from the theory of proveit.physics.quantum.algebra¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import A, Conditional, Function, Lambda, X
from proveit.linear_algebra import LinMap
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi
from proveit.physics.quantum.algebra import Hspace

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Lambda(A, Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), InSet(sub_expr2, LinMap(Hspace, X))))

Out[2]:
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

A \mapsto \left\{\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) = \left[A\right]\left(\lvert \psi \rangle\right)\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\right..

In [5]:
stored_expr.style_options()

Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()

Out[6]:
core typesub-expressionsexpression
0Lambdaparameter: 28
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 7
3Operationoperator: 17
operands: 6
4Literal
5ExprTuple7
6ExprTuple23, 8
7Lambdaparameter: 27
body: 9
8Operationoperator: 10
operands: 11
9Conditionalvalue: 12
condition: 13
10Literal
11ExprTuple21, 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Variable
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple27, 21
19Operationoperator: 25
operands: 22
20Operationoperator: 23
operand: 27
21Variable
22ExprTuple28, 27
23Operationoperator: 25
operand: 28
24ExprTuple27
25Literal
26ExprTuple28
27Variable
28Variable