# HG changeset patch # User André Apitzsch # Date 1336896459 -7200 # Node ID f83aa160d6e5d28c6351a071032c8fa3502b6661 # Parent aa148c3c0d7b06fd049b9e845eebeda2421d32bf trac 12907: replace some deprecated python functions in sage/calculus diff --git a/sage/calculus/calculus.py b/sage/calculus/calculus.py --- a/sage/calculus/calculus.py +++ b/sage/calculus/calculus.py @@ -545,10 +545,10 @@ if isinstance(v, str): v = var(v) else: - raise TypeError, "need a summation variable" + raise TypeError("need a summation variable") if v in SR(a).variables() or v in SR(b).variables(): - raise ValueError, "summation limits must not depend on the summation variable" + raise ValueError("summation limits must not depend on the summation variable") if algorithm == 'maxima': return maxima.sr_sum(expression,v,a,b) @@ -557,12 +557,12 @@ try: sum = "Sum[%s, {%s, %s, %s}]" % tuple([repr(expr._mathematica_()) for expr in (expression, v, a, b)]) except TypeError: - raise ValueError, "Mathematica cannot make sense of input" + raise ValueError("Mathematica cannot make sense of input") from sage.interfaces.mathematica import mathematica try: result = mathematica(sum) except TypeError: - raise ValueError, "Mathematica cannot make sense of: %s" % sum + raise ValueError("Mathematica cannot make sense of: %s" % sum) return result.sage() elif algorithm == 'maple': @@ -571,7 +571,7 @@ try: result = maple(sum).simplify() except TypeError: - raise ValueError, "Maple cannot make sense of: %s" % sum + raise ValueError("Maple cannot make sense of: %s" % sum) return result.sage() elif algorithm == 'giac': @@ -580,11 +580,11 @@ try: result = giac(sum) except TypeError: - raise ValueError, "Giac cannot make sense of: %s" % sum + raise ValueError("Giac cannot make sense of: %s" % sum) return result.sage() else: - raise ValueError, "unknown algorithm: %s" % algorithm + raise ValueError("unknown algorithm: %s" % algorithm) def nintegral(ex, x, a, b, desired_relative_error='1e-8', @@ -716,17 +716,17 @@ v = ex._maxima_().quad_qags(x, a, b, epsrel=desired_relative_error, limit=maximum_num_subintervals) - except TypeError, err: + except TypeError as err: if "ERROR" in str(err): - raise ValueError, "Maxima (via quadpack) cannot compute the integral" + raise ValueError("Maxima (via quadpack) cannot compute the integral") else: - raise TypeError, err + raise TypeError(err) # Maxima returns unevaluated expressions when the underlying library fails # to perfom numerical integration. See: # http://www.math.utexas.edu/pipermail/maxima/2008/012975.html if 'quad_qags' in str(v): - raise ValueError, "Maxima (via quadpack) cannot compute the integral" + raise ValueError("Maxima (via quadpack) cannot compute the integral") return float(v[0]), float(v[1]), Integer(v[2]), Integer(v[3]) @@ -945,16 +945,16 @@ elif epsilon and error < epsilon: return g elif algorithm is not None: - raise NotImplementedError, "Could not prove minimal polynomial %s (epsilon %s)" % (g, RR(error).str(no_sci=False)) + raise NotImplementedError("Could not prove minimal polynomial %s (epsilon %s)" % (g, RR(error).str(no_sci=False))) if algorithm is not None: - raise ValueError, "Could not find minimal polynomial (%s bits, degree %s)." % (bits, degree) + raise ValueError("Could not find minimal polynomial (%s bits, degree %s)." % (bits, degree)) if algorithm is None or algorithm == 'algebraic': from sage.rings.all import QQbar return QQ[var](QQbar(ex).minpoly()) - raise ValueError, "Unknown algorithm: %s" % algorithm + raise