Operators¶
- class sage.symbolic.operators.DerivativeOperator[source]¶
- Bases: - object- Derivative operator. - Acting with this operator onto a function gives a new operator (of type - FDerivativeOperator) representing the function differentiated with respect to one or multiple of its arguments.- This operator takes a list of indices specifying the position of the arguments to differentiate. For example, D[0, 0, 1] is an operator that differentiates a function twice with respect to its first argument and once with respect to its second argument. - EXAMPLES: - sage: x, y = var('x,y'); f = function('f') sage: D[0](f)(x) diff(f(x), x) sage: D[0](f)(x, y) diff(f(x, y), x) sage: D[0, 1](f)(x, y) diff(f(x, y), x, y) sage: D[0, 1](f)(x, x^2) D[0, 1](f)(x, x^2) - >>> from sage.all import * >>> x, y = var('x,y'); f = function('f') >>> D[Integer(0)](f)(x) diff(f(x), x) >>> D[Integer(0)](f)(x, y) diff(f(x, y), x) >>> D[Integer(0), Integer(1)](f)(x, y) diff(f(x, y), x, y) >>> D[Integer(0), Integer(1)](f)(x, x**Integer(2)) D[0, 1](f)(x, x^2) 
- class sage.symbolic.operators.FDerivativeOperator(function, parameter_set)[source]¶
- Bases: - object- Function derivative operators. - A function derivative operator represents a partial derivative of a function with respect to some variables. - The underlying data are the function, and the parameter set, a list recording the indices of the variables with respect to which the partial derivative is taken. - change_function(new)[source]¶
- Return a new function derivative operator with the same parameter set but for a new function. - EXAMPLES: - sage: from sage.symbolic.operators import FDerivativeOperator sage: f = function('foo') sage: b = function('bar') sage: op = FDerivativeOperator(f, [0, 1]) sage: op.change_function(bar) D[0, 1](bar) - >>> from sage.all import * >>> from sage.symbolic.operators import FDerivativeOperator >>> f = function('foo') >>> b = function('bar') >>> op = FDerivativeOperator(f, [Integer(0), Integer(1)]) >>> op.change_function(bar) D[0, 1](bar) 
 - function()[source]¶
- Return the function associated to this function derivative operator. - EXAMPLES: - sage: from sage.symbolic.operators import FDerivativeOperator sage: f = function('foo') sage: op = FDerivativeOperator(f, [0, 1]) sage: op.function() foo - >>> from sage.all import * >>> from sage.symbolic.operators import FDerivativeOperator >>> f = function('foo') >>> op = FDerivativeOperator(f, [Integer(0), Integer(1)]) >>> op.function() foo 
 - parameter_set()[source]¶
- Return the parameter set of this function derivative operator. - This is the list of indices of variables with respect to which the derivative is taken. - EXAMPLES: - sage: from sage.symbolic.operators import FDerivativeOperator sage: f = function('foo') sage: op = FDerivativeOperator(f, [0, 1]) sage: op.parameter_set() [0, 1] - >>> from sage.all import * >>> from sage.symbolic.operators import FDerivativeOperator >>> f = function('foo') >>> op = FDerivativeOperator(f, [Integer(0), Integer(1)]) >>> op.parameter_set() [0, 1] 
 
- sage.symbolic.operators.add_vararg(first, *rest)[source]¶
- Return the sum of all the arguments. - INPUT: - first,- *rest– arguments to add
 - OUTPUT: sum of the arguments - EXAMPLES: - sage: from sage.symbolic.operators import add_vararg sage: add_vararg(1, 2, 3, 4, 5, 6, 7) 28 sage: x = SR.var('x') sage: s = 1 + x + x^2 # symbolic sum sage: bool(s.operator()(*s.operands()) == s) True - >>> from sage.all import * >>> from sage.symbolic.operators import add_vararg >>> add_vararg(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6), Integer(7)) 28 >>> x = SR.var('x') >>> s = Integer(1) + x + x**Integer(2) # symbolic sum >>> bool(s.operator()(*s.operands()) == s) True 
- sage.symbolic.operators.mul_vararg(first, *rest)[source]¶
- Return the product of all the arguments. - INPUT: - first,- *rest– arguments to multiply
 - OUTPUT: product of the arguments - EXAMPLES: - sage: from sage.symbolic.operators import mul_vararg sage: mul_vararg(9, 8, 7, 6, 5, 4) 60480 sage: x = SR.var('x') sage: p = x * cos(x) * sin(x) # symbolic product sage: bool(p.operator()(*p.operands()) == p) True - >>> from sage.all import * >>> from sage.symbolic.operators import mul_vararg >>> mul_vararg(Integer(9), Integer(8), Integer(7), Integer(6), Integer(5), Integer(4)) 60480 >>> x = SR.var('x') >>> p = x * cos(x) * sin(x) # symbolic product >>> bool(p.operator()(*p.operands()) == p) True