.. _core_module: ==== Core ==== sympify ------- .. module:: sympy.core.sympify .. autofunction:: sympify assumptions ----------- .. automodule:: sympy.core.assumptions cache ----- .. module:: sympy.core.cache .. autofunction:: __cacheit basic ----- .. module:: sympy.core.basic .. autoclass:: Basic :members: .. autoclass:: Atom :members: singleton --------- .. module:: sympy.core.singleton .. autoclass:: sympy.core.singleton.SingletonRegistry :members: .. autoclass:: Singleton :members: expr ---- .. module:: sympy.core.expr .. autoclass:: Expr :members: .. autoclass:: UnevaluatedExpr :members: .. autoclass:: AtomicExpr :members: symbol ------ .. module:: sympy.core.symbol .. autoclass:: Symbol :members: .. autoclass:: Wild :members: .. autoclass:: Dummy :members: .. autofunction:: symbols .. autofunction:: var numbers ------- .. module:: sympy.core.numbers .. autoclass:: Number :members: .. autoclass:: Float :members: .. autoclass:: Rational :members: .. autoclass:: Integer :members: .. autoclass:: AlgebraicNumber :members: .. automethod:: AlgebraicNumber.__new__ .. autoclass:: NumberSymbol :members: .. autoclass:: RealNumber :members: .. autofunction:: igcd .. autofunction:: ilcm .. autofunction:: seterr .. autoclass:: Zero :members: .. autoclass:: One :members: .. autoclass:: NegativeOne :members: .. autoclass:: Half :members: .. autoclass:: NaN :members: .. autoclass:: Infinity :members: .. autoclass:: NegativeInfinity :members: .. autoclass:: ComplexInfinity :members: .. autoclass:: Exp1 :members: .. autoclass:: ImaginaryUnit :members: .. autoclass:: Pi :members: .. autoclass:: EulerGamma :members: .. autoclass:: Catalan :members: .. autoclass:: GoldenRatio :members: .. autoclass:: TribonacciConstant :members: .. autofunction:: mod_inverse .. autofunction:: equal_valued power ----- .. module:: sympy.core.power .. autoclass:: Pow :members: .. autofunction:: integer_nthroot .. autofunction:: integer_log mul --- .. module:: sympy.core.mul .. autoclass:: Mul :members: .. autofunction:: prod add --- .. module:: sympy.core.add .. autoclass:: Add :members: mod --- .. module:: sympy.core.mod .. autoclass:: Mod :members: relational ---------- .. module:: sympy.core.relational .. autoclass:: Relational :members: .. autoclass:: Rel :members: .. autoclass:: Eq :members: .. autoclass:: Ne :members: .. autoclass:: Lt :members: .. autoclass:: Le :members: .. autoclass:: Gt :members: .. autoclass:: Ge :members: .. autoclass:: Equality :members: .. autoclass:: GreaterThan :members: .. autoclass:: LessThan :members: .. autoclass:: Unequality :members: .. autoclass:: StrictGreaterThan :members: .. autoclass:: StrictLessThan :members: multidimensional ---------------- .. module:: sympy.core.multidimensional .. autoclass:: vectorize :members: function -------- .. module:: sympy.core.function .. autoclass:: Lambda :members: .. autoclass:: WildFunction :members: .. autoclass:: Derivative :members: :private-members: .. autofunction:: diff .. autoclass:: FunctionClass :members: .. autoclass:: Function :members: .. note:: Not all functions are the same SymPy defines many functions (like ``cos`` and ``factorial``). It also allows the user to create generic functions which act as argument holders. Such functions are created just like symbols: >>> from sympy import Function, cos >>> from sympy.abc import x >>> f = Function('f') >>> f(2) + f(x) f(2) + f(x) If you want to see which functions appear in an expression you can use the atoms method: >>> e = (f(x) + cos(x) + 2) >>> e.atoms(Function) {f(x), cos(x)} If you just want the function you defined, not SymPy functions, the thing to search for is AppliedUndef: >>> from sympy.core.function import AppliedUndef >>> e.atoms(AppliedUndef) {f(x)} .. autoclass:: Subs :members: .. autofunction:: expand .. autoclass:: PoleError :members: .. autofunction:: count_ops .. autofunction:: expand_mul .. autofunction:: expand_log .. autofunction:: expand_func .. autofunction:: expand_trig .. autofunction:: expand_complex .. autofunction:: expand_multinomial .. autofunction:: expand_power_exp .. autofunction:: expand_power_base .. autofunction:: nfloat evalf ----- .. module:: sympy.core.evalf .. autoclass:: EvalfMixin :members: .. autoclass:: PrecisionExhausted :members: .. autofunction:: N containers ---------- .. module:: sympy.core.containers .. autoclass:: Tuple :members: .. autoclass:: TupleKind :members: .. autoclass:: Dict :members: exprtools --------- .. module:: sympy.core.exprtools .. autofunction:: gcd_terms .. autofunction:: factor_terms kind ---- .. module:: sympy.core.kind .. autoclass:: Kind :members: .. autoclass:: NumberKind :members: .. autoclass:: UndefinedKind :members: .. autoclass:: BooleanKind :members: Sorting ------- .. autofunction:: sympy.core.sorting.default_sort_key .. autofunction:: sympy.core.sorting.ordered Random ------ .. automodule:: sympy.core.random .. autofunction:: random_complex_number .. autofunction:: verify_numerically .. autofunction:: test_derivative_numerically .. autofunction:: _randrange .. autofunction:: _randint Traversal --------- .. module:: sympy.core.traversal .. autofunction:: bottom_up .. autofunction:: postorder_traversal .. autofunction:: preorder_traversal .. autofunction:: use .. autofunction:: walk