ValueError("Unknown algorithm: %s" % algorithm) ################################################################### @@ -1145,7 +1145,7 @@ ex = SR(ex) if len(argv) != 1: - raise ValueError, "call the limit function like this, e.g. limit(expr, x=2)." + raise ValueError("call the limit function like this, e.g. limit(expr, x=2).") else: k = argv.keys()[0] v = var(k) @@ -1183,7 +1183,7 @@ import sympy l = sympy.limit(ex._sympy_(), v._sympy_(), a._sympy_()) else: - raise NotImplementedError, "sympy does not support one-sided limits" + raise NotImplementedError("sympy does not support one-sided limits") #return l.sage() return ex.parent()(l) @@ -1421,7 +1421,7 @@ kwds[str(c.lhs())]=c.rhs() else: if len(args) !=0: - raise TypeError,"at can take at most one argument, which must be a list" + raise TypeError("at can take at most one argument, which must be a list") return ex.subs(**kwds) @@ -1675,7 +1675,7 @@ syms = sage.symbolic.pynac.symbol_table.get('maxima', {}).copy() if len(x) == 0: - raise RuntimeError, "invalid symbolic expression -- ''" + raise RuntimeError("invalid symbolic expression -- ''") maxima.set('_tmp_',x) # This is inefficient since it so rarely is needed: @@ -1748,7 +1748,7 @@ is_simplified = True return symbolic_expression_from_string(s, syms, accept_sequence=True) except SyntaxError: - raise TypeError, "unable to make sense of Maxima expression '%s' in Sage"%s + raise TypeError("unable to make sense of Maxima expression '%s' in Sage"%s) finally: is_simplified = False diff --git a/sage/calculus/desolvers.py b/sage/calculus/desolvers.py --- a/sage/calculus/desolvers.py +++ b/sage/calculus/desolvers.py @@ -86,14 +86,14 @@ - for a second-order boundary solution, specify initial and final ``x`` and ``y`` boundary conditions, i.e. write `[x_0, y(x_0), x_1, y(x_1)]`. - + - gives an error if the solution is not SymbolicEquation (as happens for example for Clairaut equation) - + - ``ivar`` - (optional) the independent variable (hereafter called x), which must be specified if there is more than one independent variable in the equation. - + - ``show_method`` - (optional) if true, then Sage returns pair ``[solution, method]``, where method is the string describing method which has been used to get solution (Maxima uses the @@ -124,7 +124,7 @@ sage: y = function('y', x) sage: desolve(diff(y,x) + y - 1, y) (c + e^x)*e^(-x) - + :: sage: f = desolve(diff(y,x) + y - 1, y, ics=[10,2]); f @@ -141,7 +141,6 @@ sage: de = diff(y,x,2) - y == x sage: desolve(de, y) k1*e^x + k2*e^(-x) - x - :: @@ -166,7 +165,7 @@ :: - sage: desolve(de, y, [0,1,pi/2,4]) + sage: desolve(de, y, [0,1,pi/2,4]) 4*sin(x) + cos(x) :: @@ -178,7 +177,7 @@ sage: desolve(diff(y,x)^2+x*diff(y,x)-y==0,y,contrib_ode=True,show_method=True) [[y(x) == c^2 + c*x, y(x) == -1/4*x^2], 'clairault'] - + For equations involving more variables we specify independent variable:: sage: a,b,c,n=var('a b c n') @@ -248,17 +247,17 @@ condition at x=0, since this point is singlar point of the equation. Anyway, if the solution should be bounded at x=0, then k2=0.:: - + sage: desolve(x^2*diff(y,x,x)+x*diff(y,x)+(x^2-4)*y==0,y) k1*bessel_j(2, x) + k2*bessel_y(2, x) - + Difficult ODE produces error:: sage: desolve(sqrt(y)*diff(y,x)+e^(y)+cos(x)-sin(x+y)==0,y) # not tested Traceback (click to the left for traceback) ... NotImplementedError, "Maxima was unable to solve this ODE. Consider to set option contrib_ode to True." - + Difficult ODE produces error - moreover, takes a long time :: sage: desolve(sqrt(y)*diff(y,x)+e^(y)+cos(x)-sin(x+y)==0,y,contrib_ode=True) # not tested @@ -269,7 +268,7 @@ [[y(x) == c + log(x), y(x) == c*e^x], 'factor'] :: - + sage: desolve(diff(y,x)==(x+y)^2,y,contrib_ode=True,show_method=True) [[[x == c - arctan(sqrt(t)), y(x) == -x - sqrt(t)], [x == c + arctan(sqrt(t)), y(x) == -x + sqrt(t)]], 'lagrange'] @@ -377,7 +376,7 @@ x :: - + sage: desolve( diff(y,x,x) == 0, y, [0,1,1]) x + 1 @@ -395,10 +394,9 @@ sage: x=var('x'); f=function('f',x); k=var('k'); assume(k>0) sage: desolve(diff(f,x,2)/f==k,f,ivar=x) k1*e^(sqrt(k)*x) + k2*e^(-sqrt(k)*x) - - + AUTHORS: - + - David Joyner (1-2006) - Robert Bradshaw (10-2008) @@ -409,7 +407,7 @@ if is_SymbolicEquation(de): de = de.lhs() - de.rhs() if is_SymbolicVariable(dvar): - raise ValueError, "You have to declare dependent variable as a function, eg. y=function('y',x)" + raise ValueError("You have to declare dependent variable as a function, eg. y=function('y',x)") # for backwards compatibility if isinstance(dvar, list): dvar, ivar = dvar @@ -417,10 +415,10 @@ ivars = de.variables() ivars = [t for t in ivars if t is not dvar] if len(ivars) != 1: - raise ValueError, "Unable to determine independent variable, please specify." + raise ValueError("Unable to determine independent variable, please specify.") ivar = ivars[0] def sanitize_var(exprs): - return exprs.replace("'"+dvar_str+"("+ivar_str+")",dvar_str) + return exprs.replace("'"+dvar_str+"("+ivar_str+")",dvar_str) de00 = de._maxima_() P = de00.parent() dvar_str=P(dvar.operator()).str() @@ -428,7 +426,7 @@ de00 = de00.str() de0 = sanitize_var(de00) ode_solver="ode2" - cmd="(TEMP:%s(%s,%s,%s), if TEMP=false then TEMP else substitute(%s=%s(%s),TEMP))"%(ode_solver,de0,dvar_str,ivar_str,dvar_str,dvar_str,ivar_str) + cmd="(TEMP:%s(%s,%s,%s), if TEMP=false then TEMP else substitute(%s=%s(%s),TEMP))"%(ode_solver,de0,dvar_str,ivar_str,dvar_str,dvar_str,ivar_str) # we produce string like this # ode2('diff(y,x,2)+2*'diff(y,x,1)+y-cos(x),y(x),x) soln = P(cmd) @@ -437,14 +435,14 @@ if contrib_ode: ode_solver="contrib_ode" P("load('contrib_ode)") - cmd="(TEMP:%s(%s,%s,%s), if TEMP=false then TEMP else substitute(%s=%s(%s),TEMP))"%(ode_solver,de0,dvar_str,ivar_str,dvar_str,dvar_str,ivar_str) + cmd="(TEMP:%s(%s,%s,%s), if TEMP=false then TEMP else substitute(%s=%s(%s),TEMP))"%(ode_solver,de0,dvar_str,ivar_str,dvar_str,dvar_str,ivar_str) # we produce string like this # (TEMP:contrib_ode(x*('diff(y,x,1))^2-(x*y+1)*'diff(y,x,1)+y,y,x), if TEMP=false then TEMP else substitute(y=y(x),TEMP)) soln = P(cmd) if str(soln).strip() == 'false': - raise NotImplementedError, "Maxima was unable to solve this ODE." + raise NotImplementedError("Maxima was unable to solve this ODE.") else: - raise NotImplementedError, "Maxima was unable to solve this ODE. Consider to set option contrib_ode to True." + raise NotImplementedError("Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.") if show_method: maxima_method=P("method") @@ -453,7 +451,7 @@ if not is_SymbolicEquation(soln.sage()): if not show_method: maxima_method=P("method") - raise NotImplementedError, "Unable to use initial condition for this equation (%s)."%(str(maxima_method).strip()) + raise NotImplementedError("Unable to use initial condition for this equation (%s)."