Trac #18084: Fix bad library uses of var()

Sage library code should '''not''' use `var()`!

URL: http://trac.sagemath.org/18084
Reported by: jdemeyer
Ticket author(s): Jeroen Demeyer
Reviewer(s): Ralf Stephan, Karl-Dieter Crisman

Author: Release Manager

src/sage/calculus/desolvers.py

@@ -1188,12 +1188,12 @@ def desolve_rk4(de, dvar, ics=None, ivar=None, end_points=None, step=0.1, output
         ivar = ivars[0]
 
     if not is_SymbolicVariable(dvar):
-        from sage.calculus.var import var
+        from sage.symbolic.ring import SR
         from sage.calculus.all import diff
         from sage.symbolic.relation import solve
         if is_SymbolicEquation(de):
             de = de.lhs() - de.rhs()
-        dummy_dvar=var('dummy_dvar')
+        dummy_dvar = SR.var('dummy_dvar')
         # consider to add warning if the solution is not unique
         de=solve(de,diff(dvar,ivar),solution_dict=True)
         if len(de) != 1:
@@ -1493,12 +1493,12 @@ def desolve_odeint(des, ics, times, dvars, ivar=None, compute_jac=False, args=()
         if len(ivars)==1:
             ivar = ivars.pop()
         elif not ivars:
-            from sage.symbolic.ring import var
             try:
                 safe_names = [ 't_' + str(dvar) for dvar in dvars ]
             except TypeError:  # not iterable
                 safe_names = [ 't_' + str(dvars) ]
-            ivar = map(var, safe_names)
+            from sage.symbolic.ring import SR
+            ivar = [SR.var(name) for name in safe_names]
         else:
             raise ValueError("Unable to determine independent variable, please specify.")
 

src/sage/calculus/var.pyx

@@ -7,22 +7,23 @@ def var(*args, **kwds):
 
     INPUT:
 
-    - ``args`` - A single string ``var('x y')``, a list of strings
+    - ``args`` -- A single string ``var('x y')``, a list of strings
       ``var(['x','y'])``, or multiple strings ``var('x', 'y')``. A
       single string can be either a single variable name, or a space
       or comma separated list of variable names. In a list or tuple of
       strings, each entry is one variable. If multiple arguments are
       specified, each argument is taken to be one variable. Spaces
       before or after variable names are ignored.
 
-    - ``kwds`` - keyword arguments can be given to specify domain and
+    - ``kwds`` -- keyword arguments can be given to specify domain and
       custom latex_name for variables. See EXAMPLES for usage.
 
     .. note::
 
        The new variable is both returned and automatically injected
-       into the global namespace. If you need symbolic variable in
-       library code, it is better to use either SR.var() or SR.symbol().
+       into the global namespace. If you need a symbolic variable in
+       library code, you must use either ``SR.var()``
+       or ``SR.symbol()``.
 
     OUTPUT:
 

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

@@ -231,7 +231,6 @@ def interact(self, fig_size=1, circular=True):
         from sage.plot.plot import EMBEDDED_MODE
         from sagenb.notebook.interact import interact, selector
         from sage.misc.all import html,latex
-        from sage.all import var
 
         if not EMBEDDED_MODE:
             return "The interactive mode only runs in the Sage notebook."
@@ -269,8 +268,7 @@ def player(k=selector(values=range(self._n),nrows = 1,label='Mutate at: '), show
                     html( "Cluster variables:" )
                     table = "$\\begin{align*}\n"
                     for i in xrange(self._n):
-                        v = var('v%s'%i)
-                        table += "\t" + latex( v ) + " &= " + latex( self._cluster[i] ) + "\\\\ \\\\\n"
+                        table += "\tv_{%s} &= "%i + latex( self._cluster[i] ) + "\\\\ \\\\\n"
                     table += "\\end{align*}$"
                     html( "$ $" )
                     html( table )

src/sage/combinat/finite_state_machine.py

@@ -843,13 +843,13 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.real_mpfr import RR
 from sage.symbolic.ring import SR
-from sage.calculus.var import var
 from sage.misc.cachefunc import cached_function
 from sage.misc.latex import latex
 from sage.misc.misc import verbose
 from sage.misc.misc import srange
 from sage.functions.trig import cos, sin, atan2
 from sage.symbolic.constants import pi
+from sage.symbolic.ring import SR
 
 from copy import copy
 from copy import deepcopy
@@ -4858,7 +4858,7 @@ def adjacency_matrix(self, input=None,
 
