Abstract tensor product.
- class sympy.physics.quantum.tensorproduct.TensorProduct(*args)#
The tensor product of two or more arguments.
For matrices, this uses
matrix_tensor_productto compute the Kronecker or tensor product matrix. For other objects a symbolic
TensorProductinstance is returned. The tensor product is a non-commutative multiplication that is used primarily with operators and states in quantum mechanics.
Currently, the tensor product distinguishes between commutative and non-commutative arguments. Commutative arguments are assumed to be scalars and are pulled out in front of the
TensorProduct. Non-commutative arguments remain in the resulting
args : tuple
A sequence of the objects to take the tensor product of.
Start with a simple tensor product of SymPy matrices:
>>> from sympy import Matrix >>> from sympy.physics.quantum import TensorProduct >>> m1 = Matrix([[1,2],[3,4]]) >>> m2 = Matrix([[1,0],[0,1]]) >>> TensorProduct(m1, m2) Matrix([ [1, 0, 2, 0], [0, 1, 0, 2], [3, 0, 4, 0], [0, 3, 0, 4]]) >>> TensorProduct(m2, m1) Matrix([ [1, 2, 0, 0], [3, 4, 0, 0], [0, 0, 1, 2], [0, 0, 3, 4]])
We can also construct tensor products of non-commutative symbols:
>>> from sympy import Symbol >>> A = Symbol('A',commutative=False) >>> B = Symbol('B',commutative=False) >>> tp = TensorProduct(A, B) >>> tp AxB
We can take the dagger of a tensor product (note the order does NOT reverse like the dagger of a normal product):
>>> from sympy.physics.quantum import Dagger >>> Dagger(tp) Dagger(A)xDagger(B)
Expand can be used to distribute a tensor product across addition:
>>> C = Symbol('C',commutative=False) >>> tp = TensorProduct(A+B,C) >>> tp (A + B)xC >>> tp.expand(tensorproduct=True) AxC + BxC
- sympy.physics.quantum.tensorproduct.tensor_product_simp(e, **hints)#
Try to simplify and combine TensorProducts.
In general this will try to pull expressions inside of
TensorProducts. It currently only works for relatively simple cases where the products have only scalars, raw
TensorProducts. It is best to see what it does by showing examples.
>>> from sympy.physics.quantum import tensor_product_simp >>> from sympy.physics.quantum import TensorProduct >>> from sympy import Symbol >>> A = Symbol('A',commutative=False) >>> B = Symbol('B',commutative=False) >>> C = Symbol('C',commutative=False) >>> D = Symbol('D',commutative=False)
First see what happens to products of tensor products:
>>> e = TensorProduct(A,B)*TensorProduct(C,D) >>> e AxB*CxD >>> tensor_product_simp(e) (A*C)x(B*D)
This is the core logic of this function, and it works inside, powers, sums, commutators and anticommutators as well:
>>> tensor_product_simp(e**2) (A*C)x(B*D)**2