%(str(maxima_method).strip())) if len(ics) == 2: tempic=(ivar==ics[0])._maxima_().str() tempic=tempic+","+(dvar==ics[1])._maxima_().str() @@ -480,7 +478,7 @@ # (TEMP:ic2(ode2('diff(y,x,2)+2*'diff(y,x,1)+y-cos(x),y,x),x=0,y=3,'diff(y,x)=1),substitute(y=y(x),TEMP)) soln=P(cmd) if str(soln).strip() == 'false': - raise NotImplementedError, "Maxima was unable to solve this IVP. Remove the initial condition to get the general solution." + raise NotImplementedError("Maxima was unable to solve this IVP. Remove the initial condition to get the general solution.") if len(ics) == 4: #fixed bc2 command from Maxima - we have to ensure that %k1, %k2 do not depend on variables, should be removed when fixed in Maxima P("bc2_sage(soln,xa,ya,xb,yb):=block([programmode:true,backsubst:true,singsolve:true,temp,%k1,%k2,TEMP_k], \ @@ -490,13 +488,13 @@ temp: maplist(lambda([zz], subst(zz,soln)),TEMP_k), \ if length(temp)=1 then return(first(temp)) else return(temp))") cmd="bc2_sage(%s(%s,%s,%s),%s,%s=%s,%s,%s=%s)"%(ode_solver,de00,dvar_str,ivar_str,P(ivar==ics[0]).str(),dvar_str,P(ics[1]).str(),P(ivar==ics[2]).str(),dvar_str,P(ics[3]).str()) - cmd="(TEMP:%s,substitute(%s=%s(%s),TEMP))"%(cmd,dvar_str,dvar_str,ivar_str) + cmd="(TEMP:%s,substitute(%s=%s(%s),TEMP))"%(cmd,dvar_str,dvar_str,ivar_str) cmd=sanitize_var(cmd) # we produce string like this # (TEMP:bc2(ode2('diff(y,x,2)+2*'diff(y,x,1)+y-cos(x),y,x),x=0,y=3,x=%pi/2,y=2),substitute(y=y(x),TEMP)) soln=P(cmd) if str(soln).strip() == 'false': - raise NotImplementedError, "Maxima was unable to solve this BVP. Remove the initial condition to get the general solution." + raise NotImplementedError("Maxima was unable to solve this BVP. Remove the initial condition to get the general solution.") soln=soln.sage() if is_SymbolicEquation(soln) and soln.lhs() == dvar: @@ -550,13 +548,12 @@ # #return maxima.eval(cmd) # return de0.desolve(vars[0]).rhs() - def desolve_laplace(de, dvar, ics=None, ivar=None): """ Solves an ODE using laplace transforms. Initials conditions are optional. INPUT: - + - ``de`` - a lambda expression representing the ODE (eg, de = diff(y,x,2) == diff(y,x)+sin(x)) @@ -647,7 +644,7 @@ if is_SymbolicEquation(de): de = de.lhs() - de.rhs() if is_SymbolicVariable(dvar): - raise ValueError, "You have to declare dependent variable as a function, eg. y=function('y',x)" + raise ValueError("You have to declare dependent variable as a function, eg. y=function('y',x)") # for backwards compatibility if isinstance(dvar, list): dvar, ivar = dvar @@ -655,7 +652,7 @@ ivars = de.variables() ivars = [t for t in ivars if t != dvar] if len(ivars) != 1: - raise ValueError, "Unable to determine independent variable, please specify." + raise ValueError("Unable to determine independent variable, please specify.") ivar = ivars[0] ## verbatim copy from desolve - end @@ -666,7 +663,7 @@ cmd = sanitize_var("desolve("+de0.str()+","+str(dvar)+")") soln=P(cmd).rhs() if str(soln).strip() == 'false': - raise NotImplementedError, "Maxima was unable to solve this ODE." + raise NotImplementedError("Maxima was unable to solve this ODE.") soln=soln.sage() if ics!=None: d = len(ics) @@ -679,7 +676,7 @@ """ Solves any size system of 1st order ODE's. Initials conditions are optional. - Onedimensional systems are passed to :meth:`desolve_laplace`. + Onedimensional systems are passed to :meth:`desolve_laplace`. INPUT: @@ -739,7 +736,7 @@ if ivar is None: ivars = ivars - set(vars) if len(ivars) != 1: - raise ValueError, "Unable to determine independent variable, please specify." + raise ValueError("Unable to determine independent variable, please specify.") ivar = list(ivars)[0] dvars = [v._maxima_() for v in vars] if ics is not None: @@ -748,7 +745,7 @@ dvar.atvalue(ivar==ivar_ic, ic) soln = dvars[0].parent().desolve(des, dvars) if str(soln).strip() == 'false': - raise NotImplementedError, "Maxima was unable to solve this system." + raise NotImplementedError("Maxima was unable to solve this system.") soln = list(soln) for i, sol in enumerate(soln): soln[i] = sol.sage() @@ -757,7 +754,6 @@ for dvar, ic in zip(dvars, ics[:1]): dvar.atvalue(ivar==ivar_ic, dvar) return soln - def desolve_system_strings(des,vars,ics=None): r""" @@ -822,7 +818,6 @@ sage: P2 = parametric_plot((solnx,solny),(0,1)) Now type show(P1), show(P2) to view these. - AUTHORS: @@ -918,13 +913,13 @@ - David Joyner """ if algorithm=="table": - print "%10s %20s %25s"%("x","y","h*f(x,y)") + print("%10s %20s %25s"%("x","y","h*f(x,y)")) n=int((1.0)*(x1-x0)/h) x00=x0; y00=y0 soln = [[x00,y00]] for i in range(n+1): if algorithm=="table": - print "%10r %20r %20r"%(x00,y00,h*f(x00,y00)) + print("%10r %20r %20r"%(x00,y00,h*f(x00,y00))) y00 = y00+h*f(x00,y00) x00=x00+h soln.append([x00,y00]) @@ -1012,13 +1007,13 @@ - David Joyner """ if algorithm=="table": - print "%10s %20s %25s %20s %20s"%("t", "x","h*f(t,x,y)","y", "h*g(t,x,y)") + print("%10s %20s %25s %20s %20s"%("t", "x","h*f(t,x,y)","y", "h*g(t,x,y)")) n=int((1.0)*(t1-t0)/h) t00 = t0; x00 = x0; y00 = y0 soln = [[t00,x00,y00]] for i in range(n+1): if algorithm=="table": - print "%10r %20r %25r %20r %20r"%(t00,x00,h*f(t00,x00,y00),y00,h*g(t00,x00,y00)) + print("%10r %20r %25r %20r %20r"%(t00,x00,h*f(t00,x00,y00),y00,h*g(t00,x00,y00))) x01 = x00 + h*f(t00,x00,y00) y00 = y00 + h*g(t00,x00,y00) x00 = x01 @@ -1082,12 +1077,12 @@ sage: from sage.calculus.desolvers import desolve_rk4_determine_bounds sage: desolve_rk4_determine_bounds([0,2],1) (0, 1) - + :: - sage: desolve_rk4_determine_bounds([0,2]) + sage: desolve_rk4_determine_bounds([0,2]) (0, 10) - + :: sage: desolve_rk4_determine_bounds([0,2],[-2]) @@ -1107,7 +1102,6 @@ return (min(ics[0],end_points[0]),max(ics[0],end_points[0])) else: return (min(ics[0],end_points[0]),max(ics[0],end_points[1])) - def desolve_rk4(de, dvar, ics=None, ivar=None, end_points=None, step=0.1, output='list', **kwds): """ @@ -1115,7 +1109,7 @@ equation. See also ``ode_solver``. INPUT: - + input is similar to ``desolve`` command. The differential equation can be written in a form close to the plot_slope_field or desolve command @@ -1179,7 +1173,7 @@ sage: x,y=var('x y') sage: P=desolve_rk4(y*(2-y),y,ics=[0,.1],ivar=x,output='slope_field',end_points=[-4,6],thickness=3) - + ALGORITHM: 4th order Runge-Kutta method. Wrapper for command ``rk`` in @@ -1191,13 +1185,13 @@ - Robert Marik (10-2009) """ if ics is None: - raise ValueError, "No initial conditions, specify with ics=[x0,y0]." + raise ValueError("No initial conditions, specify with ics=[x0,y0].") if ivar is None: ivars = de.variables() ivars = [t for t in ivars if t != dvar] if len(ivars) != 1: - raise ValueError, "Unable to determine independent variable, please specify." + raise ValueError("Unable to determine independent variable, please specify.") ivar = ivars[0] if not is_SymbolicVariable(dvar): @@ -1210,7 +1204,7 @@ # consider to add warning if the solution is not unique de=solve(de,diff(dvar,ivar),solution_dict=True) if len(de) != 1: - raise NotImplementedError, "Sorry, cannot find explicit formula for right-hand side of the ODE." + raise NotImplementedError("Sorry, cannot find explicit formula for right-hand side of the ODE.") de=de[0][diff(dvar,ivar)].subs(dvar==dummy_dvar) else: dummy_dvar=dvar @@ -1254,8 +1248,7 @@ if t