         """
         def default_function(transitions):
-            var('x')
+            x = SR.var('x')
             return x**sum(transition.word_out)
 
         if entry is None:

src/sage/combinat/ribbon_tableau.py

@@ -698,9 +698,9 @@ def spin_polynomial(part, weight, length):
         sage: spin_polynomial([[6]*6, [3,3]], [4,4,2], 3)
         3*t^9 + 5*t^8 + 9*t^7 + 6*t^6 + 3*t^5
     """
-    from sage.symbolic.ring import var
+    from sage.symbolic.ring import SR
     sp = spin_polynomial_square(part,weight,length)
-    t = var('t')
+    t = SR.var('t')
     c = sp.coefficients(sparse=False)
     return sum([c[i]*t**(QQ(i)/2) for i in range(len(c))])
 

src/sage/combinat/sf/hall_littlewood.py

@@ -25,7 +25,6 @@
 #*****************************************************************************
 
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.calculus.var import var
 from sage.libs.symmetrica.all import hall_littlewood
 import sfa
 import sage.combinat.partition
@@ -90,8 +89,6 @@ def __init__(self, Sym, t = 't'):
             sage: TestSuite(HL).run()
         """
         self._sym = Sym
-        if not (t in Sym.base_ring() or var(t) in Sym.base_ring()):
-            raise ValueError("parameter t must be in the base ring")
         self.t = Sym.base_ring()(t)
         self._name_suffix = ""
         if str(t) !='t':

src/sage/combinat/sf/jack.py

@@ -35,7 +35,6 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.calculus.var import var
 import sage.categories.all
 from sage.rings.all import Integer, gcd, lcm, QQ
 from sage.rings.fraction_field import is_FractionField
@@ -70,8 +69,6 @@ def __init__(self, Sym, t='t'):
             Jack polynomials with t=1 over Rational Field
         """
         self._sym = Sym
-        if not (t in Sym.base_ring() or var(t) in Sym.base_ring()):
-            raise ValueError("parameter t must be in the base ring")
         self.t = Sym.base_ring()(t)
         self._name_suffix = ""
         if str(t) !='t':

src/sage/combinat/sf/llt.py

@@ -30,7 +30,6 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.calculus.var import var
 import sfa
 import sage.combinat.ribbon_tableau as ribbon_tableau
 import sage.combinat.skew_partition
@@ -121,8 +120,6 @@ def __init__(self, Sym, k, t='t'):
         self._k = k
         self._sym = Sym
         self._name = "level %s LLT polynomials"%self._k
-        if not (t in Sym.base_ring() or var(t) in Sym.base_ring()):
-            raise ValueError("parameter t must be in the base ring")
         self.t = Sym.base_ring()(t)
         self._name_suffix = ""
         if str(t) !='t':

src/sage/combinat/sf/macdonald.py

@@ -46,7 +46,6 @@
 #*****************************************************************************
 
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.calculus.var import var
 from sage.categories.morphism import SetMorphism
 from sage.categories.homset import Hom
 import sfa
@@ -116,15 +115,11 @@ def __init__(self, Sym, q='q', t='t'):
             sage: Sym = SymmetricFunctions(FractionField(QQ['t'])).macdonald()
             Traceback (most recent call last):
             ...
-            ValueError: parameter q must be in the base ring
+            TypeError: unable to evaluate 'q' in Fraction Field of Univariate Polynomial Ring in t over Rational Field
         """
         self._sym = Sym
         self._s = Sym.s()
-        if not (q in Sym.base_ring() or var(q) in Sym.base_ring()):
-            raise ValueError("parameter q must be in the base ring")
         self.q = Sym.base_ring()(q)
-        if not (t in Sym.base_ring() or var(t) in Sym.base_ring()):
-            raise ValueError("parameter t must be in the base ring")
         self.t = Sym.base_ring()(t)
         self._name_suffix = ""
         if str(q) !='q':

src/sage/crypto/lwe.py

@@ -96,7 +96,6 @@
    2013/164. 2013.  2013/164. http://eprint.iacr.org/2013/164
 """
 
