not in ne: sol.append(p+' '+chr(8805)+' '+str(fix(dots[i-1]))) else: sol.append(p+' > '+str(fix(dots[i-1]))) else: if sign not in chr(8804)+chr(8805): sol.append(str(fix(dots[i-1]))+' < '+p+' < '+str(fix(dots[i]))) else: build = str(fix(dots[i-1]))+' ' if str(fix(dots[i-1])) not in ne: build += chr(8804) else: build += '<' build += ' '+p+' ' if str(fix(dots[i])) not in ne: build += chr(8804) else: build += '<' build += ' '+str(fix(dots[i])) sol.append(build) if not len(sol): sol.append('No Solution') sol = ' or '.join(sol) if show: sd(sol,p,tp,False) return sol def place(eq, p, toPlace): from re import search, match mat = search(r'/[0-9]+'+p, eq) while mat: s = mat.span() eq = eq[:s[0]+1]+'('+eq[s[0]+1:s[1]]+')'+eq[s[1]:] mat = search(r'/[0-9]+'+p, eq) eq = eq.replace(p, '('+toPlace+')').replace('^','**') cont = True while cont: for i in range(len(eq)-2): if eq[i] in '0123456789' and eq[i+1]=='(': eq = eq[:i+1]+'*'+eq[i+1:] break if i == len(eq)-3: cont = False break return fix(eval(eq)) def clear(): __import__('os').system('cls' if __import__('platform').system()=='Windows' else 'clear') def run(): while True: inp = input() clear() solve(inp, True, True) solve(input(), True, True)

Super Equation Solver