Tensor Product¶
Abstract tensor product.
- class sympy.physics.quantum.tensorproduct.TensorProduct(*args)[source]¶
The tensor product of two or more arguments.
For matrices, this uses
matrix_tensor_product
to compute the Kronecker or tensor product matrix. For other objects a symbolicTensorProduct
instance 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 resultingTensorProduct
.- Parameters
args : tuple
A sequence of the objects to take the tensor product of.
Examples
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)[source]¶
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, rawTensorProducts
, notAdd
,Pow
,Commutators
ofTensorProducts
. It is best to see what it does by showing examples.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