-from sage.calculus.var import var
 from sage.functions.log import exp, log
 from sage.functions.other import sqrt, floor, ceil
 from sage.misc.functional import cyclotomic_polynomial
@@ -111,7 +110,7 @@
 from sage.structure.element import parent
 from sage.structure.sage_object import SageObject
 from sage.symbolic.constants import pi
-
+from sage.symbolic.ring import SR
 from sage.stats.distributions.discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
 from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
 
@@ -428,7 +427,7 @@ def __init__(self, n, delta=0.01, m=None):
         #            2*n*(log(c)+(1-c**2)/2) == -40*log(2)
         #              2*n*log(c)+n*(1-c**2) == -40*log(2)
         #  2*n*log(c)+n*(1-c**2) + 40*log(2) == 0
-        c = var('c')
+        c = SR.var('c')
         c = find_root(2*n*log(c)+n*(1-c**2) + 40*log(2) == 0, 1, 10)
         # Upper bound on s**2/t
         s_t_bound = (sqrt(2) * pi / c / sqrt(2*n*log(2/delta))).n()
@@ -627,7 +626,7 @@ def __init__(self, N, delta=0.01, m=None):
             m = 3*n
         # Find c>=1 such that c*exp((1-c**2)/2))**(2*n) == 2**-40
         #  i.e c>=1 such that 2*n*log(c)+n*(1-c**2) + 40*log(2) == 0
-        c = var('c')
+        c = SR.var('c')
         c = find_root(2*n*log(c)+n*(1-c**2) + 40*log(2) == 0, 1, 10)
         # Upper bound on s**2/t
         s_t_bound = (sqrt(2) * pi / c / sqrt(2*n*log(2/delta))).n()
@@ -821,4 +820,4 @@ def balance_sample(s, q=None):
     if scalar:
         return vector(ZZ, len(a), [e if e <= q2 else e-q for e in a]), c[0] if c[0] <= q2 else c[0]-q
     else:
-        return vector(ZZ, len(a), [e if e <= q2 else e-q for e in a]), vector(ZZ, len(c), [e if e <= q2 else e-q for e in c])
+        return vector(ZZ, len(a), [e if e <= q2 else e-q for e in a]), vector(ZZ, len(c), [e if e <= q2 else e-q for e in c])

src/sage/functions/piecewise.py

@@ -76,7 +76,6 @@
 from sage.symbolic.assumptions import assume, forget
 
 from sage.calculus.calculus import SR, maxima
-from sage.calculus.all import var
 
 def piecewise(list_of_pairs, var=None):
     """
@@ -732,7 +731,7 @@ def default_variable(self):
                 # pass if fun is lambda function
                 pass
         # default to x
-        v = var('x')
+        v = SR.var('x')
         self.__default_value = v
         return v
 
@@ -1114,7 +1113,7 @@ def fourier_series_cosine_coefficient(self,n,L):
             -3/5/pi
         """
         from sage.all import cos, pi
-        x = var('x')
+        x = SR.var('x')
         result = sum([(f(x)*cos(pi*x*n/L)/L).integrate(x, a, b)
                       for (a,b), f in self.list()])
         if is_Expression(result):
@@ -1147,7 +1146,7 @@ def fourier_series_sine_coefficient(self,n,L):
             0
         """
         from sage.all import sin, pi
-        x = var('x')
+        x = SR.var('x')
         result = sum([(f(x)*sin(pi*x*n/L)/L).integrate(x, a, b)
                       for (a,b), f in self.list()])
         if is_Expression(result):
@@ -1515,7 +1514,7 @@ def cosine_series_coefficient(self,n,L):
 
         """
         from sage.all import cos, pi
-        x = var('x')
+        x = SR.var('x')
         result = sum([(2*f(x)*cos(pi*x*n/L)/L).integrate(x, a, b)
                       for (a,b), f in self.list()])
         if is_Expression(result):
@@ -1556,7 +1555,7 @@ def sine_series_coefficient(self,n,L):
             4/3/pi
         """
         from sage.all import sin, pi
-        x = var('x')
+        x = SR.var('x')
         result = sum([(2*f(x)*sin(pi*x*n/L)/L).integrate(x, a, b)
                       for (a,b), f in self.list()])
         if is_Expression(result):
@@ -1606,8 +1605,8 @@ def laplace(self, x='x', s='t'):
             (s + 1)*e^(-s)/s^2 + 2*e^(-s)/s - 1/s^2
         """
         from sage.all import assume, exp, forget
-        x = var(x)
-        s = var(s)
+        x = SR.var(x)
+        s = SR.var(s)
         assume(s>0)
         result =  sum([(SR(f)*exp(-s*x)).integral(x,a,b)
                        for (a,b),f in self.list()])

src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py

@@ -55,7 +55,7 @@
 from sage.functions.trig import sin, cos, arccos
 from sage.functions.log import exp
 from sage.functions.hyperbolic import sinh, cosh, arcsinh
-
+from sage.symbolic.ring import SR
 from sage.geometry.hyperbolic_space.hyperbolic_constants import EPSILON
 
 from sage.misc.lazy_import import lazy_import
@@ -816,9 +816,8 @@ def show(self, boundary=True, **options):
             if abs(theta1 - theta2) < EPSILON:
                 theta2 += pi
             [theta1, theta2] = sorted([theta1, theta2])
-            from sage.calculus.var import var
             from sage.plot.plot import parametric_plot
-            x = var('x')
+            x = SR.var('x')
             pic = parametric_plot((radius*cos(x) + real(center),
                                    radius*sin(x) + imag(center)),
                                   (x, theta1, theta2), **opts)
@@ -1250,9 +1249,8 @@ def show(self, boundary=True, **options):
             theta2 = CC(end_2 - center).arg()
             if theta2 < theta1:
                 theta1, theta2 = theta2, theta1
-            from sage.calculus.var import var
             from sage.plot.plot import parametric_plot
-            x = var('x')
+            x = SR.var('x')
             mid = (theta1 + theta2)/2.0
             if (radius*cos(mid) + real(center))**2 + \
                (radius*sin(mid) + imag(center))**2 > 1.0:
@@ -1341,8 +1339,9 @@ def show(self, show_hyperboloid=True, **graphics_options):
             sage: g.show()
             Graphics3d Object
         """
-        from sage.calculus.var import var
-        (x,y,z) = var('x,y,z')
+        x = SR.var('x')
+        y = SR.var('y')
+        z = SR.var('z')
         opts = self.graphics_options()
         opts.update(graphics_options)
         v1,u2 = [vector(k.coordinates()) for k in self.endpoints()]

src/sage/geometry/hyperbolic_space/hyperbolic_model.py

@@ -1476,11 +1476,12 @@ def get_background_graphic(self, **bdry_options):
             sage: H = HyperbolicPlane().HM().get_background_graphic()
         """
         from sage.plot.plot3d.all import plot3d
-        from sage.all import var
+        from sage.all import SR
         hyperboloid_opacity = bdry_options.get('hyperboloid_opacity', .1)
         z_height = bdry_options.get('z_height', 7.0)
         x_max = sqrt((z_height ** 2 - 1) / 2.0)
-        (x, y) = var('x,y')
+        x = SR.var('x')
+        y = SR.var('y')
         return plot3d((1 + x ** 2 + y ** 2).sqrt(),
                       (x, -x_max, x_max), (y,-x_max, x_max),
                       opacity=hyperboloid_opacity, **bdry_options)

src/sage/geometry/riemannian_manifolds/parametrized_surface3d.py

@@ -1505,12 +1505,12 @@ def _create_geodesic_ode_system(self):
 
         """
         from sage.ext.fast_eval import fast_float
-        from sage.calculus.var import var
         from sage.gsl.ode import ode_solver
 
         u1 = self.variables[1]
         u2 = self.variables[2]
-        v1, v2 = var('v1, v2', domain='real')
+        v1 = SR.var('v1', domain='real')
+        v2 = SR.var('v2', domain='real')
 
         C = self.connection_coefficients()
 
@@ -1618,12 +1618,12 @@ def _create_pt_ode_system(self, curve, t):
         """
 
         from sage.ext.fast_eval import fast_float
-        from sage.calculus.var import var
         from sage.gsl.ode import ode_solver
 
         u1 = self.variables[1]
         u2 = self.variables[2]
-        v1, v2 = var('v1, v2', domain='real')
+        v1 = SR.var('v1', domain='real')
+        v2 = SR.var('v2', domain='real')
 
         du1 = diff(curve[0], t)
         du2 = diff(curve[1], t)